Research ArticleThe Use of a Machine Learning Method to Predict the Real-TimeLink Travel Time of Open-Pit Trucks

Xiaoyu Sun1 Hang Zhang 1 Fengliang Tian1 and Lei Yang2

1Key Laboratory of Ministry of Education on Safe Mining of Deep Metal Mines Northeastern University Shenyang 110819 China2School of Engineering RMIT University Melbourne VIC 3000 Australia

Correspondence should be addressed to Hang Zhang huhuhanggmailcom

Received 16 January 2018 Revised 28 February 2018 Accepted 12 March 2018 Published 19 April 2018

Academic Editor Panos Liatsis

Copyright copy 2018 Xiaoyu Sun et al This is an open access article distributed under the Creative Commons Attribution Licensewhich permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited

Accurate truck travel time prediction (TTP) is one of the critical factors in the dynamic optimal dispatch of open-pit mines Thisstudy divides the roads of open-pit mines into two types fixed and temporary link roads The experiment uses data obtainedfrom Fushun West Open-pit Mine (FWOM) to train three types of machine learning (ML) prediction models based on 119896-nearestneighbors (kNN) support vector machine (SVM) and random forest (RF) algorithms for each link road The results show thatthe TTP models based on SVM and RF are better than that based on kNN The prediction accuracy calculated in this studyis approximately 1579 higher than that calculated by traditional methods Meteorological features added to the TTP modelimproved the prediction accuracy by 513 Moreover this study uses the link rather than the route as the minimum TTP unitand the former shows an increase in prediction accuracy of 1182

1 Introduction

At present shovel-truck systems (STSs) are commonly usedin open-pit mining operations [1ndash3] especially for largeopen-pit minesThis is because STSs do not require extensiveinfrastructure in conjunction with a high mining intensity[4] Although the trucks are very flexible with a strongclimbing ability they also consume a large amount of fuel[5] Related statistics showed that STSs contribute 50 of theoperating costs in open-pit mines [6] Therefore almost alllarge open-pit mines are trying to optimize truck dispatchingto achieve lower costs and higher mining efficiency [7ndash10]

Many open-pit mines have begun to use an open-pitautomated truck dispatching system (OPATDS) in recentdecades [9 11] Mining efficiency has increased through theintegration of some truck dynamic dispatching principles(TDDPs) into theOPATDS [9 11 12]The TDDPs rely heavilyon an accurate truck cycle time [7 8 10] and one of itsfundamental techniques is predicting the travel time of thetrucks [11ndash14]

Several researchers have been working on travel timeprediction (TTP) for open-pit trucks (OPTs) for many years

Sun [15] first defined the average value for the predicted traveltime of a truck based on artificial statistical data Howeverthe travel time is influenced by many factors including trucktype load status road properties and weather conditionsmaking it difficult to predict the average travel time accuratelyand efficiently

Run-cai [16] used an artificial neural network (ANN) topredict the travel time of OPTs Considering the randomnessof TTP they took several factors namely road conditionstruck type and truck load status into consideration A totalof 336 data records were used in their ANN model andthe results were better than those obtained using manualstatistical methods

Jiangang [17] proposed a real-time dynamic TTP modelbased on the adaptive network-based fuzzy inference system(ANFIS) and discussed the theory and method of the ANFISnetworkTheANFIS is a hybrid learning algorithm consistingof an error backpropagation algorithm which performs witha higher calculation speed and better accuracy than theANNsused in [16]

Chanda and Gardiner [18] compared the predictive capa-bility of three truck cycle time estimation methods that is

HindawiMathematical Problems in EngineeringVolume 2018 Article ID 4368045 14 pageshttpsdoiorg10115520184368045

2 Mathematical Problems in Engineering

Table 1 Summary of the current state of TTP for OPTs

Year Authors Methods Conclusions Ref1998 Sun Manual statistics An available method [15]2005 Run-cai ANNs Better than [15] [16]2005 Jiangang ANFIS Better than [16] [17]2010 Chanda and Gardiner ANNs MRs and TALPAC Each has its advantages [18]2010 Xue et al LS-SVR An available method [21]2013 Edwards and Griffiths MRs and ANNs ANN is better than MR [19]2013 Erarslan A computer-aided system An available method [20]2014 Meng BP-ANNs and SVM SVM is better than BP-ANN [22]

computer simulation ANN and multiple regression (MR)in open-pit mining using TALPAC software and MATLABThe results indicated that both the ANN and MR modelsshowed better predictive abilities than the TALPAC modelwhich usually overestimated the travel time of longer haulroutes while underestimating that of shorter haul routesHowever the difference between the time predicted by thesetwo methods and the realistic travel time was insignificant

Edwards and Griffiths [19] attempted to predict the traveltime of open-pit excavators through the development ofESTIVATE Initially ESTIVATE utilized a MR equation topredict the time although it failed to provide an adequatelyrobust predictor Subsequently improvement to ESTIVATErsquospredictive capacity was sought through the use of ANNswhich provided a significant improvement over the MRapproach

Erarslan [20] focused on the truck speed and developed acomputer-aided system to estimate the speed data for differ-ent resistances Then the truck travel time was equivalent tothe length of the road divided by the truck speed

Considering the various influencing factors on TTP Xueet al [21] proposed a dynamic prediction method that com-prised an ensemble learning algorithm using least squaressupport vector regression (LS-SVR) The results obtainedfrom the MATLAB model showed the effectiveness and highaccuracy of their algorithms

Meng [22] compared the support vector machine (SVM)approach with the backpropagation (BP) algorithm andobserved that the SVM model performed with a higheraccuracy than the BP neural network model in TTP

Reported studies on the TTP of OPTs are summarized inTable 1 Several aspects of the table require further discussion

(1) Most of the existing studies have considered open-pit roads as a single category Unlike urban trafficnetworks there are many temporary roads in open-pit mines for example coal mines in Kuzbass wheretemporary roads constitute up to 80 of the totalroad length [23] A TTP model based on commonlyfixed roads may not be reliable because the tempo-rary roads between load and dump points changefrequently

(2) Most experiments reported in the literature werebased on the route travel time prediction (RTTP)although the number of routes from A to B exceeds

one Thus the RTTP with uncertainty must beimproved

(3) Reported studies have seldom considered the meteo-rological factorswhen the open-pitmine is extractingFor example snow or heavy rain decreases the speedof trucks and has an adverse effect on the travel timeof vehicles [24ndash27]

(4) Available predictive models have been based onsmall-scale datasets for example only hundreds ofdata records were used in [15ndash17 21] Better resultsare usually obtained when using large-scale trainingdatasets

With the rapid development of machine learning (ML)and big data technology the TTP of OPTs is expected tobecome faster and more accurate In this study the primaryobjectives and improved measures are as follows

(1) The open-pit mine roads are divided into two typeslong-term fixed roads and temporary roads Experi-ments explore the results of TTP on the two differenttypes of roads

(2) This paper uses the link rather than the route as theminimumprediction unitThe difference between thelink and route is that the route contains multiple roadnodes Independent TTP models are used to traineach link road instead of using the same TTP modelfor the entire road network

(3) The experiments in this paper explore the impactof meteorological conditions on TTP which meansmeteorological features are added to the model train-ing process

(4) The OPATDS database stores a large amount of truckcondition data For large-scale data machine learningmethods tend to have good prediction performanceMore than a million records are used to train the linktravel time prediction (LTTP) model in this study

2 Models and Experiments

21 Experimental Roadmap and Methods As shown in Fig-ure 1 Fushun West Open-pit Mine (FWOM Fushun MiningGroup Co Ltd) is located in Fushun city Liaoning province

Mathematical Problems in Engineering 3

Fushun West Open-pit Mine

Fushun FushunBeijing

Shanghai300 km

Figure 1 Location of the Fushun West Open-pit Mine

Node J

Load G

Node E

Load F

Dump ANode B

Load D

Load C

Node H

Fixed roadsTemporary roads

Y-a

xis o

f FW

OM

300

400

600

800

1000

1200

1000 1500 2000 2500 3000500X-axis of FWOM

Figure 2 Experimental roadmap of the FWOM

China approximately 50 km east of Shenyang The FWOMis the largest open-pit coal mine in Asia and produces anestimated 15 billion tons of coal [28]

The roadmap used in this experiment is shown in Fig-ure 2 which is part of the road networks of the FWOM

The nodes of transportation roads typically remain thesame at a specified time whereas roads to load points anddump points change with mining activities According to thechanging road nodes link roads can be divided into twocategories

(1) Fixed link roads for example the link roads betweennode B and node E node E and node H and node Hand node J

(2) Temporary link roads for example the link roadsbetween node B and node D node E and node F andnode G and node H

ML which is a field of computer science gives computersthe ability to learn without being explicitly programmed[35 36] ML is related to computational statistics and suitable

for predicting tasks because of its self-adaptation and self-feedback characteristics [37 38] An experimental flow chartused in the ML method is given in Figure 3 Note that theLTTPmodel of each experimental link road is independentlytrained

Figure 3 shows the three steps of LTTP using ML Asthe most crucial step training the LTTP model consists oftwo parts ML algorithms and training data These two partsare indispensable because training theML predictionmodelsrequires a large amount of data provided by the OPATDS Inthe second step LTTP model predictions are obtained fromthe test data and the prediction performance of the modelcan also be evaluated The final step involves modifying theparameters of the LTTP model until the result is acceptableIn particular the test dataset is a dataset that is independentof the training dataset [39]

22MLAlgorithms Selection ML tasks are typically classifiedinto four broad categories [40] supervised learning unsuper-vised learning reinforcement learning and semisupervised

4 Mathematical Problems in Engineering

Resultsamp

evaluation

LTTP model

Machine learning algorithm

Training data

Testdata

1

2 3

Figure 3 Experimental flowchart of ML methods

Table 2 Adaptability analysis between ML algorithms and LTTP

Algorithms Adaptability analysis ApplyANNs The effect has been thoroughly verified by many existing studies NoBNs A probabilistic model that is not suitable for this study [29] NoSVM Perfect theoretical basis with high generalization ability [30] YesRF An ensemble learning method evolved from DT better than DT [31] YesLR It solves the classification problems not suitable for this study [32] NokNN An efficient algorithm for the classification and regression tasks [33] YesDT RF has been chosen there is no need to choose DT NoHM A probabilistic model that is not suitable for this study [34] No

learning [41] The LTTP of OPTs belongs to the typicalsupervised learning task due to the labeled training data fromthe OPATDS [42] Prediction models output the travel timevalues of OPTs which can be considered to be a regressionproblem of supervised learning

There are many ML algorithms that can be used tosolve the regression problem of supervised learning suchas ANN Bayesian network (BN) SVM random forest (RF)logistic regression (LR) 119896-nearest neighbors (kNN) decisiontree (DT) AdaBoost [43] and hidden Markov model (HM)approaches [44]The adaptability analysis between LTTP andthe various ML algorithms is given in Table 2 Based on thecomparison results this paper chooses the kNN SVM andRF algorithms to build the LTTP models of OPTs

kNN is a nonparametric method used for classificationand regression and the kNN regression computes the meanof the function values of its 119896-nearest neighbors [33 45] Thegoal function regression119891kNN(119909) of kNN regression is writtenas follows [45]

119891kNN (119909) = 1119896 sdot sum119894isin119873119896(119909)

119910119894 (1)

where 119909 is an unknown pattern 119873119896(119909) is the indices of the119896-nearest neighbors of 119909 and 119910119894 is the predicted labelsThe original SVM algorithm was invented by Cortes

and Vapnik [46] and its efficiency in classification has beenverified in many case studies [47] The detailed introductionof SVM can be found in Smola and Scholkopf [48] inwhich they published the complete tutorial on support vector

regression To train the SVM regression model the followingmust be solved

minimize 12 1199082 (2a)

subject to 119910119894 minus ⟨119908 119909119894⟩ minus 119887 le 120576⟨119908 119909119894⟩ + 119887 minus 119910119894 le 120576 (2b)

where 119909119894 represents the training features with target value 119910119894⟨119908 119909119894⟩ + 119887 is the prediction value and 120576 is a free parameterthat serves as a threshold

The RF algorithm evolved from DT theory and wascreated by Ho in 1995 [31] This approach incorporatesthe bootstrap aggregating (Bagging) algorithm which is amethod for generating multiple versions of a predictor andthen using these to obtain an aggregated predictor [49] TheRF method has a higher degree of efficiency and accuracythan the DT method because of Bagging

23 Training Data Structure The training dataset is themost critical factor when training ML prediction modelsand it consists of several features and corresponding targetvalues [50] Many features commonly affect the LTTP ofOPTs which can be broadly classified into three categoriestruck features road features and meteorological featuresThe meteorological features are considered in this paperbecause rainy and snowy weather reduces both the frictioncoefficient of roads and the truck driverrsquos vision Accordingto the relevant statistics reported by the US Federal HighwayAdministration bad weather can lead to a 35 reduction incar speed [51]

Mathematical Problems in Engineering 5

Table 3 Preprocessed data for training the ML prediction models

Date Start time Arrival time Truck Id Truck type2017-03-01 162320 162657 202 BELAZ-L2017-03-02 201209 201812 503 MT-86Truck status 119909-axis start 119910-axis start 119909-axis arrival 119910-axis arrivalRun 1344 1188 2191 968Run 2576 783 3095 327

Load status Start node Arrival node Pressure(100 Pa)

Wind speed(ms)

Empty B E 1002 1Coal G H 999 06Temperature(∘C)

Relative humidity()

Precipitation(mm) Rain Travel time

(hourminsec)2 90 0 No 0003371 96 0 No 000603

Table 4 Description of the variables used in the prediction

Variables Type Role DescriptionTruck Id Numeric Feature The serial number of truckTruck type Categorical Feature The type of the truck (ie BELAZ-L BELAZ-M and MT86)Truck status Categorical Feature The status of the truck (ie running waiting and stop)119909-axis start Numeric Feature The 119909 coordinate of the truck at the starting position119910-axis start Numeric Feature The 119910 coordinate of the truck at the starting position119909-axis arrival Numeric Feature The 119909 coordinate of the truck at the ending position119910-axis arrival Numeric Feature The 119910 coordinate of the truck at the ending positionLoad status Categorical Feature The load status of the truck (ie empty and coal)Start node Categorical Feature The node code of the starting position of the roadArrival node Categorical Feature The node code of the ending position of the roadPressure Numeric Feature A fundamental atmospheric quantityWind speed Numeric Feature A fundamental atmospheric quantityTemperature Numeric Feature A fundamental atmospheric quantityRelative humidity Numeric Feature A fundamental atmospheric quantityPrecipitation Numeric Feature A fundamental atmospheric quantityRain Categorical Feature A fundamental atmospheric quantity (ie yes and no)Travel time Date time Target The travel time of the truck on each link

The data used in the following experiments originatefrom the FWOM The truck and road feature data are fromthe OPATDS while the weather data are collected fromthe China Meteorological Administration (CMA) Number54351 monitoring station The preprocessed training datasetsamples in this experiment are listed in Table 3 There are 16variables serving as the features and the target is the trucktravel time Table 4 shows the description of the target andeach feature used for the prediction in this study

24 Program and Pseudocode This study used sophisticatedalgorithms to predict the link travel time in open-pit minesand the three ML algorithms in the prediction models werebased on scikit-learn which is an open-sourceMLmodule in

the Python programming language [52 53] The pseudocodeof the methodology in this study is illustrated in Figure 4

3 Results and Discussion

31 Predictions of the ML Models For the training datasets2246746 historical records from March 2017 were exportedfrom the OPATDS database of the FWOM After datapreprocessing the structure of the training datawas similar tothose in Table 3 The experimental parameters encompassedone type of link road trained by three differentML algorithms(kNN SVM and RF) resulting in 18 LTTP models Theprediction results for the last 50 records of the test datasetsare shown in Figure 5

6 Mathematical Problems in Engineering

Figure 4 The pseudocode of the ML methodology

To derive the best LTTP model for each link road theaforementioned prediction results were evaluated based onthe mean absolute deviation (MAD) and the mean absolutepercentage error (MAPE) methods which are commonlyused for regression problem evaluation

The MAD as expressed in (3a) is a summary statistic ofstatistical dispersion or variability [54 55] The MAPE is ameasure of the accuracy of a prediction method in statisticsas written in (3b) [56] Because the MAPE is a percentageit is often easier to understand than the other statistics Forexample if the MAPE is 5 on average the forecast is off by5 [57]

MAD = sum119899119894=1 1003816100381610038161003816119909obs119894 minus 119909model1198941003816100381610038161003816119899 (3a)

MAPE = sum119899119894=1 1003816100381610038161003816(119909obs119894 minus 119909model119894) 119909obs1198941003816100381610038161003816119899 times 100 () (3b)

where 119909obs119894 represents the observation values 119909model119894 rep-resents the prediction values and 119899 is the number of datarecords

Table 5 lists the MAD and MAPE values obtained fromthe three ML methods for each experimental link road

Smaller MAD and MAPE values reflect better predictionperformance of each LTTP model and the smallest recordsare highlighted in Table 5 The results of the six experimentallink roads indicate that the LTTP models built using theSVM and RF methods are better than those using the kNNalgorithm Table 6 summarizes the optimal ML predictionmodels for each link road

The coefficient of determination 1198772 is widely used instatistical tests to evaluate the predictive capability of amodel and is also used in this study The 1198772 value with oneindependent variable is written as follows [58]

1198772 = [ 1119873 lowastsum (119909119894 minus 119909) lowast (119910119894 minus 119910)(120590119909 lowast 120590119910) ]

2

(4)

Mathematical Problems in Engineering 7

Raw valueKNN

SVMRF

000100000200000300000400000500000600000700000800000900001000001100001200

Link

trav

el tim

e

0 5 15 20 25 30 35 40 45 5010G-H

000100

000200

000300

000400

000500

000600

000700

000800

Link

trav

el tim

e

0 5 15 20 25 30 35 40 45 5010H-J

000200000300000400000500000600000700000800000900001000001100001200

Link

trav

el tim

e

0 5 15 20 25 30 35 40 45 5010E-H

000100000200000300000400000500000600000700000800000900001000001100

Link

trav

el tim

e

0 5 15 20 25 30 35 40 45 5010E-F

0 5 15 20 25 30 35 40 45 5010B-E

000200

000300

000400

000500

000600

000700

000800

000900

001000

Link

trav

el tim

e

000400000500000600000700000800000900001000001100001200001300001400001500001600001700001800001900002000002100002200

Link

trav

el tim

e

0 5 15 20 25 30 35 40 45 5010B-D

Raw valueKNN

SVMRF

Figure 5 Prediction results for the different ML methods

where119873 is the number of observations used to fit the model119909 and 119910 are themean values of 119909 and 119910 respectively 119909119894 and 119910119894are the values of observation 119894 and 120590119909 and 120590119910 are the standarddeviations of 119909 and 119910 respectively

Table 7 shows the 1198772 values of the three ML models foreach link road The 1198772 values range from 0 to 1 and 1198772 equalto 1 indicates perfect accurate prediction There are somedifferences between Tables 6 and 7 that is the optimal MLmodel of B-E H-J and G-H However the MAPE was stillselected for choosing the optimal model because the 1198772 valuecannot be used to evaluate predictive errors

32 Discussion of Traditional Averaging Methods and MLModels To compare the LTTP of MLmodels and traditionalaveraging methods controlled experiments were performedThe flow chart of traditional averaging methods is illustratedin Figure 6

For each record in the test dataset the experimentstraced back the corresponding top 10 20 30 40 and 50records and then calculated the average value as the finalprediction To improve the accuracy of the traditional aver-aging methods each calculation used only historical data forthe same truck type and load status The results obtained

8 Mathematical Problems in Engineering

Table 5 LTTP evaluation based on the different ML models

Link road Road type Evaluation kNN SVM RF

B-E

Fixed

MAD 591119864 minus 04 509119864 minus 04 456E minus 04MAPE 178119864 + 01 158119864 + 01 144E + 01

E-H MAD 944119864 minus 04 332E minus 04 637119864 minus 04MAPE 249119864 + 01 957E + 00 181119864 + 01

H-J MAD 516119864 minus 04 355119864 minus 04 354E minus 04MAPE 214119864 + 01 159119864 + 01 148E + 01

B-D

Temporary

MAD 171119864 minus 03 544E minus 04 670119864 minus 04MAPE 275119864 + 01 809E + 00 990119864 + 00

E-F MAD 959119864 minus 04 805119864 minus 04 563E minus 04MAPE 313119864 + 01 294119864 + 01 182E + 01

G-H MAD 118119864 minus 03 735E minus 04 785119864 minus 04MAPE 342119864 + 01 194E + 01 238119864 + 01

4

Rece

nt h

istor

ical

dat

a

2

Data predicted

Calculatingthe average time

(i) Same link road (ii) Same load status(iii) Same truck type

3001357

001421

001409BELAZB-E

001357

Empty

Empty

BELAZB-E

001821LoadB-E MT-86

001421EmptyB-E BELAZ

001715B-E EmptyMT-86

1

Figure 6 The flow chart of traditional averaging methods

Table 6 Summary of the optimal ML prediction models for eachlink road

Road Type Optimal ML modelB-E

FixedRF

E-H SVMH-J RFB-D

TemporarySVM

E-F RFG-H SVM

Table 7 1198772 values of the different ML models for each link road

Road SVM KNN RF Optimal ML modelB-E 028 016 041 SVME-H 083 016 067 SVMH-J 072 013 056 SVMB-D 089 023 07 SVME-F 054 024 073 RFG-H 061 019 062 RF

from the traditional averaging methods are summarized inTable 8

Smaller MAD and MAPE values mean better predictionperformance of the traditional averaging methods and the

smallest records are highlighted in Table 8The predicted val-ues obtained from the optimal ML method and a traditionalaverage method for each link road are given in Table 9 thedecrease in the MAPE is also shown

Table 9 shows that the tested ML models are superiorto the traditional averaging method in the context of LTTPbecause the former has smaller MAPEs An average increaseof 1579 in prediction accuracy is achieved in all experimen-tal link roads in which increases of 1254 and 1930 forthree fixed and three temporary roads respectively are alsoobtained

33 Discussion of Meteorological Features This study alsoconsidered the influence of meteorological features on theLTTP of an open-pit mine The data were obtained froma CMA monitoring station including 5 variables pressurewind speed temperature relative humidity and precipita-tion

The Pearson correlation coefficient (PCC) an evaluationmethod developed by Pearson [59] was used to evaluate thelinear correlation between two variables The expression ofthe PPC is as follows

120588119883119884 = cov (119883 119884)120590119883120590119884 (5)

Mathematical Problems in Engineering 9

Table 8 Results obtained from the traditional averaging methods

Road Evaluation Traditional averaging methods10 records 20 records 30 records 40 records 50 records

B-E MAD 102119864 minus 03 949119864 minus 04 917119864 minus 04 918119864 minus 04 904E minus 04MAPE 306119864 + 01 281119864 + 01 266119864 + 01 264119864 + 01 258E + 01

E-H MAD 122119864 minus 03 113119864 minus 03 109119864 minus 03 109119864 minus 03 107E minus 03MAPE 329119864 + 01 300119864 + 01 284119864 + 01 281119864 + 01 273E + 01

H-J MAD 629119864 minus 04 609119864 minus 04 587119864 minus 04 581119864 minus 04 580E minus 04MAPE 254119864 + 01 247119864 + 01 236119864 + 01 234119864 + 01 233E + 01

B-D MAD 215119864 minus 03 183E minus 03 246119864 minus 03 236119864 minus 03 205119864 minus 03MAPE 317119864 + 01 269E + 01 386119864 + 01 362119864 + 01 325119864 + 01

E-F MAD 116119864 minus 03 110E minus 03 114119864 minus 03 115119864 minus 03 116119864 minus 03MAPE 391119864 + 01 363E + 01 381119864 + 01 390119864 + 01 395119864 + 01

G-H MAD 129E minus 03 138119864 minus 03 136119864 minus 03 132119864 minus 03 130119864 minus 03MAPE 404E + 01 412119864 + 01 391119864 + 01 370119864 + 01 357119864 + 01

Table 9 Comparison between the optimal ML model and the optimal averaging method

Road Type Optimal average method (MAPE) Optimal ML model (MAPE) MAPE decrease AverageB-E

Fixed258119864 + 01 144119864 + 01 1140

1254E-H 273119864 + 01 957119864 + 00 1773H-J 233119864 + 01 148119864 + 01 850B-D

Temporary269119864 + 01 809119864 + 00 1881

1930E-F 363119864 + 01 182119864 + 01 1810G-H 404119864 + 01 194119864 + 01 2100Average 1579

Table 10 Prediction results after including meteorological data

Type Road Methods Meteorological features MAD MAPE MAPE decrease (no-yes)

Temporary

B-E RF No 690119864 minus 04 207119864 + 01 630Yes 456119864 minus 04 144119864 + 01

E-H SVM No 341119864 minus 04 169119864 + 01 728Yes 332119864 minus 04 957119864 + 00

H-J RF No 416119864 minus 04 186119864 + 01 380Yes 354119864 minus 04 148119864 + 01

Fixed

B-D SVM No 635119864 minus 04 122119864 + 01 408Yes 544119864 minus 04 809119864 + 00

E-F RF No 660119864 minus 04 217119864 + 01 350Yes 563119864 minus 04 182119864 + 01

G-H SVM No 842119864 minus 04 252119864 + 01 580Yes 735119864 minus 04 194119864 + 01

Average 513

where cov(119883 119884) is the covariance 120590119883 is the standard devia-tion of119883 and 120590119884 is the standard deviation of 119884

The PPC values of different variables are shown inFigure 7 including the 5 meteorological variables and trucktravel time A high PCC value indicates a closer relationshipbetween the two variables

Following controlled experiments the effect of meteo-rological features was investigated by adding or removingindividual features We selected the optimal ML model for

each link road The raw (observation) values and predictedresults withwithout meteorological features are shown inFigure 8

The results of the controlled experiments are shownin Table 10 the calculated decrease in the MAPE is alsoshown The results considering meteorological features arebetter than those withoutmeteorological featuresTheMAPEdecreased by 513 on average for all link roads after addingthe meteorological data

10 Mathematical Problems in Engineering

Pressure08

Wind speed04

Temperature

00

Relative humidity

Precipitation

Travel time

minus04

minus08

Pres

sure

Win

d sp

eed

Tem

pera

ture

Relat

ive h

umid

ity

Prec

ipita

tion

Trav

el tim

e

1

1

1

1

1

1

minus048 minus048

minus048

minus048

064

064

minus0041 minus0019

minus0019

005

005

minus0088

minus0088

minus082

minus082

047

012

012

047 minus064 014

014

0049

0049

minus0041

minus0054

minus0054

0045

0045

minus064

Figure 7 The PCC heat map of meteorological features

Table 11 Evaluation of LTTP based on different ML models

Link road Road type Evaluation kNN SVM RF

A-B Fixed MAD 495119864 minus 04 328119864 minus 04 299E minus 04MAPE 469119864 + 01 340119864 + 01 336E + 01

34 Discussion of LTTP and RTTP The above experimentsused the link rather than the route to predict the travel timeof OPTs However the differences between LTTP and RTTPneed to be further discussed In the ensuing discussion thelongest route between dump point A and load point G isselected as shown in Figure 9

The A-G route consists of 4 links A-B B-E E-H and H-G Among them the optimal ML prediction models of B-EE-H andH-G are SVM RF and SVM respectivelyThe sameexperimental procedure as used in Section 31 was used toobtain the optimal MLmodel for A-B and Table 11 shows theMAD and MAPE values of the three ML methods It can beseen that the RF model is the best ML method for link A-B

The SVM and RF methods are used to predict the RTTPof A-G because those two models have a good predictionperformance Thus the experiments are summarized asfollows

(i) RTTP (SVM) using the SVM algorithm to train theTTP model for the route A-G

(ii) RTTP (RF) using the RF algorithm to train the TTPmodel for the route A-G

(iii) LTTP using the optimalMLmodel for each link thatis A-B (RF) B-E (SVM) E-H (RF) and H-G (SVM)and the truck travel time of A-G is the sum of eachLTTP result

Raw values and predicted results of the above threeexperiments are shown in Figure 10 while the evaluated

Table 12 Evaluation of the results between LTTP and RTTP

Method Model Evaluation Values

RTTP SVM MAD 155119864 minus 03MAPE 208119864 + 01

RTTP RF MAD 178119864 minus 03MAPE 235119864 + 01

LTTP Assemble MAD 834E minus 04MAPE 898E + 00

results of those experiments are shown in Table 12 Both theMAD and MAPE values of the LTTP approach are smallerthan the two RTTP methods Thus using the link as theprediction unit is better than using the route

4 Conclusions

The link roads of an open-pit mine are divided into fixedand temporary roads in this paper Three ML algorithmsthat is kNN SVM and RF are used for the LTTP of OPTsThe experimental results not only reflect the self-adaptive andself-feedback characteristics of the ML algorithms but alsodemonstrate the practicality of themethod for road segmentsThe conclusions based on the results are as follows

(1) LTTP models based on ML are more efficient andaccurate than traditional averaging methods Anoverall average increase of 1579 in the predictionaccuracy is obtained for six experimental link roads

Mathematical Problems in Engineering 11

000100000200000300000400000500000600000700000800000900001000001100001200

Link

trav

el tim

e

0 10 15 20 25 30 35 40 45 505G-H (SVM)

000100

000200

000300

000400

000500

000600

000700

000800

Link

trav

el tim

e

0 10 15 20 25 30 35 40 45 505H-J (RF)

000200000300000400000500000600000700000800000900001000001100001200

Link

trav

el tim

e

0 5 15 20 25 30 35 40 45 5010E-H (SVM)

000100

000200

000300

000400

000500

000600

000700

000800

Link

trav

el tim

e

0 5 15 20 25 30 35 40 45 5010E-F (RF)

000400000500000600000700000800000900001000001100001200001300001400001500001600001700001800001900002000002100002200

Link

trav

el tim

e

0 5 15 20 25 30 35 40 45 5010B-D (SVM)

000200

000300

000400

000500

000600

000700

000800

000900

001000

Link

trav

el tim

e

0 10 15 20 25 30 35 40 45 505B-E (RF)

Raw valueWithout meteorological featuresMeteorological features

Raw valueWithout meteorological featuresMeteorological features

Figure 8 Comparison forecast results including and excluding meteorological features

For temporary roads the average accuracy increasesby 1930

(2) LTTP models established using the SVM and RFalgorithms are better than those established using thekNN approach There is no large difference betweenthe SVM and RF results although the RF algorithmrequires less space and time complexity than the SVMalgorithm

(3) This paper is original in that it considers the effectof meteorological features on LTTP The results show

that considering the effect of meteorological featureson LTTP increases the prediction accuracy by 513

(4) The differences between LTTP and RTTP are alsodiscussed and the former has a higher predictionaccuracy The MAPE decreases by 1182 for theLTTP method

Some work is already underway to incorporate the MLprediction models into the OPATDS of the FWOM whichwill be helpful in improving the dispatching efficiency of theOPTs

12 Mathematical Problems in Engineering

Node J

Load G

Node E

Load F

Dump ANode B

Load D

Load C

Node H

Fixed roadsTemporary roads

Figure 9 The location of the route A-G in the FWOM roadmap

Raw valuesRTTP (RF)

RTTP (SVM)LTTP

5 10 15 20 25 30 35 40 45 500Route A-G

000600000800001000001200001400001600001800002000002200

Truc

k tr

avel

tim

e

Figure 10 Prediction results for RTTP (RF) RTTP (SVM) andLTTP

Data Availability

The data used to support the findings of this study areavailable from the corresponding author upon request

Conflicts of Interest

The authors declare no conflicts of interest

Authorsrsquo Contributions

Xiaoyu Sun as the principal investigator provided the dataused to train the ML models Hang Zhang performed theexperiments andwrote the paper Fengliang Tian contributedthe programming Lei Yang proofread the manuscript

Acknowledgments

This work was funded by the National Natural ScienceFoundation of China (no 51674063) and the NationalKey Research and Development Program of China (no2016YFC0801608)

References

[1] J Czaplicki Shovel-Truck Systems CRC Press 2008[2] J M Czaplicki ldquoModelling and analysis of the exploitation

process of a shovel-truck systemrdquo in Shovel-Truck Systems pp79ndash89 CRC Press 2008

[3] S G Ercelebi and A Bascetin ldquoOptimization of shovel-trucksystem for surface miningrdquo Journal of the Southern AfricanInstitute of Mining and Metallurgy vol 109 no 7 pp 433ndash4392009

[4] R Mena E Zio F Kristjanpoller and A Arata ldquoAvailability-based simulation and optimization modeling framework foropen-pit mine truck allocation under dynamic constraintsrdquoInternational Journal of Mining Science and Technology vol 23no 1 pp 113ndash119 2013

[5] F Soumis J Ethier and J Elbrond ldquoTruck dispatching inan open pit minerdquo International Journal of Surface MiningReclamation and Environment vol 3 no 2 pp 115ndash119 1989

[6] A Y F Fadin Komarudin and A O Moeis ldquoSimulation-optimization truck dispatch problem using look - ahead algo-rithm in open pit minesrdquo International Journal of GEOMATEvol 13 no 36 pp 80ndash86 2017

[7] Y Tan and S Takakuwa ldquoA practical simulation approachfor an effective truck dispatching system of open pit minesusing VBArdquo in Proceedings of the 2016 Winter SimulationConference WSC 2016 pp 2394ndash2405 IEEE Washington DCUSA December 2016

[8] J Li R Bai J Mao and W Li ldquoForecast of applied effect fortruck real-time dispatch system in open-pit mine based onCSUSSrdquo in Proceedings of the 2010 International Conference onE-Product E-Service and E-Entertainment ICEEE2010 pp 1ndash4IEEE Henan China November 2010

[9] S P Alarie and M Gamache ldquoOverview of solution strategiesused in truck dispatching systems for open pit minesrdquo Interna-tional Journal of Surface Mining Reclamation and Environmentvol 16 no 1 pp 59ndash76 2002

[10] B Kolonja D R Kalasky and J M Mutmansky ldquoOptimizationof dispatching criteria for open-pit truck haulage system designusingmultiple comparisons with the best and common random

Mathematical Problems in Engineering 13

numbersrdquo in Proceedings of the 25th Conference on Winter Sim-ulation WSC 1993 pp 393ndash401 ACM Los Angeles CaliforniaUSA December 1993

[11] Q Wang Y Zhang C Chen and W Xu ldquoOpen-pit mine truckreal-time dispatching principle under macroscopic controlrdquo inProceedings of the 1st International Conference on InnovativeComputing Information and Control 2006 ICICICrsquo06 pp 702ndash705 IEEE Beijing China September 2006

[12] Y Choi ldquoSimulation of Shovel-Truck Haulage Systems byConsidering Truck Dispatch Methodsrdquo Journal of the KoreanSociety of Mineral and Energy Resources Engineers vol 50 no4 p 543 2013

[13] E Topal and S Ramazan ldquoMining truck scheduling withstochastic maintenance costrdquo Journal of Coal Science andEngineering vol 18 no 3 pp 313ndash319 2012

[14] P Chaowasakoo H Seppala H Koivo and Q Zhou ldquoDigi-talization of mine operations Scenarios to benefit in real-timetruck dispatchingrdquo International Journal of Mining Science andTechnology vol 27 no 2 pp 229ndash236 2017

[15] Q Sun ldquoRoad running time statistics method in truck schedul-ingrdquo Opencast Coal Mining Technology vol 01 pp 35ndash37 1998

[16] R Bai J Li and J Xu ldquoReal-time dynamic forecast of truck linktravel timerdquo Journal of Liaoning Technical University vol 1 pp12ndash14 2005

[17] L Jiangang ldquoReal-time dynamic forecasts of truck link traveltime based on fuzzy neural networkrdquo Journal of the China CoalSociety vol 6 pp 796ndash800 2005

[18] E K Chanda and S Gardiner ldquoA comparative study of truckcycle time prediction methods in open-pit miningrdquo Engineer-ing Construction and Architectural Management vol 17 no 5pp 446ndash460 2010

[19] D J Edwards and I J Griffiths ldquoArtificial intelligence approachto calculation of hydraulic excavator cycle time and outputrdquoMining Technology vol 109 no 1 pp 23ndash29 2013

[20] K Erarslan ldquoModelling performance and retarder chart of off-highway trucks by cubic splines for cycle time estimationrdquoMining Technology vol 114 pp 161ndash166 2013

[21] X Xue W Sun and R Liang ldquoA new method of real-timedynamic forecast of truck link travel time in open minesrdquoJournal of the China Coal Society vol 37 no 8 pp 1418ndash14222012

[22] X Meng Research on scheduling services of open-pit mine basedon real-time travel time prediction China University of Miningand Technology 2014

[23] V Shalamanov V Pershin S Shabaev and D Boiko ldquoJustifi-cation of the Optimal Granulometric Composition of CrushedRocks for Open-Pit Mine Road Surfacingrdquo in Proceedings of the1st International InnovativeMining Symposium 2017 KemerovoRussia April 2017

[24] M Hofmann and M OrsquoMahony ldquoThe impact of adverseweather conditions on urban bus performance measuresrdquoin Proceedings of the 8th International IEEE Conference onIntelligent Transportation Systems pp 431ndash436 IEEE ViennaAustria September 2005

[25] T H Maze M Agarwal and G Burchett ldquoWhether weathermatters to traffic demand traffic safety and traffic operationsand flowrdquoTransportation Research Record no 1948 pp 170ndash1762006

[26] S A Silvester I S Lowndes and D M Hargreaves ldquoAcomputational study of particulate emissions from an openpit quarry under neutral atmospheric conditionsrdquo AtmosphericEnvironment vol 43 no 40 pp 6415ndash6424 2009

[27] I Tsapakis T Cheng and A Bolbol ldquoImpact of weather condi-tions on macroscopic urban travel timesrdquo Journal of TransportGeography vol 28 pp 204ndash211 2013

[28] TheMinistry of Land and Resources ldquoPRCThe basic situationof mineral resources in fushunrdquo httpwwwmlrgovcnkczyglkczydjtj201208t20120813 1130832htm

[29] G F Cooper and E Herskovits ldquoA Bayesian method forthe induction of probabilistic networks from datardquo MachineLearning vol 9 no 4 pp 309ndash347 1992

[30] C Yunqiang Z X Sean and T S Huang ldquoOne-class svm forlearning in image retrievalrdquo in In Proceedings 2001 InternationalConference on Image Processing (Cat No01CH37205) pp 34ndash372001

[31] T K Ho ldquoIn Random decision forestsrdquo in Proceedings of 3rdInternational Conference on Document Analysis and Recogni-tion IEEE 1995

[32] D G Kleinbaum and M Klein ldquoAnalysis of Matched DataUsing Logistic Regressionrdquo in Logistic Regression pp 389ndash428Springer New York NY USA 2010

[33] N S Altman ldquoAn introduction to kernel and nearest-neighbornonparametric regressionrdquo The American Statistician vol 46no 3 pp 175ndash185 1992

[34] S R Eddy ldquoProfile hiddenMarkovmodelsrdquo Bioinformatics vol14 no 9 pp 755ndash763 1998

[35] J R Koza F H Bennett D Andre and M A Keane ldquoAuto-mated design of both the topology and sizing of analog electricalcircuits using genetic programmingrdquo in In Artificial intelligencein design rsquo96 pp 151ndash170 Springer Netherlands 1996

[36] T Oladipupo ldquoIntroduction to machine learningrdquo in In Newadvances in machine learning InTech 2010

[37] H Mannila ldquoData mining machine learning statistics anddatabasesrdquo in Proceedings of the 8th International Conferenceon Scientific and Statistical Data Base Management IEEEStockholm Sweden Sweden 2002

[38] M Troc and O Unold ldquoSelf-adaptation of parameters in alearning classifier system ensemble machinerdquo InternationalJournal of Applied Mathematics and Computer Science vol 20no 1 pp 157ndash174 2010

[39] T Hastie R Tibshirani and J Friedman The Elements ofStatistical Learning Springer-Verlag New York NY USA 2009

[40] N J Nilsson ldquoArtificial intelligence A modern approachrdquoArtificial Intelligence vol 82 no 1-2 pp 369ndash380 1996

[41] I Kavakiotis O Tsave A Salifoglou N Maglaveras I Vla-havas and I Chouvarda ldquoMachine Learning and Data MiningMethods in Diabetes Researchrdquo Computational and StructuralBiotechnology Journal vol 15 pp 104ndash116 2017

[42] M Mohri A Rostamizadeh and A Talwalkar Foundations ofmachine learning MIT press 2012

[43] Y Freund and R E Schapire ldquoA decision-theoretic generaliza-tion of on-line learning and an application to boostingrdquo Journalof Computer and System Sciences vol 55 no 1 part 2 pp 119ndash139 1997

[44] R S Michalski J G Carbonell and T M Mitchell ldquoMachinelearning 1983rdquo

[45] O Kramer ldquoK-nearest neighborsrdquo in Dimensionality reductionwith unsupervised nearest neighbors vol 51 pp 13ndash23 SpringerBerlin Heidelberg Germany 2013

[46] C Cortes and V Vapnik ldquoSupport-vector networksrdquo MachineLearning vol 20 no 3 pp 273ndash297 1995

Mathematical Problems in Engineering 3

Fushun West Open-pit Mine

Fushun FushunBeijing

Shanghai300 km

Figure 1 Location of the Fushun West Open-pit Mine

Node J

Load G

Node E

Load F

Dump ANode B

Load D

Load C

Node H

Fixed roadsTemporary roads

Y-a

xis o

f FW

OM

300

400

600

800

1000

1200

1000 1500 2000 2500 3000500X-axis of FWOM

Figure 2 Experimental roadmap of the FWOM

China approximately 50 km east of Shenyang The FWOMis the largest open-pit coal mine in Asia and produces anestimated 15 billion tons of coal [28]

The roadmap used in this experiment is shown in Fig-ure 2 which is part of the road networks of the FWOM

The nodes of transportation roads typically remain thesame at a specified time whereas roads to load points anddump points change with mining activities According to thechanging road nodes link roads can be divided into twocategories

(1) Fixed link roads for example the link roads betweennode B and node E node E and node H and node Hand node J

(2) Temporary link roads for example the link roadsbetween node B and node D node E and node F andnode G and node H

ML which is a field of computer science gives computersthe ability to learn without being explicitly programmed[35 36] ML is related to computational statistics and suitable

for predicting tasks because of its self-adaptation and self-feedback characteristics [37 38] An experimental flow chartused in the ML method is given in Figure 3 Note that theLTTPmodel of each experimental link road is independentlytrained

Figure 3 shows the three steps of LTTP using ML Asthe most crucial step training the LTTP model consists oftwo parts ML algorithms and training data These two partsare indispensable because training theML predictionmodelsrequires a large amount of data provided by the OPATDS Inthe second step LTTP model predictions are obtained fromthe test data and the prediction performance of the modelcan also be evaluated The final step involves modifying theparameters of the LTTP model until the result is acceptableIn particular the test dataset is a dataset that is independentof the training dataset [39]

22MLAlgorithms Selection ML tasks are typically classifiedinto four broad categories [40] supervised learning unsuper-vised learning reinforcement learning and semisupervised

4 Mathematical Problems in Engineering

Resultsamp

evaluation

LTTP model

Machine learning algorithm

Training data

Testdata

1

2 3

Figure 3 Experimental flowchart of ML methods

Table 2 Adaptability analysis between ML algorithms and LTTP

Algorithms Adaptability analysis ApplyANNs The effect has been thoroughly verified by many existing studies NoBNs A probabilistic model that is not suitable for this study [29] NoSVM Perfect theoretical basis with high generalization ability [30] YesRF An ensemble learning method evolved from DT better than DT [31] YesLR It solves the classification problems not suitable for this study [32] NokNN An efficient algorithm for the classification and regression tasks [33] YesDT RF has been chosen there is no need to choose DT NoHM A probabilistic model that is not suitable for this study [34] No

learning [41] The LTTP of OPTs belongs to the typicalsupervised learning task due to the labeled training data fromthe OPATDS [42] Prediction models output the travel timevalues of OPTs which can be considered to be a regressionproblem of supervised learning

There are many ML algorithms that can be used tosolve the regression problem of supervised learning suchas ANN Bayesian network (BN) SVM random forest (RF)logistic regression (LR) 119896-nearest neighbors (kNN) decisiontree (DT) AdaBoost [43] and hidden Markov model (HM)approaches [44]The adaptability analysis between LTTP andthe various ML algorithms is given in Table 2 Based on thecomparison results this paper chooses the kNN SVM andRF algorithms to build the LTTP models of OPTs

kNN is a nonparametric method used for classificationand regression and the kNN regression computes the meanof the function values of its 119896-nearest neighbors [33 45] Thegoal function regression119891kNN(119909) of kNN regression is writtenas follows [45]

119891kNN (119909) = 1119896 sdot sum119894isin119873119896(119909)

119910119894 (1)

where 119909 is an unknown pattern 119873119896(119909) is the indices of the119896-nearest neighbors of 119909 and 119910119894 is the predicted labelsThe original SVM algorithm was invented by Cortes

and Vapnik [46] and its efficiency in classification has beenverified in many case studies [47] The detailed introductionof SVM can be found in Smola and Scholkopf [48] inwhich they published the complete tutorial on support vector

regression To train the SVM regression model the followingmust be solved

minimize 12 1199082 (2a)

subject to 119910119894 minus ⟨119908 119909119894⟩ minus 119887 le 120576⟨119908 119909119894⟩ + 119887 minus 119910119894 le 120576 (2b)

where 119909119894 represents the training features with target value 119910119894⟨119908 119909119894⟩ + 119887 is the prediction value and 120576 is a free parameterthat serves as a threshold

The RF algorithm evolved from DT theory and wascreated by Ho in 1995 [31] This approach incorporatesthe bootstrap aggregating (Bagging) algorithm which is amethod for generating multiple versions of a predictor andthen using these to obtain an aggregated predictor [49] TheRF method has a higher degree of efficiency and accuracythan the DT method because of Bagging

23 Training Data Structure The training dataset is themost critical factor when training ML prediction modelsand it consists of several features and corresponding targetvalues [50] Many features commonly affect the LTTP ofOPTs which can be broadly classified into three categoriestruck features road features and meteorological featuresThe meteorological features are considered in this paperbecause rainy and snowy weather reduces both the frictioncoefficient of roads and the truck driverrsquos vision Accordingto the relevant statistics reported by the US Federal HighwayAdministration bad weather can lead to a 35 reduction incar speed [51]

Mathematical Problems in Engineering 5

Table 3 Preprocessed data for training the ML prediction models

Date Start time Arrival time Truck Id Truck type2017-03-01 162320 162657 202 BELAZ-L2017-03-02 201209 201812 503 MT-86Truck status 119909-axis start 119910-axis start 119909-axis arrival 119910-axis arrivalRun 1344 1188 2191 968Run 2576 783 3095 327

Load status Start node Arrival node Pressure(100 Pa)

Wind speed(ms)

Empty B E 1002 1Coal G H 999 06Temperature(∘C)

Relative humidity()

Precipitation(mm) Rain Travel time

(hourminsec)2 90 0 No 0003371 96 0 No 000603

Table 4 Description of the variables used in the prediction

Variables Type Role DescriptionTruck Id Numeric Feature The serial number of truckTruck type Categorical Feature The type of the truck (ie BELAZ-L BELAZ-M and MT86)Truck status Categorical Feature The status of the truck (ie running waiting and stop)119909-axis start Numeric Feature The 119909 coordinate of the truck at the starting position119910-axis start Numeric Feature The 119910 coordinate of the truck at the starting position119909-axis arrival Numeric Feature The 119909 coordinate of the truck at the ending position119910-axis arrival Numeric Feature The 119910 coordinate of the truck at the ending positionLoad status Categorical Feature The load status of the truck (ie empty and coal)Start node Categorical Feature The node code of the starting position of the roadArrival node Categorical Feature The node code of the ending position of the roadPressure Numeric Feature A fundamental atmospheric quantityWind speed Numeric Feature A fundamental atmospheric quantityTemperature Numeric Feature A fundamental atmospheric quantityRelative humidity Numeric Feature A fundamental atmospheric quantityPrecipitation Numeric Feature A fundamental atmospheric quantityRain Categorical Feature A fundamental atmospheric quantity (ie yes and no)Travel time Date time Target The travel time of the truck on each link

The data used in the following experiments originatefrom the FWOM The truck and road feature data are fromthe OPATDS while the weather data are collected fromthe China Meteorological Administration (CMA) Number54351 monitoring station The preprocessed training datasetsamples in this experiment are listed in Table 3 There are 16variables serving as the features and the target is the trucktravel time Table 4 shows the description of the target andeach feature used for the prediction in this study

24 Program and Pseudocode This study used sophisticatedalgorithms to predict the link travel time in open-pit minesand the three ML algorithms in the prediction models werebased on scikit-learn which is an open-sourceMLmodule in

the Python programming language [52 53] The pseudocodeof the methodology in this study is illustrated in Figure 4

3 Results and Discussion

31 Predictions of the ML Models For the training datasets2246746 historical records from March 2017 were exportedfrom the OPATDS database of the FWOM After datapreprocessing the structure of the training datawas similar tothose in Table 3 The experimental parameters encompassedone type of link road trained by three differentML algorithms(kNN SVM and RF) resulting in 18 LTTP models Theprediction results for the last 50 records of the test datasetsare shown in Figure 5

6 Mathematical Problems in Engineering

Figure 4 The pseudocode of the ML methodology

To derive the best LTTP model for each link road theaforementioned prediction results were evaluated based onthe mean absolute deviation (MAD) and the mean absolutepercentage error (MAPE) methods which are commonlyused for regression problem evaluation

The MAD as expressed in (3a) is a summary statistic ofstatistical dispersion or variability [54 55] The MAPE is ameasure of the accuracy of a prediction method in statisticsas written in (3b) [56] Because the MAPE is a percentageit is often easier to understand than the other statistics Forexample if the MAPE is 5 on average the forecast is off by5 [57]

MAD = sum119899119894=1 1003816100381610038161003816119909obs119894 minus 119909model1198941003816100381610038161003816119899 (3a)

MAPE = sum119899119894=1 1003816100381610038161003816(119909obs119894 minus 119909model119894) 119909obs1198941003816100381610038161003816119899 times 100 () (3b)

where 119909obs119894 represents the observation values 119909model119894 rep-resents the prediction values and 119899 is the number of datarecords

Table 5 lists the MAD and MAPE values obtained fromthe three ML methods for each experimental link road

Smaller MAD and MAPE values reflect better predictionperformance of each LTTP model and the smallest recordsare highlighted in Table 5 The results of the six experimentallink roads indicate that the LTTP models built using theSVM and RF methods are better than those using the kNNalgorithm Table 6 summarizes the optimal ML predictionmodels for each link road

The coefficient of determination 1198772 is widely used instatistical tests to evaluate the predictive capability of amodel and is also used in this study The 1198772 value with oneindependent variable is written as follows [58]

1198772 = [ 1119873 lowastsum (119909119894 minus 119909) lowast (119910119894 minus 119910)(120590119909 lowast 120590119910) ]

2

(4)

Mathematical Problems in Engineering 7

Raw valueKNN

SVMRF

000100000200000300000400000500000600000700000800000900001000001100001200

Link

trav

el tim

e

0 5 15 20 25 30 35 40 45 5010G-H

000100

000200

000300

000400

000500

000600

000700

000800

Link

trav

el tim

e

0 5 15 20 25 30 35 40 45 5010H-J

000200000300000400000500000600000700000800000900001000001100001200

Link

trav

el tim

e

0 5 15 20 25 30 35 40 45 5010E-H

000100000200000300000400000500000600000700000800000900001000001100

Link

trav

el tim

e

0 5 15 20 25 30 35 40 45 5010E-F

0 5 15 20 25 30 35 40 45 5010B-E

000200

000300

000400

000500

000600

000700

000800

000900

001000

Link

trav

el tim

e

000400000500000600000700000800000900001000001100001200001300001400001500001600001700001800001900002000002100002200

Link

trav

el tim

e

0 5 15 20 25 30 35 40 45 5010B-D

Raw valueKNN

SVMRF

Figure 5 Prediction results for the different ML methods

where119873 is the number of observations used to fit the model119909 and 119910 are themean values of 119909 and 119910 respectively 119909119894 and 119910119894are the values of observation 119894 and 120590119909 and 120590119910 are the standarddeviations of 119909 and 119910 respectively

Table 7 shows the 1198772 values of the three ML models foreach link road The 1198772 values range from 0 to 1 and 1198772 equalto 1 indicates perfect accurate prediction There are somedifferences between Tables 6 and 7 that is the optimal MLmodel of B-E H-J and G-H However the MAPE was stillselected for choosing the optimal model because the 1198772 valuecannot be used to evaluate predictive errors

32 Discussion of Traditional Averaging Methods and MLModels To compare the LTTP of MLmodels and traditionalaveraging methods controlled experiments were performedThe flow chart of traditional averaging methods is illustratedin Figure 6

For each record in the test dataset the experimentstraced back the corresponding top 10 20 30 40 and 50records and then calculated the average value as the finalprediction To improve the accuracy of the traditional aver-aging methods each calculation used only historical data forthe same truck type and load status The results obtained

8 Mathematical Problems in Engineering

Table 5 LTTP evaluation based on the different ML models

Link road Road type Evaluation kNN SVM RF

B-E

Fixed

MAD 591119864 minus 04 509119864 minus 04 456E minus 04MAPE 178119864 + 01 158119864 + 01 144E + 01

E-H MAD 944119864 minus 04 332E minus 04 637119864 minus 04MAPE 249119864 + 01 957E + 00 181119864 + 01

H-J MAD 516119864 minus 04 355119864 minus 04 354E minus 04MAPE 214119864 + 01 159119864 + 01 148E + 01

B-D

Temporary

MAD 171119864 minus 03 544E minus 04 670119864 minus 04MAPE 275119864 + 01 809E + 00 990119864 + 00

E-F MAD 959119864 minus 04 805119864 minus 04 563E minus 04MAPE 313119864 + 01 294119864 + 01 182E + 01

G-H MAD 118119864 minus 03 735E minus 04 785119864 minus 04MAPE 342119864 + 01 194E + 01 238119864 + 01

4

Rece

nt h

istor

ical

dat

a

2

Data predicted

Calculatingthe average time

(i) Same link road (ii) Same load status(iii) Same truck type

3001357

001421

001409BELAZB-E

001357

Empty

Empty

BELAZB-E

001821LoadB-E MT-86

001421EmptyB-E BELAZ

001715B-E EmptyMT-86

1

Figure 6 The flow chart of traditional averaging methods

Table 6 Summary of the optimal ML prediction models for eachlink road

Road Type Optimal ML modelB-E

FixedRF

E-H SVMH-J RFB-D

TemporarySVM

E-F RFG-H SVM

Table 7 1198772 values of the different ML models for each link road

Road SVM KNN RF Optimal ML modelB-E 028 016 041 SVME-H 083 016 067 SVMH-J 072 013 056 SVMB-D 089 023 07 SVME-F 054 024 073 RFG-H 061 019 062 RF

from the traditional averaging methods are summarized inTable 8

Smaller MAD and MAPE values mean better predictionperformance of the traditional averaging methods and the

smallest records are highlighted in Table 8The predicted val-ues obtained from the optimal ML method and a traditionalaverage method for each link road are given in Table 9 thedecrease in the MAPE is also shown

Table 9 shows that the tested ML models are superiorto the traditional averaging method in the context of LTTPbecause the former has smaller MAPEs An average increaseof 1579 in prediction accuracy is achieved in all experimen-tal link roads in which increases of 1254 and 1930 forthree fixed and three temporary roads respectively are alsoobtained

33 Discussion of Meteorological Features This study alsoconsidered the influence of meteorological features on theLTTP of an open-pit mine The data were obtained froma CMA monitoring station including 5 variables pressurewind speed temperature relative humidity and precipita-tion

The Pearson correlation coefficient (PCC) an evaluationmethod developed by Pearson [59] was used to evaluate thelinear correlation between two variables The expression ofthe PPC is as follows

120588119883119884 = cov (119883 119884)120590119883120590119884 (5)

Mathematical Problems in Engineering 9

Table 8 Results obtained from the traditional averaging methods

Road Evaluation Traditional averaging methods10 records 20 records 30 records 40 records 50 records

B-E MAD 102119864 minus 03 949119864 minus 04 917119864 minus 04 918119864 minus 04 904E minus 04MAPE 306119864 + 01 281119864 + 01 266119864 + 01 264119864 + 01 258E + 01

E-H MAD 122119864 minus 03 113119864 minus 03 109119864 minus 03 109119864 minus 03 107E minus 03MAPE 329119864 + 01 300119864 + 01 284119864 + 01 281119864 + 01 273E + 01

H-J MAD 629119864 minus 04 609119864 minus 04 587119864 minus 04 581119864 minus 04 580E minus 04MAPE 254119864 + 01 247119864 + 01 236119864 + 01 234119864 + 01 233E + 01

B-D MAD 215119864 minus 03 183E minus 03 246119864 minus 03 236119864 minus 03 205119864 minus 03MAPE 317119864 + 01 269E + 01 386119864 + 01 362119864 + 01 325119864 + 01

E-F MAD 116119864 minus 03 110E minus 03 114119864 minus 03 115119864 minus 03 116119864 minus 03MAPE 391119864 + 01 363E + 01 381119864 + 01 390119864 + 01 395119864 + 01

G-H MAD 129E minus 03 138119864 minus 03 136119864 minus 03 132119864 minus 03 130119864 minus 03MAPE 404E + 01 412119864 + 01 391119864 + 01 370119864 + 01 357119864 + 01

Table 9 Comparison between the optimal ML model and the optimal averaging method

Road Type Optimal average method (MAPE) Optimal ML model (MAPE) MAPE decrease AverageB-E

Fixed258119864 + 01 144119864 + 01 1140

1254E-H 273119864 + 01 957119864 + 00 1773H-J 233119864 + 01 148119864 + 01 850B-D

Temporary269119864 + 01 809119864 + 00 1881

1930E-F 363119864 + 01 182119864 + 01 1810G-H 404119864 + 01 194119864 + 01 2100Average 1579

Table 10 Prediction results after including meteorological data

Type Road Methods Meteorological features MAD MAPE MAPE decrease (no-yes)

Temporary

B-E RF No 690119864 minus 04 207119864 + 01 630Yes 456119864 minus 04 144119864 + 01

E-H SVM No 341119864 minus 04 169119864 + 01 728Yes 332119864 minus 04 957119864 + 00

H-J RF No 416119864 minus 04 186119864 + 01 380Yes 354119864 minus 04 148119864 + 01

Fixed

B-D SVM No 635119864 minus 04 122119864 + 01 408Yes 544119864 minus 04 809119864 + 00

E-F RF No 660119864 minus 04 217119864 + 01 350Yes 563119864 minus 04 182119864 + 01

G-H SVM No 842119864 minus 04 252119864 + 01 580Yes 735119864 minus 04 194119864 + 01

Average 513

where cov(119883 119884) is the covariance 120590119883 is the standard devia-tion of119883 and 120590119884 is the standard deviation of 119884

The PPC values of different variables are shown inFigure 7 including the 5 meteorological variables and trucktravel time A high PCC value indicates a closer relationshipbetween the two variables

Following controlled experiments the effect of meteo-rological features was investigated by adding or removingindividual features We selected the optimal ML model for

each link road The raw (observation) values and predictedresults withwithout meteorological features are shown inFigure 8

The results of the controlled experiments are shownin Table 10 the calculated decrease in the MAPE is alsoshown The results considering meteorological features arebetter than those withoutmeteorological featuresTheMAPEdecreased by 513 on average for all link roads after addingthe meteorological data

10 Mathematical Problems in Engineering

Pressure08

Wind speed04

Temperature

00

Relative humidity

Precipitation

Travel time

minus04

minus08

Pres

sure

Win

d sp

eed

Tem

pera

ture

Relat

ive h

umid

ity

Prec

ipita

tion

Trav

el tim

e

1

1

1

1

1

1

minus048 minus048

minus048

minus048

064

064

minus0041 minus0019

minus0019

005

005

minus0088

minus0088

minus082

minus082

047

012

012

047 minus064 014

014

0049

0049

minus0041

minus0054

minus0054

0045

0045

minus064

Figure 7 The PCC heat map of meteorological features

Table 11 Evaluation of LTTP based on different ML models

Link road Road type Evaluation kNN SVM RF

A-B Fixed MAD 495119864 minus 04 328119864 minus 04 299E minus 04MAPE 469119864 + 01 340119864 + 01 336E + 01

34 Discussion of LTTP and RTTP The above experimentsused the link rather than the route to predict the travel timeof OPTs However the differences between LTTP and RTTPneed to be further discussed In the ensuing discussion thelongest route between dump point A and load point G isselected as shown in Figure 9

The A-G route consists of 4 links A-B B-E E-H and H-G Among them the optimal ML prediction models of B-EE-H andH-G are SVM RF and SVM respectivelyThe sameexperimental procedure as used in Section 31 was used toobtain the optimal MLmodel for A-B and Table 11 shows theMAD and MAPE values of the three ML methods It can beseen that the RF model is the best ML method for link A-B

The SVM and RF methods are used to predict the RTTPof A-G because those two models have a good predictionperformance Thus the experiments are summarized asfollows

(i) RTTP (SVM) using the SVM algorithm to train theTTP model for the route A-G

(ii) RTTP (RF) using the RF algorithm to train the TTPmodel for the route A-G

(iii) LTTP using the optimalMLmodel for each link thatis A-B (RF) B-E (SVM) E-H (RF) and H-G (SVM)and the truck travel time of A-G is the sum of eachLTTP result

Raw values and predicted results of the above threeexperiments are shown in Figure 10 while the evaluated

Table 12 Evaluation of the results between LTTP and RTTP

Method Model Evaluation Values

RTTP SVM MAD 155119864 minus 03MAPE 208119864 + 01

RTTP RF MAD 178119864 minus 03MAPE 235119864 + 01

LTTP Assemble MAD 834E minus 04MAPE 898E + 00

results of those experiments are shown in Table 12 Both theMAD and MAPE values of the LTTP approach are smallerthan the two RTTP methods Thus using the link as theprediction unit is better than using the route

4 Conclusions

The link roads of an open-pit mine are divided into fixedand temporary roads in this paper Three ML algorithmsthat is kNN SVM and RF are used for the LTTP of OPTsThe experimental results not only reflect the self-adaptive andself-feedback characteristics of the ML algorithms but alsodemonstrate the practicality of themethod for road segmentsThe conclusions based on the results are as follows

(1) LTTP models based on ML are more efficient andaccurate than traditional averaging methods Anoverall average increase of 1579 in the predictionaccuracy is obtained for six experimental link roads

Mathematical Problems in Engineering 11

000100000200000300000400000500000600000700000800000900001000001100001200

Link

trav

el tim

e

0 10 15 20 25 30 35 40 45 505G-H (SVM)

000100

000200

000300

000400

000500

000600

000700

000800

Link

trav

el tim

e

0 10 15 20 25 30 35 40 45 505H-J (RF)

000200000300000400000500000600000700000800000900001000001100001200

Link

trav

el tim

e

0 5 15 20 25 30 35 40 45 5010E-H (SVM)

000100

000200

000300

000400

000500

000600

000700

000800

Link

trav

el tim

e

0 5 15 20 25 30 35 40 45 5010E-F (RF)

000400000500000600000700000800000900001000001100001200001300001400001500001600001700001800001900002000002100002200

Link

trav

el tim

e

0 5 15 20 25 30 35 40 45 5010B-D (SVM)

000200

000300

000400

000500

000600

000700

000800

000900

001000

Link

trav

el tim

e

0 10 15 20 25 30 35 40 45 505B-E (RF)

Raw valueWithout meteorological featuresMeteorological features

Raw valueWithout meteorological featuresMeteorological features

Figure 8 Comparison forecast results including and excluding meteorological features

For temporary roads the average accuracy increasesby 1930

(2) LTTP models established using the SVM and RFalgorithms are better than those established using thekNN approach There is no large difference betweenthe SVM and RF results although the RF algorithmrequires less space and time complexity than the SVMalgorithm

(3) This paper is original in that it considers the effectof meteorological features on LTTP The results show

that considering the effect of meteorological featureson LTTP increases the prediction accuracy by 513

(4) The differences between LTTP and RTTP are alsodiscussed and the former has a higher predictionaccuracy The MAPE decreases by 1182 for theLTTP method

Some work is already underway to incorporate the MLprediction models into the OPATDS of the FWOM whichwill be helpful in improving the dispatching efficiency of theOPTs

12 Mathematical Problems in Engineering

Node J

Load G

Node E

Load F

Dump ANode B

Load D

Load C

Node H

Fixed roadsTemporary roads

Figure 9 The location of the route A-G in the FWOM roadmap

Raw valuesRTTP (RF)

RTTP (SVM)LTTP

5 10 15 20 25 30 35 40 45 500Route A-G

000600000800001000001200001400001600001800002000002200

Truc

k tr

avel

tim

e

Figure 10 Prediction results for RTTP (RF) RTTP (SVM) andLTTP

Data Availability

The data used to support the findings of this study areavailable from the corresponding author upon request

Conflicts of Interest

The authors declare no conflicts of interest

Authorsrsquo Contributions

Xiaoyu Sun as the principal investigator provided the dataused to train the ML models Hang Zhang performed theexperiments andwrote the paper Fengliang Tian contributedthe programming Lei Yang proofread the manuscript

Acknowledgments

This work was funded by the National Natural ScienceFoundation of China (no 51674063) and the NationalKey Research and Development Program of China (no2016YFC0801608)

References

[1] J Czaplicki Shovel-Truck Systems CRC Press 2008[2] J M Czaplicki ldquoModelling and analysis of the exploitation

process of a shovel-truck systemrdquo in Shovel-Truck Systems pp79ndash89 CRC Press 2008

[3] S G Ercelebi and A Bascetin ldquoOptimization of shovel-trucksystem for surface miningrdquo Journal of the Southern AfricanInstitute of Mining and Metallurgy vol 109 no 7 pp 433ndash4392009

[4] R Mena E Zio F Kristjanpoller and A Arata ldquoAvailability-based simulation and optimization modeling framework foropen-pit mine truck allocation under dynamic constraintsrdquoInternational Journal of Mining Science and Technology vol 23no 1 pp 113ndash119 2013

[5] F Soumis J Ethier and J Elbrond ldquoTruck dispatching inan open pit minerdquo International Journal of Surface MiningReclamation and Environment vol 3 no 2 pp 115ndash119 1989

[6] A Y F Fadin Komarudin and A O Moeis ldquoSimulation-optimization truck dispatch problem using look - ahead algo-rithm in open pit minesrdquo International Journal of GEOMATEvol 13 no 36 pp 80ndash86 2017

[7] Y Tan and S Takakuwa ldquoA practical simulation approachfor an effective truck dispatching system of open pit minesusing VBArdquo in Proceedings of the 2016 Winter SimulationConference WSC 2016 pp 2394ndash2405 IEEE Washington DCUSA December 2016

[8] J Li R Bai J Mao and W Li ldquoForecast of applied effect fortruck real-time dispatch system in open-pit mine based onCSUSSrdquo in Proceedings of the 2010 International Conference onE-Product E-Service and E-Entertainment ICEEE2010 pp 1ndash4IEEE Henan China November 2010

[9] S P Alarie and M Gamache ldquoOverview of solution strategiesused in truck dispatching systems for open pit minesrdquo Interna-tional Journal of Surface Mining Reclamation and Environmentvol 16 no 1 pp 59ndash76 2002

[10] B Kolonja D R Kalasky and J M Mutmansky ldquoOptimizationof dispatching criteria for open-pit truck haulage system designusingmultiple comparisons with the best and common random

Mathematical Problems in Engineering 13

numbersrdquo in Proceedings of the 25th Conference on Winter Sim-ulation WSC 1993 pp 393ndash401 ACM Los Angeles CaliforniaUSA December 1993

[11] Q Wang Y Zhang C Chen and W Xu ldquoOpen-pit mine truckreal-time dispatching principle under macroscopic controlrdquo inProceedings of the 1st International Conference on InnovativeComputing Information and Control 2006 ICICICrsquo06 pp 702ndash705 IEEE Beijing China September 2006

[12] Y Choi ldquoSimulation of Shovel-Truck Haulage Systems byConsidering Truck Dispatch Methodsrdquo Journal of the KoreanSociety of Mineral and Energy Resources Engineers vol 50 no4 p 543 2013

[13] E Topal and S Ramazan ldquoMining truck scheduling withstochastic maintenance costrdquo Journal of Coal Science andEngineering vol 18 no 3 pp 313ndash319 2012

[14] P Chaowasakoo H Seppala H Koivo and Q Zhou ldquoDigi-talization of mine operations Scenarios to benefit in real-timetruck dispatchingrdquo International Journal of Mining Science andTechnology vol 27 no 2 pp 229ndash236 2017

[15] Q Sun ldquoRoad running time statistics method in truck schedul-ingrdquo Opencast Coal Mining Technology vol 01 pp 35ndash37 1998

[16] R Bai J Li and J Xu ldquoReal-time dynamic forecast of truck linktravel timerdquo Journal of Liaoning Technical University vol 1 pp12ndash14 2005

[17] L Jiangang ldquoReal-time dynamic forecasts of truck link traveltime based on fuzzy neural networkrdquo Journal of the China CoalSociety vol 6 pp 796ndash800 2005

[18] E K Chanda and S Gardiner ldquoA comparative study of truckcycle time prediction methods in open-pit miningrdquo Engineer-ing Construction and Architectural Management vol 17 no 5pp 446ndash460 2010

[19] D J Edwards and I J Griffiths ldquoArtificial intelligence approachto calculation of hydraulic excavator cycle time and outputrdquoMining Technology vol 109 no 1 pp 23ndash29 2013

[20] K Erarslan ldquoModelling performance and retarder chart of off-highway trucks by cubic splines for cycle time estimationrdquoMining Technology vol 114 pp 161ndash166 2013

[21] X Xue W Sun and R Liang ldquoA new method of real-timedynamic forecast of truck link travel time in open minesrdquoJournal of the China Coal Society vol 37 no 8 pp 1418ndash14222012

[22] X Meng Research on scheduling services of open-pit mine basedon real-time travel time prediction China University of Miningand Technology 2014

[23] V Shalamanov V Pershin S Shabaev and D Boiko ldquoJustifi-cation of the Optimal Granulometric Composition of CrushedRocks for Open-Pit Mine Road Surfacingrdquo in Proceedings of the1st International InnovativeMining Symposium 2017 KemerovoRussia April 2017

[24] M Hofmann and M OrsquoMahony ldquoThe impact of adverseweather conditions on urban bus performance measuresrdquoin Proceedings of the 8th International IEEE Conference onIntelligent Transportation Systems pp 431ndash436 IEEE ViennaAustria September 2005

[25] T H Maze M Agarwal and G Burchett ldquoWhether weathermatters to traffic demand traffic safety and traffic operationsand flowrdquoTransportation Research Record no 1948 pp 170ndash1762006

[26] S A Silvester I S Lowndes and D M Hargreaves ldquoAcomputational study of particulate emissions from an openpit quarry under neutral atmospheric conditionsrdquo AtmosphericEnvironment vol 43 no 40 pp 6415ndash6424 2009

[27] I Tsapakis T Cheng and A Bolbol ldquoImpact of weather condi-tions on macroscopic urban travel timesrdquo Journal of TransportGeography vol 28 pp 204ndash211 2013

[28] TheMinistry of Land and Resources ldquoPRCThe basic situationof mineral resources in fushunrdquo httpwwwmlrgovcnkczyglkczydjtj201208t20120813 1130832htm

[29] G F Cooper and E Herskovits ldquoA Bayesian method forthe induction of probabilistic networks from datardquo MachineLearning vol 9 no 4 pp 309ndash347 1992

[30] C Yunqiang Z X Sean and T S Huang ldquoOne-class svm forlearning in image retrievalrdquo in In Proceedings 2001 InternationalConference on Image Processing (Cat No01CH37205) pp 34ndash372001

[31] T K Ho ldquoIn Random decision forestsrdquo in Proceedings of 3rdInternational Conference on Document Analysis and Recogni-tion IEEE 1995

[32] D G Kleinbaum and M Klein ldquoAnalysis of Matched DataUsing Logistic Regressionrdquo in Logistic Regression pp 389ndash428Springer New York NY USA 2010

[33] N S Altman ldquoAn introduction to kernel and nearest-neighbornonparametric regressionrdquo The American Statistician vol 46no 3 pp 175ndash185 1992

[34] S R Eddy ldquoProfile hiddenMarkovmodelsrdquo Bioinformatics vol14 no 9 pp 755ndash763 1998

[35] J R Koza F H Bennett D Andre and M A Keane ldquoAuto-mated design of both the topology and sizing of analog electricalcircuits using genetic programmingrdquo in In Artificial intelligencein design rsquo96 pp 151ndash170 Springer Netherlands 1996

[36] T Oladipupo ldquoIntroduction to machine learningrdquo in In Newadvances in machine learning InTech 2010

[37] H Mannila ldquoData mining machine learning statistics anddatabasesrdquo in Proceedings of the 8th International Conferenceon Scientific and Statistical Data Base Management IEEEStockholm Sweden Sweden 2002

[38] M Troc and O Unold ldquoSelf-adaptation of parameters in alearning classifier system ensemble machinerdquo InternationalJournal of Applied Mathematics and Computer Science vol 20no 1 pp 157ndash174 2010

[39] T Hastie R Tibshirani and J Friedman The Elements ofStatistical Learning Springer-Verlag New York NY USA 2009

[40] N J Nilsson ldquoArtificial intelligence A modern approachrdquoArtificial Intelligence vol 82 no 1-2 pp 369ndash380 1996

[41] I Kavakiotis O Tsave A Salifoglou N Maglaveras I Vla-havas and I Chouvarda ldquoMachine Learning and Data MiningMethods in Diabetes Researchrdquo Computational and StructuralBiotechnology Journal vol 15 pp 104ndash116 2017

[42] M Mohri A Rostamizadeh and A Talwalkar Foundations ofmachine learning MIT press 2012

[43] Y Freund and R E Schapire ldquoA decision-theoretic generaliza-tion of on-line learning and an application to boostingrdquo Journalof Computer and System Sciences vol 55 no 1 part 2 pp 119ndash139 1997

[44] R S Michalski J G Carbonell and T M Mitchell ldquoMachinelearning 1983rdquo

[45] O Kramer ldquoK-nearest neighborsrdquo in Dimensionality reductionwith unsupervised nearest neighbors vol 51 pp 13ndash23 SpringerBerlin Heidelberg Germany 2013

[46] C Cortes and V Vapnik ldquoSupport-vector networksrdquo MachineLearning vol 20 no 3 pp 273ndash297 1995

4 Mathematical Problems in Engineering

Resultsamp

evaluation

LTTP model

Machine learning algorithm

Training data

Testdata

1

2 3

Figure 3 Experimental flowchart of ML methods

Table 2 Adaptability analysis between ML algorithms and LTTP

Algorithms Adaptability analysis ApplyANNs The effect has been thoroughly verified by many existing studies NoBNs A probabilistic model that is not suitable for this study [29] NoSVM Perfect theoretical basis with high generalization ability [30] YesRF An ensemble learning method evolved from DT better than DT [31] YesLR It solves the classification problems not suitable for this study [32] NokNN An efficient algorithm for the classification and regression tasks [33] YesDT RF has been chosen there is no need to choose DT NoHM A probabilistic model that is not suitable for this study [34] No

learning [41] The LTTP of OPTs belongs to the typicalsupervised learning task due to the labeled training data fromthe OPATDS [42] Prediction models output the travel timevalues of OPTs which can be considered to be a regressionproblem of supervised learning

There are many ML algorithms that can be used tosolve the regression problem of supervised learning suchas ANN Bayesian network (BN) SVM random forest (RF)logistic regression (LR) 119896-nearest neighbors (kNN) decisiontree (DT) AdaBoost [43] and hidden Markov model (HM)approaches [44]The adaptability analysis between LTTP andthe various ML algorithms is given in Table 2 Based on thecomparison results this paper chooses the kNN SVM andRF algorithms to build the LTTP models of OPTs

kNN is a nonparametric method used for classificationand regression and the kNN regression computes the meanof the function values of its 119896-nearest neighbors [33 45] Thegoal function regression119891kNN(119909) of kNN regression is writtenas follows [45]

119891kNN (119909) = 1119896 sdot sum119894isin119873119896(119909)

119910119894 (1)

where 119909 is an unknown pattern 119873119896(119909) is the indices of the119896-nearest neighbors of 119909 and 119910119894 is the predicted labelsThe original SVM algorithm was invented by Cortes

and Vapnik [46] and its efficiency in classification has beenverified in many case studies [47] The detailed introductionof SVM can be found in Smola and Scholkopf [48] inwhich they published the complete tutorial on support vector

regression To train the SVM regression model the followingmust be solved

minimize 12 1199082 (2a)

subject to 119910119894 minus ⟨119908 119909119894⟩ minus 119887 le 120576⟨119908 119909119894⟩ + 119887 minus 119910119894 le 120576 (2b)

where 119909119894 represents the training features with target value 119910119894⟨119908 119909119894⟩ + 119887 is the prediction value and 120576 is a free parameterthat serves as a threshold

The RF algorithm evolved from DT theory and wascreated by Ho in 1995 [31] This approach incorporatesthe bootstrap aggregating (Bagging) algorithm which is amethod for generating multiple versions of a predictor andthen using these to obtain an aggregated predictor [49] TheRF method has a higher degree of efficiency and accuracythan the DT method because of Bagging

23 Training Data Structure The training dataset is themost critical factor when training ML prediction modelsand it consists of several features and corresponding targetvalues [50] Many features commonly affect the LTTP ofOPTs which can be broadly classified into three categoriestruck features road features and meteorological featuresThe meteorological features are considered in this paperbecause rainy and snowy weather reduces both the frictioncoefficient of roads and the truck driverrsquos vision Accordingto the relevant statistics reported by the US Federal HighwayAdministration bad weather can lead to a 35 reduction incar speed [51]

Mathematical Problems in Engineering 5

Table 3 Preprocessed data for training the ML prediction models

Date Start time Arrival time Truck Id Truck type2017-03-01 162320 162657 202 BELAZ-L2017-03-02 201209 201812 503 MT-86Truck status 119909-axis start 119910-axis start 119909-axis arrival 119910-axis arrivalRun 1344 1188 2191 968Run 2576 783 3095 327

Load status Start node Arrival node Pressure(100 Pa)

Wind speed(ms)

Empty B E 1002 1Coal G H 999 06Temperature(∘C)

Relative humidity()

Precipitation(mm) Rain Travel time

(hourminsec)2 90 0 No 0003371 96 0 No 000603

Table 4 Description of the variables used in the prediction

Variables Type Role DescriptionTruck Id Numeric Feature The serial number of truckTruck type Categorical Feature The type of the truck (ie BELAZ-L BELAZ-M and MT86)Truck status Categorical Feature The status of the truck (ie running waiting and stop)119909-axis start Numeric Feature The 119909 coordinate of the truck at the starting position119910-axis start Numeric Feature The 119910 coordinate of the truck at the starting position119909-axis arrival Numeric Feature The 119909 coordinate of the truck at the ending position119910-axis arrival Numeric Feature The 119910 coordinate of the truck at the ending positionLoad status Categorical Feature The load status of the truck (ie empty and coal)Start node Categorical Feature The node code of the starting position of the roadArrival node Categorical Feature The node code of the ending position of the roadPressure Numeric Feature A fundamental atmospheric quantityWind speed Numeric Feature A fundamental atmospheric quantityTemperature Numeric Feature A fundamental atmospheric quantityRelative humidity Numeric Feature A fundamental atmospheric quantityPrecipitation Numeric Feature A fundamental atmospheric quantityRain Categorical Feature A fundamental atmospheric quantity (ie yes and no)Travel time Date time Target The travel time of the truck on each link

The data used in the following experiments originatefrom the FWOM The truck and road feature data are fromthe OPATDS while the weather data are collected fromthe China Meteorological Administration (CMA) Number54351 monitoring station The preprocessed training datasetsamples in this experiment are listed in Table 3 There are 16variables serving as the features and the target is the trucktravel time Table 4 shows the description of the target andeach feature used for the prediction in this study

24 Program and Pseudocode This study used sophisticatedalgorithms to predict the link travel time in open-pit minesand the three ML algorithms in the prediction models werebased on scikit-learn which is an open-sourceMLmodule in

the Python programming language [52 53] The pseudocodeof the methodology in this study is illustrated in Figure 4

3 Results and Discussion

31 Predictions of the ML Models For the training datasets2246746 historical records from March 2017 were exportedfrom the OPATDS database of the FWOM After datapreprocessing the structure of the training datawas similar tothose in Table 3 The experimental parameters encompassedone type of link road trained by three differentML algorithms(kNN SVM and RF) resulting in 18 LTTP models Theprediction results for the last 50 records of the test datasetsare shown in Figure 5

6 Mathematical Problems in Engineering

Figure 4 The pseudocode of the ML methodology

To derive the best LTTP model for each link road theaforementioned prediction results were evaluated based onthe mean absolute deviation (MAD) and the mean absolutepercentage error (MAPE) methods which are commonlyused for regression problem evaluation

The MAD as expressed in (3a) is a summary statistic ofstatistical dispersion or variability [54 55] The MAPE is ameasure of the accuracy of a prediction method in statisticsas written in (3b) [56] Because the MAPE is a percentageit is often easier to understand than the other statistics Forexample if the MAPE is 5 on average the forecast is off by5 [57]

MAD = sum119899119894=1 1003816100381610038161003816119909obs119894 minus 119909model1198941003816100381610038161003816119899 (3a)

MAPE = sum119899119894=1 1003816100381610038161003816(119909obs119894 minus 119909model119894) 119909obs1198941003816100381610038161003816119899 times 100 () (3b)

where 119909obs119894 represents the observation values 119909model119894 rep-resents the prediction values and 119899 is the number of datarecords

Table 5 lists the MAD and MAPE values obtained fromthe three ML methods for each experimental link road

Smaller MAD and MAPE values reflect better predictionperformance of each LTTP model and the smallest recordsare highlighted in Table 5 The results of the six experimentallink roads indicate that the LTTP models built using theSVM and RF methods are better than those using the kNNalgorithm Table 6 summarizes the optimal ML predictionmodels for each link road

The coefficient of determination 1198772 is widely used instatistical tests to evaluate the predictive capability of amodel and is also used in this study The 1198772 value with oneindependent variable is written as follows [58]

1198772 = [ 1119873 lowastsum (119909119894 minus 119909) lowast (119910119894 minus 119910)(120590119909 lowast 120590119910) ]

2

(4)

Mathematical Problems in Engineering 7

Raw valueKNN

SVMRF

000100000200000300000400000500000600000700000800000900001000001100001200

Link

trav

el tim

e

0 5 15 20 25 30 35 40 45 5010G-H

000100

000200

000300

000400

000500

000600

000700

000800

Link

trav

el tim

e

0 5 15 20 25 30 35 40 45 5010H-J

000200000300000400000500000600000700000800000900001000001100001200

Link

trav

el tim

e

0 5 15 20 25 30 35 40 45 5010E-H

000100000200000300000400000500000600000700000800000900001000001100

Link

trav

el tim

e

0 5 15 20 25 30 35 40 45 5010E-F

0 5 15 20 25 30 35 40 45 5010B-E

000200

000300

000400

000500

000600

000700

000800

000900

001000

Link

trav

el tim

e

000400000500000600000700000800000900001000001100001200001300001400001500001600001700001800001900002000002100002200

Link

trav

el tim

e

0 5 15 20 25 30 35 40 45 5010B-D

Raw valueKNN

SVMRF

Figure 5 Prediction results for the different ML methods

where119873 is the number of observations used to fit the model119909 and 119910 are themean values of 119909 and 119910 respectively 119909119894 and 119910119894are the values of observation 119894 and 120590119909 and 120590119910 are the standarddeviations of 119909 and 119910 respectively

Table 7 shows the 1198772 values of the three ML models foreach link road The 1198772 values range from 0 to 1 and 1198772 equalto 1 indicates perfect accurate prediction There are somedifferences between Tables 6 and 7 that is the optimal MLmodel of B-E H-J and G-H However the MAPE was stillselected for choosing the optimal model because the 1198772 valuecannot be used to evaluate predictive errors

32 Discussion of Traditional Averaging Methods and MLModels To compare the LTTP of MLmodels and traditionalaveraging methods controlled experiments were performedThe flow chart of traditional averaging methods is illustratedin Figure 6

For each record in the test dataset the experimentstraced back the corresponding top 10 20 30 40 and 50records and then calculated the average value as the finalprediction To improve the accuracy of the traditional aver-aging methods each calculation used only historical data forthe same truck type and load status The results obtained

8 Mathematical Problems in Engineering

Table 5 LTTP evaluation based on the different ML models

Link road Road type Evaluation kNN SVM RF

B-E

Fixed

MAD 591119864 minus 04 509119864 minus 04 456E minus 04MAPE 178119864 + 01 158119864 + 01 144E + 01

E-H MAD 944119864 minus 04 332E minus 04 637119864 minus 04MAPE 249119864 + 01 957E + 00 181119864 + 01

H-J MAD 516119864 minus 04 355119864 minus 04 354E minus 04MAPE 214119864 + 01 159119864 + 01 148E + 01

B-D

Temporary

MAD 171119864 minus 03 544E minus 04 670119864 minus 04MAPE 275119864 + 01 809E + 00 990119864 + 00

E-F MAD 959119864 minus 04 805119864 minus 04 563E minus 04MAPE 313119864 + 01 294119864 + 01 182E + 01

G-H MAD 118119864 minus 03 735E minus 04 785119864 minus 04MAPE 342119864 + 01 194E + 01 238119864 + 01

4

Rece

nt h

istor

ical

dat

a

2

Data predicted

Calculatingthe average time

(i) Same link road (ii) Same load status(iii) Same truck type

3001357

001421

001409BELAZB-E

001357

Empty

Empty

BELAZB-E

001821LoadB-E MT-86

001421EmptyB-E BELAZ

001715B-E EmptyMT-86

1

Figure 6 The flow chart of traditional averaging methods

Table 6 Summary of the optimal ML prediction models for eachlink road

Road Type Optimal ML modelB-E

FixedRF

E-H SVMH-J RFB-D

TemporarySVM

E-F RFG-H SVM

Table 7 1198772 values of the different ML models for each link road

Road SVM KNN RF Optimal ML modelB-E 028 016 041 SVME-H 083 016 067 SVMH-J 072 013 056 SVMB-D 089 023 07 SVME-F 054 024 073 RFG-H 061 019 062 RF

from the traditional averaging methods are summarized inTable 8

Smaller MAD and MAPE values mean better predictionperformance of the traditional averaging methods and the

smallest records are highlighted in Table 8The predicted val-ues obtained from the optimal ML method and a traditionalaverage method for each link road are given in Table 9 thedecrease in the MAPE is also shown

Table 9 shows that the tested ML models are superiorto the traditional averaging method in the context of LTTPbecause the former has smaller MAPEs An average increaseof 1579 in prediction accuracy is achieved in all experimen-tal link roads in which increases of 1254 and 1930 forthree fixed and three temporary roads respectively are alsoobtained

33 Discussion of Meteorological Features This study alsoconsidered the influence of meteorological features on theLTTP of an open-pit mine The data were obtained froma CMA monitoring station including 5 variables pressurewind speed temperature relative humidity and precipita-tion

The Pearson correlation coefficient (PCC) an evaluationmethod developed by Pearson [59] was used to evaluate thelinear correlation between two variables The expression ofthe PPC is as follows

120588119883119884 = cov (119883 119884)120590119883120590119884 (5)

Mathematical Problems in Engineering 9

Table 8 Results obtained from the traditional averaging methods

Road Evaluation Traditional averaging methods10 records 20 records 30 records 40 records 50 records

B-E MAD 102119864 minus 03 949119864 minus 04 917119864 minus 04 918119864 minus 04 904E minus 04MAPE 306119864 + 01 281119864 + 01 266119864 + 01 264119864 + 01 258E + 01

E-H MAD 122119864 minus 03 113119864 minus 03 109119864 minus 03 109119864 minus 03 107E minus 03MAPE 329119864 + 01 300119864 + 01 284119864 + 01 281119864 + 01 273E + 01

H-J MAD 629119864 minus 04 609119864 minus 04 587119864 minus 04 581119864 minus 04 580E minus 04MAPE 254119864 + 01 247119864 + 01 236119864 + 01 234119864 + 01 233E + 01

B-D MAD 215119864 minus 03 183E minus 03 246119864 minus 03 236119864 minus 03 205119864 minus 03MAPE 317119864 + 01 269E + 01 386119864 + 01 362119864 + 01 325119864 + 01

E-F MAD 116119864 minus 03 110E minus 03 114119864 minus 03 115119864 minus 03 116119864 minus 03MAPE 391119864 + 01 363E + 01 381119864 + 01 390119864 + 01 395119864 + 01

G-H MAD 129E minus 03 138119864 minus 03 136119864 minus 03 132119864 minus 03 130119864 minus 03MAPE 404E + 01 412119864 + 01 391119864 + 01 370119864 + 01 357119864 + 01

Table 9 Comparison between the optimal ML model and the optimal averaging method

Road Type Optimal average method (MAPE) Optimal ML model (MAPE) MAPE decrease AverageB-E

Fixed258119864 + 01 144119864 + 01 1140

1254E-H 273119864 + 01 957119864 + 00 1773H-J 233119864 + 01 148119864 + 01 850B-D

Temporary269119864 + 01 809119864 + 00 1881

1930E-F 363119864 + 01 182119864 + 01 1810G-H 404119864 + 01 194119864 + 01 2100Average 1579

Table 10 Prediction results after including meteorological data

Type Road Methods Meteorological features MAD MAPE MAPE decrease (no-yes)

Temporary

B-E RF No 690119864 minus 04 207119864 + 01 630Yes 456119864 minus 04 144119864 + 01

E-H SVM No 341119864 minus 04 169119864 + 01 728Yes 332119864 minus 04 957119864 + 00

H-J RF No 416119864 minus 04 186119864 + 01 380Yes 354119864 minus 04 148119864 + 01

Fixed

B-D SVM No 635119864 minus 04 122119864 + 01 408Yes 544119864 minus 04 809119864 + 00

E-F RF No 660119864 minus 04 217119864 + 01 350Yes 563119864 minus 04 182119864 + 01

G-H SVM No 842119864 minus 04 252119864 + 01 580Yes 735119864 minus 04 194119864 + 01

Average 513

where cov(119883 119884) is the covariance 120590119883 is the standard devia-tion of119883 and 120590119884 is the standard deviation of 119884

The PPC values of different variables are shown inFigure 7 including the 5 meteorological variables and trucktravel time A high PCC value indicates a closer relationshipbetween the two variables

Following controlled experiments the effect of meteo-rological features was investigated by adding or removingindividual features We selected the optimal ML model for

each link road The raw (observation) values and predictedresults withwithout meteorological features are shown inFigure 8

The results of the controlled experiments are shownin Table 10 the calculated decrease in the MAPE is alsoshown The results considering meteorological features arebetter than those withoutmeteorological featuresTheMAPEdecreased by 513 on average for all link roads after addingthe meteorological data

10 Mathematical Problems in Engineering

Pressure08

Wind speed04

Temperature

00

Relative humidity

Precipitation

Travel time

minus04

minus08

Pres

sure

Win

d sp

eed

Tem

pera

ture

Relat

ive h

umid

ity

Prec

ipita

tion

Trav

el tim

e

1

1

1

1

1

1

minus048 minus048

minus048

minus048

064

064

minus0041 minus0019

minus0019

005

005

minus0088

minus0088

minus082

minus082

047

012

012

047 minus064 014

014

0049

0049

minus0041

minus0054

minus0054

0045

0045

minus064

Figure 7 The PCC heat map of meteorological features

Table 11 Evaluation of LTTP based on different ML models

Link road Road type Evaluation kNN SVM RF

A-B Fixed MAD 495119864 minus 04 328119864 minus 04 299E minus 04MAPE 469119864 + 01 340119864 + 01 336E + 01

34 Discussion of LTTP and RTTP The above experimentsused the link rather than the route to predict the travel timeof OPTs However the differences between LTTP and RTTPneed to be further discussed In the ensuing discussion thelongest route between dump point A and load point G isselected as shown in Figure 9

The A-G route consists of 4 links A-B B-E E-H and H-G Among them the optimal ML prediction models of B-EE-H andH-G are SVM RF and SVM respectivelyThe sameexperimental procedure as used in Section 31 was used toobtain the optimal MLmodel for A-B and Table 11 shows theMAD and MAPE values of the three ML methods It can beseen that the RF model is the best ML method for link A-B

The SVM and RF methods are used to predict the RTTPof A-G because those two models have a good predictionperformance Thus the experiments are summarized asfollows

(i) RTTP (SVM) using the SVM algorithm to train theTTP model for the route A-G

(ii) RTTP (RF) using the RF algorithm to train the TTPmodel for the route A-G

(iii) LTTP using the optimalMLmodel for each link thatis A-B (RF) B-E (SVM) E-H (RF) and H-G (SVM)and the truck travel time of A-G is the sum of eachLTTP result

Raw values and predicted results of the above threeexperiments are shown in Figure 10 while the evaluated

Table 12 Evaluation of the results between LTTP and RTTP

Method Model Evaluation Values

RTTP SVM MAD 155119864 minus 03MAPE 208119864 + 01

RTTP RF MAD 178119864 minus 03MAPE 235119864 + 01

LTTP Assemble MAD 834E minus 04MAPE 898E + 00

results of those experiments are shown in Table 12 Both theMAD and MAPE values of the LTTP approach are smallerthan the two RTTP methods Thus using the link as theprediction unit is better than using the route

4 Conclusions

The link roads of an open-pit mine are divided into fixedand temporary roads in this paper Three ML algorithmsthat is kNN SVM and RF are used for the LTTP of OPTsThe experimental results not only reflect the self-adaptive andself-feedback characteristics of the ML algorithms but alsodemonstrate the practicality of themethod for road segmentsThe conclusions based on the results are as follows

(1) LTTP models based on ML are more efficient andaccurate than traditional averaging methods Anoverall average increase of 1579 in the predictionaccuracy is obtained for six experimental link roads

Mathematical Problems in Engineering 11

000100000200000300000400000500000600000700000800000900001000001100001200

Link

trav

el tim

e

0 10 15 20 25 30 35 40 45 505G-H (SVM)

000100

000200

000300

000400

000500

000600

000700

000800

Link

trav

el tim

e

0 10 15 20 25 30 35 40 45 505H-J (RF)

000200000300000400000500000600000700000800000900001000001100001200

Link

trav

el tim

e

0 5 15 20 25 30 35 40 45 5010E-H (SVM)

000100

000200

000300

000400

000500

000600

000700

000800

Link

trav

el tim

e

0 5 15 20 25 30 35 40 45 5010E-F (RF)

000400000500000600000700000800000900001000001100001200001300001400001500001600001700001800001900002000002100002200

Link

trav

el tim

e

0 5 15 20 25 30 35 40 45 5010B-D (SVM)

000200

000300

000400

000500

000600

000700

000800

000900

001000

Link

trav

el tim

e

0 10 15 20 25 30 35 40 45 505B-E (RF)

Raw valueWithout meteorological featuresMeteorological features

Raw valueWithout meteorological featuresMeteorological features

Figure 8 Comparison forecast results including and excluding meteorological features

For temporary roads the average accuracy increasesby 1930

(2) LTTP models established using the SVM and RFalgorithms are better than those established using thekNN approach There is no large difference betweenthe SVM and RF results although the RF algorithmrequires less space and time complexity than the SVMalgorithm

(3) This paper is original in that it considers the effectof meteorological features on LTTP The results show

that considering the effect of meteorological featureson LTTP increases the prediction accuracy by 513

(4) The differences between LTTP and RTTP are alsodiscussed and the former has a higher predictionaccuracy The MAPE decreases by 1182 for theLTTP method

Some work is already underway to incorporate the MLprediction models into the OPATDS of the FWOM whichwill be helpful in improving the dispatching efficiency of theOPTs

12 Mathematical Problems in Engineering

Node J

Load G

Node E

Load F

Dump ANode B

Load D

Load C

Node H

Fixed roadsTemporary roads

Figure 9 The location of the route A-G in the FWOM roadmap

Raw valuesRTTP (RF)

RTTP (SVM)LTTP

5 10 15 20 25 30 35 40 45 500Route A-G

000600000800001000001200001400001600001800002000002200

Truc

k tr

avel

tim

e

Figure 10 Prediction results for RTTP (RF) RTTP (SVM) andLTTP

Data Availability

The data used to support the findings of this study areavailable from the corresponding author upon request

Conflicts of Interest

The authors declare no conflicts of interest

Authorsrsquo Contributions

Xiaoyu Sun as the principal investigator provided the dataused to train the ML models Hang Zhang performed theexperiments andwrote the paper Fengliang Tian contributedthe programming Lei Yang proofread the manuscript

Acknowledgments

This work was funded by the National Natural ScienceFoundation of China (no 51674063) and the NationalKey Research and Development Program of China (no2016YFC0801608)

References

[1] J Czaplicki Shovel-Truck Systems CRC Press 2008[2] J M Czaplicki ldquoModelling and analysis of the exploitation

process of a shovel-truck systemrdquo in Shovel-Truck Systems pp79ndash89 CRC Press 2008

[3] S G Ercelebi and A Bascetin ldquoOptimization of shovel-trucksystem for surface miningrdquo Journal of the Southern AfricanInstitute of Mining and Metallurgy vol 109 no 7 pp 433ndash4392009

[4] R Mena E Zio F Kristjanpoller and A Arata ldquoAvailability-based simulation and optimization modeling framework foropen-pit mine truck allocation under dynamic constraintsrdquoInternational Journal of Mining Science and Technology vol 23no 1 pp 113ndash119 2013

[5] F Soumis J Ethier and J Elbrond ldquoTruck dispatching inan open pit minerdquo International Journal of Surface MiningReclamation and Environment vol 3 no 2 pp 115ndash119 1989

[6] A Y F Fadin Komarudin and A O Moeis ldquoSimulation-optimization truck dispatch problem using look - ahead algo-rithm in open pit minesrdquo International Journal of GEOMATEvol 13 no 36 pp 80ndash86 2017

[7] Y Tan and S Takakuwa ldquoA practical simulation approachfor an effective truck dispatching system of open pit minesusing VBArdquo in Proceedings of the 2016 Winter SimulationConference WSC 2016 pp 2394ndash2405 IEEE Washington DCUSA December 2016

[8] J Li R Bai J Mao and W Li ldquoForecast of applied effect fortruck real-time dispatch system in open-pit mine based onCSUSSrdquo in Proceedings of the 2010 International Conference onE-Product E-Service and E-Entertainment ICEEE2010 pp 1ndash4IEEE Henan China November 2010

[9] S P Alarie and M Gamache ldquoOverview of solution strategiesused in truck dispatching systems for open pit minesrdquo Interna-tional Journal of Surface Mining Reclamation and Environmentvol 16 no 1 pp 59ndash76 2002

[10] B Kolonja D R Kalasky and J M Mutmansky ldquoOptimizationof dispatching criteria for open-pit truck haulage system designusingmultiple comparisons with the best and common random

Mathematical Problems in Engineering 13

numbersrdquo in Proceedings of the 25th Conference on Winter Sim-ulation WSC 1993 pp 393ndash401 ACM Los Angeles CaliforniaUSA December 1993

[11] Q Wang Y Zhang C Chen and W Xu ldquoOpen-pit mine truckreal-time dispatching principle under macroscopic controlrdquo inProceedings of the 1st International Conference on InnovativeComputing Information and Control 2006 ICICICrsquo06 pp 702ndash705 IEEE Beijing China September 2006

[12] Y Choi ldquoSimulation of Shovel-Truck Haulage Systems byConsidering Truck Dispatch Methodsrdquo Journal of the KoreanSociety of Mineral and Energy Resources Engineers vol 50 no4 p 543 2013

[13] E Topal and S Ramazan ldquoMining truck scheduling withstochastic maintenance costrdquo Journal of Coal Science andEngineering vol 18 no 3 pp 313ndash319 2012

[14] P Chaowasakoo H Seppala H Koivo and Q Zhou ldquoDigi-talization of mine operations Scenarios to benefit in real-timetruck dispatchingrdquo International Journal of Mining Science andTechnology vol 27 no 2 pp 229ndash236 2017

[15] Q Sun ldquoRoad running time statistics method in truck schedul-ingrdquo Opencast Coal Mining Technology vol 01 pp 35ndash37 1998

[16] R Bai J Li and J Xu ldquoReal-time dynamic forecast of truck linktravel timerdquo Journal of Liaoning Technical University vol 1 pp12ndash14 2005

[17] L Jiangang ldquoReal-time dynamic forecasts of truck link traveltime based on fuzzy neural networkrdquo Journal of the China CoalSociety vol 6 pp 796ndash800 2005

[18] E K Chanda and S Gardiner ldquoA comparative study of truckcycle time prediction methods in open-pit miningrdquo Engineer-ing Construction and Architectural Management vol 17 no 5pp 446ndash460 2010

[19] D J Edwards and I J Griffiths ldquoArtificial intelligence approachto calculation of hydraulic excavator cycle time and outputrdquoMining Technology vol 109 no 1 pp 23ndash29 2013

[20] K Erarslan ldquoModelling performance and retarder chart of off-highway trucks by cubic splines for cycle time estimationrdquoMining Technology vol 114 pp 161ndash166 2013

[21] X Xue W Sun and R Liang ldquoA new method of real-timedynamic forecast of truck link travel time in open minesrdquoJournal of the China Coal Society vol 37 no 8 pp 1418ndash14222012

[22] X Meng Research on scheduling services of open-pit mine basedon real-time travel time prediction China University of Miningand Technology 2014

[23] V Shalamanov V Pershin S Shabaev and D Boiko ldquoJustifi-cation of the Optimal Granulometric Composition of CrushedRocks for Open-Pit Mine Road Surfacingrdquo in Proceedings of the1st International InnovativeMining Symposium 2017 KemerovoRussia April 2017

[24] M Hofmann and M OrsquoMahony ldquoThe impact of adverseweather conditions on urban bus performance measuresrdquoin Proceedings of the 8th International IEEE Conference onIntelligent Transportation Systems pp 431ndash436 IEEE ViennaAustria September 2005

[25] T H Maze M Agarwal and G Burchett ldquoWhether weathermatters to traffic demand traffic safety and traffic operationsand flowrdquoTransportation Research Record no 1948 pp 170ndash1762006

[26] S A Silvester I S Lowndes and D M Hargreaves ldquoAcomputational study of particulate emissions from an openpit quarry under neutral atmospheric conditionsrdquo AtmosphericEnvironment vol 43 no 40 pp 6415ndash6424 2009

[27] I Tsapakis T Cheng and A Bolbol ldquoImpact of weather condi-tions on macroscopic urban travel timesrdquo Journal of TransportGeography vol 28 pp 204ndash211 2013

[28] TheMinistry of Land and Resources ldquoPRCThe basic situationof mineral resources in fushunrdquo httpwwwmlrgovcnkczyglkczydjtj201208t20120813 1130832htm

[29] G F Cooper and E Herskovits ldquoA Bayesian method forthe induction of probabilistic networks from datardquo MachineLearning vol 9 no 4 pp 309ndash347 1992

[30] C Yunqiang Z X Sean and T S Huang ldquoOne-class svm forlearning in image retrievalrdquo in In Proceedings 2001 InternationalConference on Image Processing (Cat No01CH37205) pp 34ndash372001

[31] T K Ho ldquoIn Random decision forestsrdquo in Proceedings of 3rdInternational Conference on Document Analysis and Recogni-tion IEEE 1995

[32] D G Kleinbaum and M Klein ldquoAnalysis of Matched DataUsing Logistic Regressionrdquo in Logistic Regression pp 389ndash428Springer New York NY USA 2010

[33] N S Altman ldquoAn introduction to kernel and nearest-neighbornonparametric regressionrdquo The American Statistician vol 46no 3 pp 175ndash185 1992

[34] S R Eddy ldquoProfile hiddenMarkovmodelsrdquo Bioinformatics vol14 no 9 pp 755ndash763 1998

[35] J R Koza F H Bennett D Andre and M A Keane ldquoAuto-mated design of both the topology and sizing of analog electricalcircuits using genetic programmingrdquo in In Artificial intelligencein design rsquo96 pp 151ndash170 Springer Netherlands 1996

[36] T Oladipupo ldquoIntroduction to machine learningrdquo in In Newadvances in machine learning InTech 2010

[37] H Mannila ldquoData mining machine learning statistics anddatabasesrdquo in Proceedings of the 8th International Conferenceon Scientific and Statistical Data Base Management IEEEStockholm Sweden Sweden 2002

[38] M Troc and O Unold ldquoSelf-adaptation of parameters in alearning classifier system ensemble machinerdquo InternationalJournal of Applied Mathematics and Computer Science vol 20no 1 pp 157ndash174 2010

[39] T Hastie R Tibshirani and J Friedman The Elements ofStatistical Learning Springer-Verlag New York NY USA 2009

[40] N J Nilsson ldquoArtificial intelligence A modern approachrdquoArtificial Intelligence vol 82 no 1-2 pp 369ndash380 1996

[41] I Kavakiotis O Tsave A Salifoglou N Maglaveras I Vla-havas and I Chouvarda ldquoMachine Learning and Data MiningMethods in Diabetes Researchrdquo Computational and StructuralBiotechnology Journal vol 15 pp 104ndash116 2017

[42] M Mohri A Rostamizadeh and A Talwalkar Foundations ofmachine learning MIT press 2012

[43] Y Freund and R E Schapire ldquoA decision-theoretic generaliza-tion of on-line learning and an application to boostingrdquo Journalof Computer and System Sciences vol 55 no 1 part 2 pp 119ndash139 1997

[44] R S Michalski J G Carbonell and T M Mitchell ldquoMachinelearning 1983rdquo

[45] O Kramer ldquoK-nearest neighborsrdquo in Dimensionality reductionwith unsupervised nearest neighbors vol 51 pp 13ndash23 SpringerBerlin Heidelberg Germany 2013

[46] C Cortes and V Vapnik ldquoSupport-vector networksrdquo MachineLearning vol 20 no 3 pp 273ndash297 1995

Mathematical Problems in Engineering 5

Table 3 Preprocessed data for training the ML prediction models

Date Start time Arrival time Truck Id Truck type2017-03-01 162320 162657 202 BELAZ-L2017-03-02 201209 201812 503 MT-86Truck status 119909-axis start 119910-axis start 119909-axis arrival 119910-axis arrivalRun 1344 1188 2191 968Run 2576 783 3095 327

Load status Start node Arrival node Pressure(100 Pa)

Wind speed(ms)

Empty B E 1002 1Coal G H 999 06Temperature(∘C)

Relative humidity()

Precipitation(mm) Rain Travel time

(hourminsec)2 90 0 No 0003371 96 0 No 000603

Table 4 Description of the variables used in the prediction

Variables Type Role DescriptionTruck Id Numeric Feature The serial number of truckTruck type Categorical Feature The type of the truck (ie BELAZ-L BELAZ-M and MT86)Truck status Categorical Feature The status of the truck (ie running waiting and stop)119909-axis start Numeric Feature The 119909 coordinate of the truck at the starting position119910-axis start Numeric Feature The 119910 coordinate of the truck at the starting position119909-axis arrival Numeric Feature The 119909 coordinate of the truck at the ending position119910-axis arrival Numeric Feature The 119910 coordinate of the truck at the ending positionLoad status Categorical Feature The load status of the truck (ie empty and coal)Start node Categorical Feature The node code of the starting position of the roadArrival node Categorical Feature The node code of the ending position of the roadPressure Numeric Feature A fundamental atmospheric quantityWind speed Numeric Feature A fundamental atmospheric quantityTemperature Numeric Feature A fundamental atmospheric quantityRelative humidity Numeric Feature A fundamental atmospheric quantityPrecipitation Numeric Feature A fundamental atmospheric quantityRain Categorical Feature A fundamental atmospheric quantity (ie yes and no)Travel time Date time Target The travel time of the truck on each link

The data used in the following experiments originatefrom the FWOM The truck and road feature data are fromthe OPATDS while the weather data are collected fromthe China Meteorological Administration (CMA) Number54351 monitoring station The preprocessed training datasetsamples in this experiment are listed in Table 3 There are 16variables serving as the features and the target is the trucktravel time Table 4 shows the description of the target andeach feature used for the prediction in this study

24 Program and Pseudocode This study used sophisticatedalgorithms to predict the link travel time in open-pit minesand the three ML algorithms in the prediction models werebased on scikit-learn which is an open-sourceMLmodule in

the Python programming language [52 53] The pseudocodeof the methodology in this study is illustrated in Figure 4

3 Results and Discussion

31 Predictions of the ML Models For the training datasets2246746 historical records from March 2017 were exportedfrom the OPATDS database of the FWOM After datapreprocessing the structure of the training datawas similar tothose in Table 3 The experimental parameters encompassedone type of link road trained by three differentML algorithms(kNN SVM and RF) resulting in 18 LTTP models Theprediction results for the last 50 records of the test datasetsare shown in Figure 5

6 Mathematical Problems in Engineering

Figure 4 The pseudocode of the ML methodology

To derive the best LTTP model for each link road theaforementioned prediction results were evaluated based onthe mean absolute deviation (MAD) and the mean absolutepercentage error (MAPE) methods which are commonlyused for regression problem evaluation

The MAD as expressed in (3a) is a summary statistic ofstatistical dispersion or variability [54 55] The MAPE is ameasure of the accuracy of a prediction method in statisticsas written in (3b) [56] Because the MAPE is a percentageit is often easier to understand than the other statistics Forexample if the MAPE is 5 on average the forecast is off by5 [57]

MAD = sum119899119894=1 1003816100381610038161003816119909obs119894 minus 119909model1198941003816100381610038161003816119899 (3a)

MAPE = sum119899119894=1 1003816100381610038161003816(119909obs119894 minus 119909model119894) 119909obs1198941003816100381610038161003816119899 times 100 () (3b)

where 119909obs119894 represents the observation values 119909model119894 rep-resents the prediction values and 119899 is the number of datarecords

Table 5 lists the MAD and MAPE values obtained fromthe three ML methods for each experimental link road

Smaller MAD and MAPE values reflect better predictionperformance of each LTTP model and the smallest recordsare highlighted in Table 5 The results of the six experimentallink roads indicate that the LTTP models built using theSVM and RF methods are better than those using the kNNalgorithm Table 6 summarizes the optimal ML predictionmodels for each link road

The coefficient of determination 1198772 is widely used instatistical tests to evaluate the predictive capability of amodel and is also used in this study The 1198772 value with oneindependent variable is written as follows [58]

1198772 = [ 1119873 lowastsum (119909119894 minus 119909) lowast (119910119894 minus 119910)(120590119909 lowast 120590119910) ]

2

(4)

Mathematical Problems in Engineering 7

Raw valueKNN

SVMRF

000100000200000300000400000500000600000700000800000900001000001100001200

Link

trav

el tim

e

0 5 15 20 25 30 35 40 45 5010G-H

000100

000200

000300

000400

000500

000600

000700

000800

Link

trav

el tim

e

0 5 15 20 25 30 35 40 45 5010H-J

000200000300000400000500000600000700000800000900001000001100001200

Link

trav

el tim

e

0 5 15 20 25 30 35 40 45 5010E-H

000100000200000300000400000500000600000700000800000900001000001100

Link

trav

el tim

e

0 5 15 20 25 30 35 40 45 5010E-F

0 5 15 20 25 30 35 40 45 5010B-E

000200

000300

000400

000500

000600

000700

000800

000900

001000

Link

trav

el tim

e

000400000500000600000700000800000900001000001100001200001300001400001500001600001700001800001900002000002100002200

Link

trav

el tim

e

0 5 15 20 25 30 35 40 45 5010B-D

Raw valueKNN

SVMRF

Figure 5 Prediction results for the different ML methods

where119873 is the number of observations used to fit the model119909 and 119910 are themean values of 119909 and 119910 respectively 119909119894 and 119910119894are the values of observation 119894 and 120590119909 and 120590119910 are the standarddeviations of 119909 and 119910 respectively

Table 7 shows the 1198772 values of the three ML models foreach link road The 1198772 values range from 0 to 1 and 1198772 equalto 1 indicates perfect accurate prediction There are somedifferences between Tables 6 and 7 that is the optimal MLmodel of B-E H-J and G-H However the MAPE was stillselected for choosing the optimal model because the 1198772 valuecannot be used to evaluate predictive errors

32 Discussion of Traditional Averaging Methods and MLModels To compare the LTTP of MLmodels and traditionalaveraging methods controlled experiments were performedThe flow chart of traditional averaging methods is illustratedin Figure 6

For each record in the test dataset the experimentstraced back the corresponding top 10 20 30 40 and 50records and then calculated the average value as the finalprediction To improve the accuracy of the traditional aver-aging methods each calculation used only historical data forthe same truck type and load status The results obtained

8 Mathematical Problems in Engineering

Table 5 LTTP evaluation based on the different ML models

Link road Road type Evaluation kNN SVM RF

B-E

Fixed

MAD 591119864 minus 04 509119864 minus 04 456E minus 04MAPE 178119864 + 01 158119864 + 01 144E + 01

E-H MAD 944119864 minus 04 332E minus 04 637119864 minus 04MAPE 249119864 + 01 957E + 00 181119864 + 01

H-J MAD 516119864 minus 04 355119864 minus 04 354E minus 04MAPE 214119864 + 01 159119864 + 01 148E + 01

B-D

Temporary

MAD 171119864 minus 03 544E minus 04 670119864 minus 04MAPE 275119864 + 01 809E + 00 990119864 + 00

E-F MAD 959119864 minus 04 805119864 minus 04 563E minus 04MAPE 313119864 + 01 294119864 + 01 182E + 01

G-H MAD 118119864 minus 03 735E minus 04 785119864 minus 04MAPE 342119864 + 01 194E + 01 238119864 + 01

4

Rece

nt h

istor

ical

dat

a

2

Data predicted

Calculatingthe average time

(i) Same link road (ii) Same load status(iii) Same truck type

3001357

001421

001409BELAZB-E

001357

Empty

Empty

BELAZB-E

001821LoadB-E MT-86

001421EmptyB-E BELAZ

001715B-E EmptyMT-86

1

Figure 6 The flow chart of traditional averaging methods

Table 6 Summary of the optimal ML prediction models for eachlink road

Road Type Optimal ML modelB-E

FixedRF

E-H SVMH-J RFB-D

TemporarySVM

E-F RFG-H SVM

Table 7 1198772 values of the different ML models for each link road

Road SVM KNN RF Optimal ML modelB-E 028 016 041 SVME-H 083 016 067 SVMH-J 072 013 056 SVMB-D 089 023 07 SVME-F 054 024 073 RFG-H 061 019 062 RF

from the traditional averaging methods are summarized inTable 8

Smaller MAD and MAPE values mean better predictionperformance of the traditional averaging methods and the

smallest records are highlighted in Table 8The predicted val-ues obtained from the optimal ML method and a traditionalaverage method for each link road are given in Table 9 thedecrease in the MAPE is also shown

Table 9 shows that the tested ML models are superiorto the traditional averaging method in the context of LTTPbecause the former has smaller MAPEs An average increaseof 1579 in prediction accuracy is achieved in all experimen-tal link roads in which increases of 1254 and 1930 forthree fixed and three temporary roads respectively are alsoobtained

33 Discussion of Meteorological Features This study alsoconsidered the influence of meteorological features on theLTTP of an open-pit mine The data were obtained froma CMA monitoring station including 5 variables pressurewind speed temperature relative humidity and precipita-tion

The Pearson correlation coefficient (PCC) an evaluationmethod developed by Pearson [59] was used to evaluate thelinear correlation between two variables The expression ofthe PPC is as follows

120588119883119884 = cov (119883 119884)120590119883120590119884 (5)

Mathematical Problems in Engineering 9

Table 8 Results obtained from the traditional averaging methods

Road Evaluation Traditional averaging methods10 records 20 records 30 records 40 records 50 records

B-E MAD 102119864 minus 03 949119864 minus 04 917119864 minus 04 918119864 minus 04 904E minus 04MAPE 306119864 + 01 281119864 + 01 266119864 + 01 264119864 + 01 258E + 01

E-H MAD 122119864 minus 03 113119864 minus 03 109119864 minus 03 109119864 minus 03 107E minus 03MAPE 329119864 + 01 300119864 + 01 284119864 + 01 281119864 + 01 273E + 01

H-J MAD 629119864 minus 04 609119864 minus 04 587119864 minus 04 581119864 minus 04 580E minus 04MAPE 254119864 + 01 247119864 + 01 236119864 + 01 234119864 + 01 233E + 01

B-D MAD 215119864 minus 03 183E minus 03 246119864 minus 03 236119864 minus 03 205119864 minus 03MAPE 317119864 + 01 269E + 01 386119864 + 01 362119864 + 01 325119864 + 01

E-F MAD 116119864 minus 03 110E minus 03 114119864 minus 03 115119864 minus 03 116119864 minus 03MAPE 391119864 + 01 363E + 01 381119864 + 01 390119864 + 01 395119864 + 01

G-H MAD 129E minus 03 138119864 minus 03 136119864 minus 03 132119864 minus 03 130119864 minus 03MAPE 404E + 01 412119864 + 01 391119864 + 01 370119864 + 01 357119864 + 01

Table 9 Comparison between the optimal ML model and the optimal averaging method

Road Type Optimal average method (MAPE) Optimal ML model (MAPE) MAPE decrease AverageB-E

Fixed258119864 + 01 144119864 + 01 1140

1254E-H 273119864 + 01 957119864 + 00 1773H-J 233119864 + 01 148119864 + 01 850B-D

Temporary269119864 + 01 809119864 + 00 1881

1930E-F 363119864 + 01 182119864 + 01 1810G-H 404119864 + 01 194119864 + 01 2100Average 1579

Table 10 Prediction results after including meteorological data

Type Road Methods Meteorological features MAD MAPE MAPE decrease (no-yes)

Temporary

B-E RF No 690119864 minus 04 207119864 + 01 630Yes 456119864 minus 04 144119864 + 01

E-H SVM No 341119864 minus 04 169119864 + 01 728Yes 332119864 minus 04 957119864 + 00

H-J RF No 416119864 minus 04 186119864 + 01 380Yes 354119864 minus 04 148119864 + 01

Fixed

B-D SVM No 635119864 minus 04 122119864 + 01 408Yes 544119864 minus 04 809119864 + 00

E-F RF No 660119864 minus 04 217119864 + 01 350Yes 563119864 minus 04 182119864 + 01

G-H SVM No 842119864 minus 04 252119864 + 01 580Yes 735119864 minus 04 194119864 + 01

Average 513

where cov(119883 119884) is the covariance 120590119883 is the standard devia-tion of119883 and 120590119884 is the standard deviation of 119884

The PPC values of different variables are shown inFigure 7 including the 5 meteorological variables and trucktravel time A high PCC value indicates a closer relationshipbetween the two variables

Following controlled experiments the effect of meteo-rological features was investigated by adding or removingindividual features We selected the optimal ML model for

each link road The raw (observation) values and predictedresults withwithout meteorological features are shown inFigure 8

The results of the controlled experiments are shownin Table 10 the calculated decrease in the MAPE is alsoshown The results considering meteorological features arebetter than those withoutmeteorological featuresTheMAPEdecreased by 513 on average for all link roads after addingthe meteorological data

10 Mathematical Problems in Engineering

Pressure08

Wind speed04

Temperature

00

Relative humidity

Precipitation

Travel time

minus04

minus08

Pres

sure

Win

d sp

eed

Tem

pera

ture

Relat

ive h

umid

ity

Prec

ipita

tion

Trav

el tim

e

1

1

1

1

1

1

minus048 minus048

minus048

minus048

064

064

minus0041 minus0019

minus0019

005

005

minus0088

minus0088

minus082

minus082

047

012

012

047 minus064 014

014

0049

0049

minus0041

minus0054

minus0054

0045

0045

minus064

Figure 7 The PCC heat map of meteorological features

Table 11 Evaluation of LTTP based on different ML models

Link road Road type Evaluation kNN SVM RF

A-B Fixed MAD 495119864 minus 04 328119864 minus 04 299E minus 04MAPE 469119864 + 01 340119864 + 01 336E + 01

34 Discussion of LTTP and RTTP The above experimentsused the link rather than the route to predict the travel timeof OPTs However the differences between LTTP and RTTPneed to be further discussed In the ensuing discussion thelongest route between dump point A and load point G isselected as shown in Figure 9

The A-G route consists of 4 links A-B B-E E-H and H-G Among them the optimal ML prediction models of B-EE-H andH-G are SVM RF and SVM respectivelyThe sameexperimental procedure as used in Section 31 was used toobtain the optimal MLmodel for A-B and Table 11 shows theMAD and MAPE values of the three ML methods It can beseen that the RF model is the best ML method for link A-B

The SVM and RF methods are used to predict the RTTPof A-G because those two models have a good predictionperformance Thus the experiments are summarized asfollows

(i) RTTP (SVM) using the SVM algorithm to train theTTP model for the route A-G

(ii) RTTP (RF) using the RF algorithm to train the TTPmodel for the route A-G

(iii) LTTP using the optimalMLmodel for each link thatis A-B (RF) B-E (SVM) E-H (RF) and H-G (SVM)and the truck travel time of A-G is the sum of eachLTTP result

Raw values and predicted results of the above threeexperiments are shown in Figure 10 while the evaluated

Table 12 Evaluation of the results between LTTP and RTTP

Method Model Evaluation Values

RTTP SVM MAD 155119864 minus 03MAPE 208119864 + 01

RTTP RF MAD 178119864 minus 03MAPE 235119864 + 01

LTTP Assemble MAD 834E minus 04MAPE 898E + 00

results of those experiments are shown in Table 12 Both theMAD and MAPE values of the LTTP approach are smallerthan the two RTTP methods Thus using the link as theprediction unit is better than using the route

4 Conclusions

The link roads of an open-pit mine are divided into fixedand temporary roads in this paper Three ML algorithmsthat is kNN SVM and RF are used for the LTTP of OPTsThe experimental results not only reflect the self-adaptive andself-feedback characteristics of the ML algorithms but alsodemonstrate the practicality of themethod for road segmentsThe conclusions based on the results are as follows

(1) LTTP models based on ML are more efficient andaccurate than traditional averaging methods Anoverall average increase of 1579 in the predictionaccuracy is obtained for six experimental link roads

Mathematical Problems in Engineering 11

000100000200000300000400000500000600000700000800000900001000001100001200

Link

trav

el tim

e

0 10 15 20 25 30 35 40 45 505G-H (SVM)

000100

000200

000300

000400

000500

000600

000700

000800

Link

trav

el tim

e

0 10 15 20 25 30 35 40 45 505H-J (RF)

000200000300000400000500000600000700000800000900001000001100001200

Link

trav

el tim

e

0 5 15 20 25 30 35 40 45 5010E-H (SVM)

000100

000200

000300

000400

000500

000600

000700

000800

Link

trav

el tim

e

0 5 15 20 25 30 35 40 45 5010E-F (RF)

000400000500000600000700000800000900001000001100001200001300001400001500001600001700001800001900002000002100002200

Link

trav

el tim

e

0 5 15 20 25 30 35 40 45 5010B-D (SVM)

000200

000300

000400

000500

000600

000700

000800

000900

001000

Link

trav

el tim

e

0 10 15 20 25 30 35 40 45 505B-E (RF)

Raw valueWithout meteorological featuresMeteorological features

Raw valueWithout meteorological featuresMeteorological features

Figure 8 Comparison forecast results including and excluding meteorological features

For temporary roads the average accuracy increasesby 1930

(2) LTTP models established using the SVM and RFalgorithms are better than those established using thekNN approach There is no large difference betweenthe SVM and RF results although the RF algorithmrequires less space and time complexity than the SVMalgorithm

(3) This paper is original in that it considers the effectof meteorological features on LTTP The results show

that considering the effect of meteorological featureson LTTP increases the prediction accuracy by 513

(4) The differences between LTTP and RTTP are alsodiscussed and the former has a higher predictionaccuracy The MAPE decreases by 1182 for theLTTP method

Some work is already underway to incorporate the MLprediction models into the OPATDS of the FWOM whichwill be helpful in improving the dispatching efficiency of theOPTs

12 Mathematical Problems in Engineering

Node J

Load G

Node E

Load F

Dump ANode B

Load D

Load C

Node H

Fixed roadsTemporary roads

Figure 9 The location of the route A-G in the FWOM roadmap

Raw valuesRTTP (RF)

RTTP (SVM)LTTP

5 10 15 20 25 30 35 40 45 500Route A-G

000600000800001000001200001400001600001800002000002200

Truc

k tr

avel

tim

e

Figure 10 Prediction results for RTTP (RF) RTTP (SVM) andLTTP

Data Availability

The data used to support the findings of this study areavailable from the corresponding author upon request

Conflicts of Interest

The authors declare no conflicts of interest

Authorsrsquo Contributions

Xiaoyu Sun as the principal investigator provided the dataused to train the ML models Hang Zhang performed theexperiments andwrote the paper Fengliang Tian contributedthe programming Lei Yang proofread the manuscript

Acknowledgments

This work was funded by the National Natural ScienceFoundation of China (no 51674063) and the NationalKey Research and Development Program of China (no2016YFC0801608)

References

[1] J Czaplicki Shovel-Truck Systems CRC Press 2008[2] J M Czaplicki ldquoModelling and analysis of the exploitation

process of a shovel-truck systemrdquo in Shovel-Truck Systems pp79ndash89 CRC Press 2008

[3] S G Ercelebi and A Bascetin ldquoOptimization of shovel-trucksystem for surface miningrdquo Journal of the Southern AfricanInstitute of Mining and Metallurgy vol 109 no 7 pp 433ndash4392009

[4] R Mena E Zio F Kristjanpoller and A Arata ldquoAvailability-based simulation and optimization modeling framework foropen-pit mine truck allocation under dynamic constraintsrdquoInternational Journal of Mining Science and Technology vol 23no 1 pp 113ndash119 2013

[5] F Soumis J Ethier and J Elbrond ldquoTruck dispatching inan open pit minerdquo International Journal of Surface MiningReclamation and Environment vol 3 no 2 pp 115ndash119 1989

[6] A Y F Fadin Komarudin and A O Moeis ldquoSimulation-optimization truck dispatch problem using look - ahead algo-rithm in open pit minesrdquo International Journal of GEOMATEvol 13 no 36 pp 80ndash86 2017

[7] Y Tan and S Takakuwa ldquoA practical simulation approachfor an effective truck dispatching system of open pit minesusing VBArdquo in Proceedings of the 2016 Winter SimulationConference WSC 2016 pp 2394ndash2405 IEEE Washington DCUSA December 2016

[8] J Li R Bai J Mao and W Li ldquoForecast of applied effect fortruck real-time dispatch system in open-pit mine based onCSUSSrdquo in Proceedings of the 2010 International Conference onE-Product E-Service and E-Entertainment ICEEE2010 pp 1ndash4IEEE Henan China November 2010

[9] S P Alarie and M Gamache ldquoOverview of solution strategiesused in truck dispatching systems for open pit minesrdquo Interna-tional Journal of Surface Mining Reclamation and Environmentvol 16 no 1 pp 59ndash76 2002

[10] B Kolonja D R Kalasky and J M Mutmansky ldquoOptimizationof dispatching criteria for open-pit truck haulage system designusingmultiple comparisons with the best and common random

Mathematical Problems in Engineering 13

numbersrdquo in Proceedings of the 25th Conference on Winter Sim-ulation WSC 1993 pp 393ndash401 ACM Los Angeles CaliforniaUSA December 1993

[11] Q Wang Y Zhang C Chen and W Xu ldquoOpen-pit mine truckreal-time dispatching principle under macroscopic controlrdquo inProceedings of the 1st International Conference on InnovativeComputing Information and Control 2006 ICICICrsquo06 pp 702ndash705 IEEE Beijing China September 2006

[12] Y Choi ldquoSimulation of Shovel-Truck Haulage Systems byConsidering Truck Dispatch Methodsrdquo Journal of the KoreanSociety of Mineral and Energy Resources Engineers vol 50 no4 p 543 2013

[13] E Topal and S Ramazan ldquoMining truck scheduling withstochastic maintenance costrdquo Journal of Coal Science andEngineering vol 18 no 3 pp 313ndash319 2012

[14] P Chaowasakoo H Seppala H Koivo and Q Zhou ldquoDigi-talization of mine operations Scenarios to benefit in real-timetruck dispatchingrdquo International Journal of Mining Science andTechnology vol 27 no 2 pp 229ndash236 2017

[15] Q Sun ldquoRoad running time statistics method in truck schedul-ingrdquo Opencast Coal Mining Technology vol 01 pp 35ndash37 1998

[16] R Bai J Li and J Xu ldquoReal-time dynamic forecast of truck linktravel timerdquo Journal of Liaoning Technical University vol 1 pp12ndash14 2005

[17] L Jiangang ldquoReal-time dynamic forecasts of truck link traveltime based on fuzzy neural networkrdquo Journal of the China CoalSociety vol 6 pp 796ndash800 2005

[18] E K Chanda and S Gardiner ldquoA comparative study of truckcycle time prediction methods in open-pit miningrdquo Engineer-ing Construction and Architectural Management vol 17 no 5pp 446ndash460 2010

[19] D J Edwards and I J Griffiths ldquoArtificial intelligence approachto calculation of hydraulic excavator cycle time and outputrdquoMining Technology vol 109 no 1 pp 23ndash29 2013

[20] K Erarslan ldquoModelling performance and retarder chart of off-highway trucks by cubic splines for cycle time estimationrdquoMining Technology vol 114 pp 161ndash166 2013

[21] X Xue W Sun and R Liang ldquoA new method of real-timedynamic forecast of truck link travel time in open minesrdquoJournal of the China Coal Society vol 37 no 8 pp 1418ndash14222012

[22] X Meng Research on scheduling services of open-pit mine basedon real-time travel time prediction China University of Miningand Technology 2014

[23] V Shalamanov V Pershin S Shabaev and D Boiko ldquoJustifi-cation of the Optimal Granulometric Composition of CrushedRocks for Open-Pit Mine Road Surfacingrdquo in Proceedings of the1st International InnovativeMining Symposium 2017 KemerovoRussia April 2017

[24] M Hofmann and M OrsquoMahony ldquoThe impact of adverseweather conditions on urban bus performance measuresrdquoin Proceedings of the 8th International IEEE Conference onIntelligent Transportation Systems pp 431ndash436 IEEE ViennaAustria September 2005

[25] T H Maze M Agarwal and G Burchett ldquoWhether weathermatters to traffic demand traffic safety and traffic operationsand flowrdquoTransportation Research Record no 1948 pp 170ndash1762006

[26] S A Silvester I S Lowndes and D M Hargreaves ldquoAcomputational study of particulate emissions from an openpit quarry under neutral atmospheric conditionsrdquo AtmosphericEnvironment vol 43 no 40 pp 6415ndash6424 2009

[27] I Tsapakis T Cheng and A Bolbol ldquoImpact of weather condi-tions on macroscopic urban travel timesrdquo Journal of TransportGeography vol 28 pp 204ndash211 2013

[28] TheMinistry of Land and Resources ldquoPRCThe basic situationof mineral resources in fushunrdquo httpwwwmlrgovcnkczyglkczydjtj201208t20120813 1130832htm

[29] G F Cooper and E Herskovits ldquoA Bayesian method forthe induction of probabilistic networks from datardquo MachineLearning vol 9 no 4 pp 309ndash347 1992

[30] C Yunqiang Z X Sean and T S Huang ldquoOne-class svm forlearning in image retrievalrdquo in In Proceedings 2001 InternationalConference on Image Processing (Cat No01CH37205) pp 34ndash372001

[31] T K Ho ldquoIn Random decision forestsrdquo in Proceedings of 3rdInternational Conference on Document Analysis and Recogni-tion IEEE 1995

[32] D G Kleinbaum and M Klein ldquoAnalysis of Matched DataUsing Logistic Regressionrdquo in Logistic Regression pp 389ndash428Springer New York NY USA 2010

[33] N S Altman ldquoAn introduction to kernel and nearest-neighbornonparametric regressionrdquo The American Statistician vol 46no 3 pp 175ndash185 1992

[34] S R Eddy ldquoProfile hiddenMarkovmodelsrdquo Bioinformatics vol14 no 9 pp 755ndash763 1998

[35] J R Koza F H Bennett D Andre and M A Keane ldquoAuto-mated design of both the topology and sizing of analog electricalcircuits using genetic programmingrdquo in In Artificial intelligencein design rsquo96 pp 151ndash170 Springer Netherlands 1996

[36] T Oladipupo ldquoIntroduction to machine learningrdquo in In Newadvances in machine learning InTech 2010

[37] H Mannila ldquoData mining machine learning statistics anddatabasesrdquo in Proceedings of the 8th International Conferenceon Scientific and Statistical Data Base Management IEEEStockholm Sweden Sweden 2002

[38] M Troc and O Unold ldquoSelf-adaptation of parameters in alearning classifier system ensemble machinerdquo InternationalJournal of Applied Mathematics and Computer Science vol 20no 1 pp 157ndash174 2010

[39] T Hastie R Tibshirani and J Friedman The Elements ofStatistical Learning Springer-Verlag New York NY USA 2009

[40] N J Nilsson ldquoArtificial intelligence A modern approachrdquoArtificial Intelligence vol 82 no 1-2 pp 369ndash380 1996

[41] I Kavakiotis O Tsave A Salifoglou N Maglaveras I Vla-havas and I Chouvarda ldquoMachine Learning and Data MiningMethods in Diabetes Researchrdquo Computational and StructuralBiotechnology Journal vol 15 pp 104ndash116 2017

[42] M Mohri A Rostamizadeh and A Talwalkar Foundations ofmachine learning MIT press 2012

[43] Y Freund and R E Schapire ldquoA decision-theoretic generaliza-tion of on-line learning and an application to boostingrdquo Journalof Computer and System Sciences vol 55 no 1 part 2 pp 119ndash139 1997

[44] R S Michalski J G Carbonell and T M Mitchell ldquoMachinelearning 1983rdquo

[45] O Kramer ldquoK-nearest neighborsrdquo in Dimensionality reductionwith unsupervised nearest neighbors vol 51 pp 13ndash23 SpringerBerlin Heidelberg Germany 2013

[46] C Cortes and V Vapnik ldquoSupport-vector networksrdquo MachineLearning vol 20 no 3 pp 273ndash297 1995

6 Mathematical Problems in Engineering

Figure 4 The pseudocode of the ML methodology

To derive the best LTTP model for each link road theaforementioned prediction results were evaluated based onthe mean absolute deviation (MAD) and the mean absolutepercentage error (MAPE) methods which are commonlyused for regression problem evaluation

The MAD as expressed in (3a) is a summary statistic ofstatistical dispersion or variability [54 55] The MAPE is ameasure of the accuracy of a prediction method in statisticsas written in (3b) [56] Because the MAPE is a percentageit is often easier to understand than the other statistics Forexample if the MAPE is 5 on average the forecast is off by5 [57]

MAD = sum119899119894=1 1003816100381610038161003816119909obs119894 minus 119909model1198941003816100381610038161003816119899 (3a)

MAPE = sum119899119894=1 1003816100381610038161003816(119909obs119894 minus 119909model119894) 119909obs1198941003816100381610038161003816119899 times 100 () (3b)

where 119909obs119894 represents the observation values 119909model119894 rep-resents the prediction values and 119899 is the number of datarecords

Table 5 lists the MAD and MAPE values obtained fromthe three ML methods for each experimental link road

Smaller MAD and MAPE values reflect better predictionperformance of each LTTP model and the smallest recordsare highlighted in Table 5 The results of the six experimentallink roads indicate that the LTTP models built using theSVM and RF methods are better than those using the kNNalgorithm Table 6 summarizes the optimal ML predictionmodels for each link road

The coefficient of determination 1198772 is widely used instatistical tests to evaluate the predictive capability of amodel and is also used in this study The 1198772 value with oneindependent variable is written as follows [58]

1198772 = [ 1119873 lowastsum (119909119894 minus 119909) lowast (119910119894 minus 119910)(120590119909 lowast 120590119910) ]

2

(4)

Mathematical Problems in Engineering 7

Raw valueKNN

SVMRF

000100000200000300000400000500000600000700000800000900001000001100001200

Link

trav

el tim

e

0 5 15 20 25 30 35 40 45 5010G-H

000100

000200

000300

000400

000500

000600

000700

000800

Link

trav

el tim

e

0 5 15 20 25 30 35 40 45 5010H-J

000200000300000400000500000600000700000800000900001000001100001200

Link

trav

el tim

e

0 5 15 20 25 30 35 40 45 5010E-H

000100000200000300000400000500000600000700000800000900001000001100

Link

trav

el tim

e

0 5 15 20 25 30 35 40 45 5010E-F

0 5 15 20 25 30 35 40 45 5010B-E

000200

000300

000400

000500

000600

000700

000800

000900

001000

Link

trav

el tim

e

000400000500000600000700000800000900001000001100001200001300001400001500001600001700001800001900002000002100002200

Link

trav

el tim

e

0 5 15 20 25 30 35 40 45 5010B-D

Raw valueKNN

SVMRF

Figure 5 Prediction results for the different ML methods

where119873 is the number of observations used to fit the model119909 and 119910 are themean values of 119909 and 119910 respectively 119909119894 and 119910119894are the values of observation 119894 and 120590119909 and 120590119910 are the standarddeviations of 119909 and 119910 respectively

Table 7 shows the 1198772 values of the three ML models foreach link road The 1198772 values range from 0 to 1 and 1198772 equalto 1 indicates perfect accurate prediction There are somedifferences between Tables 6 and 7 that is the optimal MLmodel of B-E H-J and G-H However the MAPE was stillselected for choosing the optimal model because the 1198772 valuecannot be used to evaluate predictive errors

32 Discussion of Traditional Averaging Methods and MLModels To compare the LTTP of MLmodels and traditionalaveraging methods controlled experiments were performedThe flow chart of traditional averaging methods is illustratedin Figure 6

For each record in the test dataset the experimentstraced back the corresponding top 10 20 30 40 and 50records and then calculated the average value as the finalprediction To improve the accuracy of the traditional aver-aging methods each calculation used only historical data forthe same truck type and load status The results obtained

8 Mathematical Problems in Engineering

Table 5 LTTP evaluation based on the different ML models

Link road Road type Evaluation kNN SVM RF

B-E

Fixed

MAD 591119864 minus 04 509119864 minus 04 456E minus 04MAPE 178119864 + 01 158119864 + 01 144E + 01

E-H MAD 944119864 minus 04 332E minus 04 637119864 minus 04MAPE 249119864 + 01 957E + 00 181119864 + 01

H-J MAD 516119864 minus 04 355119864 minus 04 354E minus 04MAPE 214119864 + 01 159119864 + 01 148E + 01

B-D

Temporary

MAD 171119864 minus 03 544E minus 04 670119864 minus 04MAPE 275119864 + 01 809E + 00 990119864 + 00

E-F MAD 959119864 minus 04 805119864 minus 04 563E minus 04MAPE 313119864 + 01 294119864 + 01 182E + 01

G-H MAD 118119864 minus 03 735E minus 04 785119864 minus 04MAPE 342119864 + 01 194E + 01 238119864 + 01

4

Rece

nt h

istor

ical

dat

a

2

Data predicted

Calculatingthe average time

(i) Same link road (ii) Same load status(iii) Same truck type

3001357

001421

001409BELAZB-E

001357

Empty

Empty

BELAZB-E

001821LoadB-E MT-86

001421EmptyB-E BELAZ

001715B-E EmptyMT-86

1

Figure 6 The flow chart of traditional averaging methods

Table 6 Summary of the optimal ML prediction models for eachlink road

Road Type Optimal ML modelB-E

FixedRF

E-H SVMH-J RFB-D

TemporarySVM

E-F RFG-H SVM

Table 7 1198772 values of the different ML models for each link road

Road SVM KNN RF Optimal ML modelB-E 028 016 041 SVME-H 083 016 067 SVMH-J 072 013 056 SVMB-D 089 023 07 SVME-F 054 024 073 RFG-H 061 019 062 RF

from the traditional averaging methods are summarized inTable 8

Smaller MAD and MAPE values mean better predictionperformance of the traditional averaging methods and the

smallest records are highlighted in Table 8The predicted val-ues obtained from the optimal ML method and a traditionalaverage method for each link road are given in Table 9 thedecrease in the MAPE is also shown

Table 9 shows that the tested ML models are superiorto the traditional averaging method in the context of LTTPbecause the former has smaller MAPEs An average increaseof 1579 in prediction accuracy is achieved in all experimen-tal link roads in which increases of 1254 and 1930 forthree fixed and three temporary roads respectively are alsoobtained

33 Discussion of Meteorological Features This study alsoconsidered the influence of meteorological features on theLTTP of an open-pit mine The data were obtained froma CMA monitoring station including 5 variables pressurewind speed temperature relative humidity and precipita-tion

The Pearson correlation coefficient (PCC) an evaluationmethod developed by Pearson [59] was used to evaluate thelinear correlation between two variables The expression ofthe PPC is as follows

120588119883119884 = cov (119883 119884)120590119883120590119884 (5)

Mathematical Problems in Engineering 9

Table 8 Results obtained from the traditional averaging methods

Road Evaluation Traditional averaging methods10 records 20 records 30 records 40 records 50 records

B-E MAD 102119864 minus 03 949119864 minus 04 917119864 minus 04 918119864 minus 04 904E minus 04MAPE 306119864 + 01 281119864 + 01 266119864 + 01 264119864 + 01 258E + 01

E-H MAD 122119864 minus 03 113119864 minus 03 109119864 minus 03 109119864 minus 03 107E minus 03MAPE 329119864 + 01 300119864 + 01 284119864 + 01 281119864 + 01 273E + 01

H-J MAD 629119864 minus 04 609119864 minus 04 587119864 minus 04 581119864 minus 04 580E minus 04MAPE 254119864 + 01 247119864 + 01 236119864 + 01 234119864 + 01 233E + 01

B-D MAD 215119864 minus 03 183E minus 03 246119864 minus 03 236119864 minus 03 205119864 minus 03MAPE 317119864 + 01 269E + 01 386119864 + 01 362119864 + 01 325119864 + 01

E-F MAD 116119864 minus 03 110E minus 03 114119864 minus 03 115119864 minus 03 116119864 minus 03MAPE 391119864 + 01 363E + 01 381119864 + 01 390119864 + 01 395119864 + 01

G-H MAD 129E minus 03 138119864 minus 03 136119864 minus 03 132119864 minus 03 130119864 minus 03MAPE 404E + 01 412119864 + 01 391119864 + 01 370119864 + 01 357119864 + 01

Table 9 Comparison between the optimal ML model and the optimal averaging method

Road Type Optimal average method (MAPE) Optimal ML model (MAPE) MAPE decrease AverageB-E

Fixed258119864 + 01 144119864 + 01 1140

1254E-H 273119864 + 01 957119864 + 00 1773H-J 233119864 + 01 148119864 + 01 850B-D

Temporary269119864 + 01 809119864 + 00 1881

1930E-F 363119864 + 01 182119864 + 01 1810G-H 404119864 + 01 194119864 + 01 2100Average 1579

Table 10 Prediction results after including meteorological data

Type Road Methods Meteorological features MAD MAPE MAPE decrease (no-yes)

Temporary

B-E RF No 690119864 minus 04 207119864 + 01 630Yes 456119864 minus 04 144119864 + 01

E-H SVM No 341119864 minus 04 169119864 + 01 728Yes 332119864 minus 04 957119864 + 00

H-J RF No 416119864 minus 04 186119864 + 01 380Yes 354119864 minus 04 148119864 + 01

Fixed

B-D SVM No 635119864 minus 04 122119864 + 01 408Yes 544119864 minus 04 809119864 + 00

E-F RF No 660119864 minus 04 217119864 + 01 350Yes 563119864 minus 04 182119864 + 01

G-H SVM No 842119864 minus 04 252119864 + 01 580Yes 735119864 minus 04 194119864 + 01

Average 513

where cov(119883 119884) is the covariance 120590119883 is the standard devia-tion of119883 and 120590119884 is the standard deviation of 119884

The PPC values of different variables are shown inFigure 7 including the 5 meteorological variables and trucktravel time A high PCC value indicates a closer relationshipbetween the two variables

Following controlled experiments the effect of meteo-rological features was investigated by adding or removingindividual features We selected the optimal ML model for

each link road The raw (observation) values and predictedresults withwithout meteorological features are shown inFigure 8

The results of the controlled experiments are shownin Table 10 the calculated decrease in the MAPE is alsoshown The results considering meteorological features arebetter than those withoutmeteorological featuresTheMAPEdecreased by 513 on average for all link roads after addingthe meteorological data

10 Mathematical Problems in Engineering

Pressure08

Wind speed04

Temperature

00

Relative humidity

Precipitation

Travel time

minus04

minus08

Pres

sure

Win

d sp

eed

Tem

pera

ture

Relat

ive h

umid

ity

Prec

ipita

tion

Trav

el tim

e

1

1

1

1

1

1

minus048 minus048

minus048

minus048

064

064

minus0041 minus0019

minus0019

005

005

minus0088

minus0088

minus082

minus082

047

012

012

047 minus064 014

014

0049

0049

minus0041

minus0054

minus0054

0045

0045

minus064

Figure 7 The PCC heat map of meteorological features

Table 11 Evaluation of LTTP based on different ML models

Link road Road type Evaluation kNN SVM RF

A-B Fixed MAD 495119864 minus 04 328119864 minus 04 299E minus 04MAPE 469119864 + 01 340119864 + 01 336E + 01

34 Discussion of LTTP and RTTP The above experimentsused the link rather than the route to predict the travel timeof OPTs However the differences between LTTP and RTTPneed to be further discussed In the ensuing discussion thelongest route between dump point A and load point G isselected as shown in Figure 9

The A-G route consists of 4 links A-B B-E E-H and H-G Among them the optimal ML prediction models of B-EE-H andH-G are SVM RF and SVM respectivelyThe sameexperimental procedure as used in Section 31 was used toobtain the optimal MLmodel for A-B and Table 11 shows theMAD and MAPE values of the three ML methods It can beseen that the RF model is the best ML method for link A-B

The SVM and RF methods are used to predict the RTTPof A-G because those two models have a good predictionperformance Thus the experiments are summarized asfollows

(i) RTTP (SVM) using the SVM algorithm to train theTTP model for the route A-G

(ii) RTTP (RF) using the RF algorithm to train the TTPmodel for the route A-G

(iii) LTTP using the optimalMLmodel for each link thatis A-B (RF) B-E (SVM) E-H (RF) and H-G (SVM)and the truck travel time of A-G is the sum of eachLTTP result

Raw values and predicted results of the above threeexperiments are shown in Figure 10 while the evaluated

Table 12 Evaluation of the results between LTTP and RTTP

Method Model Evaluation Values

RTTP SVM MAD 155119864 minus 03MAPE 208119864 + 01

RTTP RF MAD 178119864 minus 03MAPE 235119864 + 01

LTTP Assemble MAD 834E minus 04MAPE 898E + 00

results of those experiments are shown in Table 12 Both theMAD and MAPE values of the LTTP approach are smallerthan the two RTTP methods Thus using the link as theprediction unit is better than using the route

4 Conclusions

The link roads of an open-pit mine are divided into fixedand temporary roads in this paper Three ML algorithmsthat is kNN SVM and RF are used for the LTTP of OPTsThe experimental results not only reflect the self-adaptive andself-feedback characteristics of the ML algorithms but alsodemonstrate the practicality of themethod for road segmentsThe conclusions based on the results are as follows

(1) LTTP models based on ML are more efficient andaccurate than traditional averaging methods Anoverall average increase of 1579 in the predictionaccuracy is obtained for six experimental link roads

Mathematical Problems in Engineering 11

000100000200000300000400000500000600000700000800000900001000001100001200

Link

trav

el tim

e

0 10 15 20 25 30 35 40 45 505G-H (SVM)

000100

000200

000300

000400

000500

000600

000700

000800

Link

trav

el tim

e

0 10 15 20 25 30 35 40 45 505H-J (RF)

000200000300000400000500000600000700000800000900001000001100001200

Link

trav

el tim

e

0 5 15 20 25 30 35 40 45 5010E-H (SVM)

000100

000200

000300

000400

000500

000600

000700

000800

Link

trav

el tim

e

0 5 15 20 25 30 35 40 45 5010E-F (RF)

000400000500000600000700000800000900001000001100001200001300001400001500001600001700001800001900002000002100002200

Link

trav

el tim

e

0 5 15 20 25 30 35 40 45 5010B-D (SVM)

000200

000300

000400

000500

000600

000700

000800

000900

001000

Link

trav

el tim

e

0 10 15 20 25 30 35 40 45 505B-E (RF)

Raw valueWithout meteorological featuresMeteorological features

Raw valueWithout meteorological featuresMeteorological features

Figure 8 Comparison forecast results including and excluding meteorological features

For temporary roads the average accuracy increasesby 1930

(2) LTTP models established using the SVM and RFalgorithms are better than those established using thekNN approach There is no large difference betweenthe SVM and RF results although the RF algorithmrequires less space and time complexity than the SVMalgorithm

(3) This paper is original in that it considers the effectof meteorological features on LTTP The results show

that considering the effect of meteorological featureson LTTP increases the prediction accuracy by 513

(4) The differences between LTTP and RTTP are alsodiscussed and the former has a higher predictionaccuracy The MAPE decreases by 1182 for theLTTP method

Some work is already underway to incorporate the MLprediction models into the OPATDS of the FWOM whichwill be helpful in improving the dispatching efficiency of theOPTs

12 Mathematical Problems in Engineering

Node J

Load G

Node E

Load F

Dump ANode B

Load D

Load C

Node H

Fixed roadsTemporary roads

Figure 9 The location of the route A-G in the FWOM roadmap

Raw valuesRTTP (RF)

RTTP (SVM)LTTP

5 10 15 20 25 30 35 40 45 500Route A-G

000600000800001000001200001400001600001800002000002200

Truc

k tr

avel

tim

e

Figure 10 Prediction results for RTTP (RF) RTTP (SVM) andLTTP

Data Availability

The data used to support the findings of this study areavailable from the corresponding author upon request

Conflicts of Interest

The authors declare no conflicts of interest

Authorsrsquo Contributions

Xiaoyu Sun as the principal investigator provided the dataused to train the ML models Hang Zhang performed theexperiments andwrote the paper Fengliang Tian contributedthe programming Lei Yang proofread the manuscript

Acknowledgments

This work was funded by the National Natural ScienceFoundation of China (no 51674063) and the NationalKey Research and Development Program of China (no2016YFC0801608)

References

[1] J Czaplicki Shovel-Truck Systems CRC Press 2008[2] J M Czaplicki ldquoModelling and analysis of the exploitation

process of a shovel-truck systemrdquo in Shovel-Truck Systems pp79ndash89 CRC Press 2008

[3] S G Ercelebi and A Bascetin ldquoOptimization of shovel-trucksystem for surface miningrdquo Journal of the Southern AfricanInstitute of Mining and Metallurgy vol 109 no 7 pp 433ndash4392009

[4] R Mena E Zio F Kristjanpoller and A Arata ldquoAvailability-based simulation and optimization modeling framework foropen-pit mine truck allocation under dynamic constraintsrdquoInternational Journal of Mining Science and Technology vol 23no 1 pp 113ndash119 2013

[5] F Soumis J Ethier and J Elbrond ldquoTruck dispatching inan open pit minerdquo International Journal of Surface MiningReclamation and Environment vol 3 no 2 pp 115ndash119 1989

[6] A Y F Fadin Komarudin and A O Moeis ldquoSimulation-optimization truck dispatch problem using look - ahead algo-rithm in open pit minesrdquo International Journal of GEOMATEvol 13 no 36 pp 80ndash86 2017

[7] Y Tan and S Takakuwa ldquoA practical simulation approachfor an effective truck dispatching system of open pit minesusing VBArdquo in Proceedings of the 2016 Winter SimulationConference WSC 2016 pp 2394ndash2405 IEEE Washington DCUSA December 2016

[8] J Li R Bai J Mao and W Li ldquoForecast of applied effect fortruck real-time dispatch system in open-pit mine based onCSUSSrdquo in Proceedings of the 2010 International Conference onE-Product E-Service and E-Entertainment ICEEE2010 pp 1ndash4IEEE Henan China November 2010

[9] S P Alarie and M Gamache ldquoOverview of solution strategiesused in truck dispatching systems for open pit minesrdquo Interna-tional Journal of Surface Mining Reclamation and Environmentvol 16 no 1 pp 59ndash76 2002

[10] B Kolonja D R Kalasky and J M Mutmansky ldquoOptimizationof dispatching criteria for open-pit truck haulage system designusingmultiple comparisons with the best and common random

Mathematical Problems in Engineering 13

numbersrdquo in Proceedings of the 25th Conference on Winter Sim-ulation WSC 1993 pp 393ndash401 ACM Los Angeles CaliforniaUSA December 1993

[11] Q Wang Y Zhang C Chen and W Xu ldquoOpen-pit mine truckreal-time dispatching principle under macroscopic controlrdquo inProceedings of the 1st International Conference on InnovativeComputing Information and Control 2006 ICICICrsquo06 pp 702ndash705 IEEE Beijing China September 2006

[12] Y Choi ldquoSimulation of Shovel-Truck Haulage Systems byConsidering Truck Dispatch Methodsrdquo Journal of the KoreanSociety of Mineral and Energy Resources Engineers vol 50 no4 p 543 2013

[13] E Topal and S Ramazan ldquoMining truck scheduling withstochastic maintenance costrdquo Journal of Coal Science andEngineering vol 18 no 3 pp 313ndash319 2012

[14] P Chaowasakoo H Seppala H Koivo and Q Zhou ldquoDigi-talization of mine operations Scenarios to benefit in real-timetruck dispatchingrdquo International Journal of Mining Science andTechnology vol 27 no 2 pp 229ndash236 2017

[15] Q Sun ldquoRoad running time statistics method in truck schedul-ingrdquo Opencast Coal Mining Technology vol 01 pp 35ndash37 1998

[16] R Bai J Li and J Xu ldquoReal-time dynamic forecast of truck linktravel timerdquo Journal of Liaoning Technical University vol 1 pp12ndash14 2005

[17] L Jiangang ldquoReal-time dynamic forecasts of truck link traveltime based on fuzzy neural networkrdquo Journal of the China CoalSociety vol 6 pp 796ndash800 2005

[18] E K Chanda and S Gardiner ldquoA comparative study of truckcycle time prediction methods in open-pit miningrdquo Engineer-ing Construction and Architectural Management vol 17 no 5pp 446ndash460 2010

[19] D J Edwards and I J Griffiths ldquoArtificial intelligence approachto calculation of hydraulic excavator cycle time and outputrdquoMining Technology vol 109 no 1 pp 23ndash29 2013

[20] K Erarslan ldquoModelling performance and retarder chart of off-highway trucks by cubic splines for cycle time estimationrdquoMining Technology vol 114 pp 161ndash166 2013

[21] X Xue W Sun and R Liang ldquoA new method of real-timedynamic forecast of truck link travel time in open minesrdquoJournal of the China Coal Society vol 37 no 8 pp 1418ndash14222012

[22] X Meng Research on scheduling services of open-pit mine basedon real-time travel time prediction China University of Miningand Technology 2014

[23] V Shalamanov V Pershin S Shabaev and D Boiko ldquoJustifi-cation of the Optimal Granulometric Composition of CrushedRocks for Open-Pit Mine Road Surfacingrdquo in Proceedings of the1st International InnovativeMining Symposium 2017 KemerovoRussia April 2017

[24] M Hofmann and M OrsquoMahony ldquoThe impact of adverseweather conditions on urban bus performance measuresrdquoin Proceedings of the 8th International IEEE Conference onIntelligent Transportation Systems pp 431ndash436 IEEE ViennaAustria September 2005

[25] T H Maze M Agarwal and G Burchett ldquoWhether weathermatters to traffic demand traffic safety and traffic operationsand flowrdquoTransportation Research Record no 1948 pp 170ndash1762006

[26] S A Silvester I S Lowndes and D M Hargreaves ldquoAcomputational study of particulate emissions from an openpit quarry under neutral atmospheric conditionsrdquo AtmosphericEnvironment vol 43 no 40 pp 6415ndash6424 2009

[27] I Tsapakis T Cheng and A Bolbol ldquoImpact of weather condi-tions on macroscopic urban travel timesrdquo Journal of TransportGeography vol 28 pp 204ndash211 2013

[28] TheMinistry of Land and Resources ldquoPRCThe basic situationof mineral resources in fushunrdquo httpwwwmlrgovcnkczyglkczydjtj201208t20120813 1130832htm

[29] G F Cooper and E Herskovits ldquoA Bayesian method forthe induction of probabilistic networks from datardquo MachineLearning vol 9 no 4 pp 309ndash347 1992

[30] C Yunqiang Z X Sean and T S Huang ldquoOne-class svm forlearning in image retrievalrdquo in In Proceedings 2001 InternationalConference on Image Processing (Cat No01CH37205) pp 34ndash372001

[31] T K Ho ldquoIn Random decision forestsrdquo in Proceedings of 3rdInternational Conference on Document Analysis and Recogni-tion IEEE 1995

[32] D G Kleinbaum and M Klein ldquoAnalysis of Matched DataUsing Logistic Regressionrdquo in Logistic Regression pp 389ndash428Springer New York NY USA 2010

[33] N S Altman ldquoAn introduction to kernel and nearest-neighbornonparametric regressionrdquo The American Statistician vol 46no 3 pp 175ndash185 1992

[34] S R Eddy ldquoProfile hiddenMarkovmodelsrdquo Bioinformatics vol14 no 9 pp 755ndash763 1998

[35] J R Koza F H Bennett D Andre and M A Keane ldquoAuto-mated design of both the topology and sizing of analog electricalcircuits using genetic programmingrdquo in In Artificial intelligencein design rsquo96 pp 151ndash170 Springer Netherlands 1996

[36] T Oladipupo ldquoIntroduction to machine learningrdquo in In Newadvances in machine learning InTech 2010

[37] H Mannila ldquoData mining machine learning statistics anddatabasesrdquo in Proceedings of the 8th International Conferenceon Scientific and Statistical Data Base Management IEEEStockholm Sweden Sweden 2002

[38] M Troc and O Unold ldquoSelf-adaptation of parameters in alearning classifier system ensemble machinerdquo InternationalJournal of Applied Mathematics and Computer Science vol 20no 1 pp 157ndash174 2010

[39] T Hastie R Tibshirani and J Friedman The Elements ofStatistical Learning Springer-Verlag New York NY USA 2009

[40] N J Nilsson ldquoArtificial intelligence A modern approachrdquoArtificial Intelligence vol 82 no 1-2 pp 369ndash380 1996

[41] I Kavakiotis O Tsave A Salifoglou N Maglaveras I Vla-havas and I Chouvarda ldquoMachine Learning and Data MiningMethods in Diabetes Researchrdquo Computational and StructuralBiotechnology Journal vol 15 pp 104ndash116 2017

[42] M Mohri A Rostamizadeh and A Talwalkar Foundations ofmachine learning MIT press 2012

[43] Y Freund and R E Schapire ldquoA decision-theoretic generaliza-tion of on-line learning and an application to boostingrdquo Journalof Computer and System Sciences vol 55 no 1 part 2 pp 119ndash139 1997

[44] R S Michalski J G Carbonell and T M Mitchell ldquoMachinelearning 1983rdquo

[45] O Kramer ldquoK-nearest neighborsrdquo in Dimensionality reductionwith unsupervised nearest neighbors vol 51 pp 13ndash23 SpringerBerlin Heidelberg Germany 2013

[46] C Cortes and V Vapnik ldquoSupport-vector networksrdquo MachineLearning vol 20 no 3 pp 273ndash297 1995

Mathematical Problems in Engineering 7

Raw valueKNN

SVMRF

000100000200000300000400000500000600000700000800000900001000001100001200

Link

trav

el tim

e

0 5 15 20 25 30 35 40 45 5010G-H

000100

000200

000300

000400

000500

000600

000700

000800

Link

trav

el tim

e

0 5 15 20 25 30 35 40 45 5010H-J

000200000300000400000500000600000700000800000900001000001100001200

Link

trav

el tim

e

0 5 15 20 25 30 35 40 45 5010E-H

000100000200000300000400000500000600000700000800000900001000001100

Link

trav

el tim

e

0 5 15 20 25 30 35 40 45 5010E-F

0 5 15 20 25 30 35 40 45 5010B-E

000200

000300

000400

000500

000600

000700

000800

000900

001000

Link

trav

el tim

e

000400000500000600000700000800000900001000001100001200001300001400001500001600001700001800001900002000002100002200

Link

trav

el tim

e

0 5 15 20 25 30 35 40 45 5010B-D

Raw valueKNN

SVMRF

Figure 5 Prediction results for the different ML methods

where119873 is the number of observations used to fit the model119909 and 119910 are themean values of 119909 and 119910 respectively 119909119894 and 119910119894are the values of observation 119894 and 120590119909 and 120590119910 are the standarddeviations of 119909 and 119910 respectively

Table 7 shows the 1198772 values of the three ML models foreach link road The 1198772 values range from 0 to 1 and 1198772 equalto 1 indicates perfect accurate prediction There are somedifferences between Tables 6 and 7 that is the optimal MLmodel of B-E H-J and G-H However the MAPE was stillselected for choosing the optimal model because the 1198772 valuecannot be used to evaluate predictive errors

32 Discussion of Traditional Averaging Methods and MLModels To compare the LTTP of MLmodels and traditionalaveraging methods controlled experiments were performedThe flow chart of traditional averaging methods is illustratedin Figure 6

For each record in the test dataset the experimentstraced back the corresponding top 10 20 30 40 and 50records and then calculated the average value as the finalprediction To improve the accuracy of the traditional aver-aging methods each calculation used only historical data forthe same truck type and load status The results obtained

8 Mathematical Problems in Engineering

Table 5 LTTP evaluation based on the different ML models

Link road Road type Evaluation kNN SVM RF

B-E

Fixed

MAD 591119864 minus 04 509119864 minus 04 456E minus 04MAPE 178119864 + 01 158119864 + 01 144E + 01

E-H MAD 944119864 minus 04 332E minus 04 637119864 minus 04MAPE 249119864 + 01 957E + 00 181119864 + 01

H-J MAD 516119864 minus 04 355119864 minus 04 354E minus 04MAPE 214119864 + 01 159119864 + 01 148E + 01

B-D

Temporary

MAD 171119864 minus 03 544E minus 04 670119864 minus 04MAPE 275119864 + 01 809E + 00 990119864 + 00

E-F MAD 959119864 minus 04 805119864 minus 04 563E minus 04MAPE 313119864 + 01 294119864 + 01 182E + 01

G-H MAD 118119864 minus 03 735E minus 04 785119864 minus 04MAPE 342119864 + 01 194E + 01 238119864 + 01

4

Rece

nt h

istor

ical

dat

a

2

Data predicted

Calculatingthe average time

(i) Same link road (ii) Same load status(iii) Same truck type

3001357

001421

001409BELAZB-E

001357

Empty

Empty

BELAZB-E

001821LoadB-E MT-86

001421EmptyB-E BELAZ

001715B-E EmptyMT-86

1

Figure 6 The flow chart of traditional averaging methods

Table 6 Summary of the optimal ML prediction models for eachlink road

Road Type Optimal ML modelB-E

FixedRF

E-H SVMH-J RFB-D

TemporarySVM

E-F RFG-H SVM

Table 7 1198772 values of the different ML models for each link road

Road SVM KNN RF Optimal ML modelB-E 028 016 041 SVME-H 083 016 067 SVMH-J 072 013 056 SVMB-D 089 023 07 SVME-F 054 024 073 RFG-H 061 019 062 RF

from the traditional averaging methods are summarized inTable 8

Smaller MAD and MAPE values mean better predictionperformance of the traditional averaging methods and the

smallest records are highlighted in Table 8The predicted val-ues obtained from the optimal ML method and a traditionalaverage method for each link road are given in Table 9 thedecrease in the MAPE is also shown

Table 9 shows that the tested ML models are superiorto the traditional averaging method in the context of LTTPbecause the former has smaller MAPEs An average increaseof 1579 in prediction accuracy is achieved in all experimen-tal link roads in which increases of 1254 and 1930 forthree fixed and three temporary roads respectively are alsoobtained

33 Discussion of Meteorological Features This study alsoconsidered the influence of meteorological features on theLTTP of an open-pit mine The data were obtained froma CMA monitoring station including 5 variables pressurewind speed temperature relative humidity and precipita-tion

The Pearson correlation coefficient (PCC) an evaluationmethod developed by Pearson [59] was used to evaluate thelinear correlation between two variables The expression ofthe PPC is as follows

120588119883119884 = cov (119883 119884)120590119883120590119884 (5)

Mathematical Problems in Engineering 9

Table 8 Results obtained from the traditional averaging methods

Road Evaluation Traditional averaging methods10 records 20 records 30 records 40 records 50 records

B-E MAD 102119864 minus 03 949119864 minus 04 917119864 minus 04 918119864 minus 04 904E minus 04MAPE 306119864 + 01 281119864 + 01 266119864 + 01 264119864 + 01 258E + 01

E-H MAD 122119864 minus 03 113119864 minus 03 109119864 minus 03 109119864 minus 03 107E minus 03MAPE 329119864 + 01 300119864 + 01 284119864 + 01 281119864 + 01 273E + 01

H-J MAD 629119864 minus 04 609119864 minus 04 587119864 minus 04 581119864 minus 04 580E minus 04MAPE 254119864 + 01 247119864 + 01 236119864 + 01 234119864 + 01 233E + 01

B-D MAD 215119864 minus 03 183E minus 03 246119864 minus 03 236119864 minus 03 205119864 minus 03MAPE 317119864 + 01 269E + 01 386119864 + 01 362119864 + 01 325119864 + 01

E-F MAD 116119864 minus 03 110E minus 03 114119864 minus 03 115119864 minus 03 116119864 minus 03MAPE 391119864 + 01 363E + 01 381119864 + 01 390119864 + 01 395119864 + 01

G-H MAD 129E minus 03 138119864 minus 03 136119864 minus 03 132119864 minus 03 130119864 minus 03MAPE 404E + 01 412119864 + 01 391119864 + 01 370119864 + 01 357119864 + 01

Table 9 Comparison between the optimal ML model and the optimal averaging method

Road Type Optimal average method (MAPE) Optimal ML model (MAPE) MAPE decrease AverageB-E

Fixed258119864 + 01 144119864 + 01 1140

1254E-H 273119864 + 01 957119864 + 00 1773H-J 233119864 + 01 148119864 + 01 850B-D

Temporary269119864 + 01 809119864 + 00 1881

1930E-F 363119864 + 01 182119864 + 01 1810G-H 404119864 + 01 194119864 + 01 2100Average 1579

Table 10 Prediction results after including meteorological data

Type Road Methods Meteorological features MAD MAPE MAPE decrease (no-yes)

Temporary

B-E RF No 690119864 minus 04 207119864 + 01 630Yes 456119864 minus 04 144119864 + 01

E-H SVM No 341119864 minus 04 169119864 + 01 728Yes 332119864 minus 04 957119864 + 00

H-J RF No 416119864 minus 04 186119864 + 01 380Yes 354119864 minus 04 148119864 + 01

Fixed

B-D SVM No 635119864 minus 04 122119864 + 01 408Yes 544119864 minus 04 809119864 + 00

E-F RF No 660119864 minus 04 217119864 + 01 350Yes 563119864 minus 04 182119864 + 01

G-H SVM No 842119864 minus 04 252119864 + 01 580Yes 735119864 minus 04 194119864 + 01

Average 513

where cov(119883 119884) is the covariance 120590119883 is the standard devia-tion of119883 and 120590119884 is the standard deviation of 119884

The PPC values of different variables are shown inFigure 7 including the 5 meteorological variables and trucktravel time A high PCC value indicates a closer relationshipbetween the two variables

Following controlled experiments the effect of meteo-rological features was investigated by adding or removingindividual features We selected the optimal ML model for

each link road The raw (observation) values and predictedresults withwithout meteorological features are shown inFigure 8

The results of the controlled experiments are shownin Table 10 the calculated decrease in the MAPE is alsoshown The results considering meteorological features arebetter than those withoutmeteorological featuresTheMAPEdecreased by 513 on average for all link roads after addingthe meteorological data

10 Mathematical Problems in Engineering

Pressure08

Wind speed04

Temperature

00

Relative humidity

Precipitation

Travel time

minus04

minus08

Pres

sure

Win

d sp

eed

Tem

pera

ture

Relat

ive h

umid

ity

Prec

ipita

tion

Trav

el tim

e

1

1

1

1

1

1

minus048 minus048

minus048

minus048

064

064

minus0041 minus0019

minus0019

005

005

minus0088

minus0088

minus082

minus082

047

012

012

047 minus064 014

014

0049

0049

minus0041

minus0054

minus0054

0045

0045

minus064

Figure 7 The PCC heat map of meteorological features

Table 11 Evaluation of LTTP based on different ML models

Link road Road type Evaluation kNN SVM RF

A-B Fixed MAD 495119864 minus 04 328119864 minus 04 299E minus 04MAPE 469119864 + 01 340119864 + 01 336E + 01

34 Discussion of LTTP and RTTP The above experimentsused the link rather than the route to predict the travel timeof OPTs However the differences between LTTP and RTTPneed to be further discussed In the ensuing discussion thelongest route between dump point A and load point G isselected as shown in Figure 9

The A-G route consists of 4 links A-B B-E E-H and H-G Among them the optimal ML prediction models of B-EE-H andH-G are SVM RF and SVM respectivelyThe sameexperimental procedure as used in Section 31 was used toobtain the optimal MLmodel for A-B and Table 11 shows theMAD and MAPE values of the three ML methods It can beseen that the RF model is the best ML method for link A-B

The SVM and RF methods are used to predict the RTTPof A-G because those two models have a good predictionperformance Thus the experiments are summarized asfollows

(i) RTTP (SVM) using the SVM algorithm to train theTTP model for the route A-G

(ii) RTTP (RF) using the RF algorithm to train the TTPmodel for the route A-G

(iii) LTTP using the optimalMLmodel for each link thatis A-B (RF) B-E (SVM) E-H (RF) and H-G (SVM)and the truck travel time of A-G is the sum of eachLTTP result

Raw values and predicted results of the above threeexperiments are shown in Figure 10 while the evaluated

Table 12 Evaluation of the results between LTTP and RTTP

Method Model Evaluation Values

RTTP SVM MAD 155119864 minus 03MAPE 208119864 + 01

RTTP RF MAD 178119864 minus 03MAPE 235119864 + 01

LTTP Assemble MAD 834E minus 04MAPE 898E + 00

results of those experiments are shown in Table 12 Both theMAD and MAPE values of the LTTP approach are smallerthan the two RTTP methods Thus using the link as theprediction unit is better than using the route

4 Conclusions

The link roads of an open-pit mine are divided into fixedand temporary roads in this paper Three ML algorithmsthat is kNN SVM and RF are used for the LTTP of OPTsThe experimental results not only reflect the self-adaptive andself-feedback characteristics of the ML algorithms but alsodemonstrate the practicality of themethod for road segmentsThe conclusions based on the results are as follows

(1) LTTP models based on ML are more efficient andaccurate than traditional averaging methods Anoverall average increase of 1579 in the predictionaccuracy is obtained for six experimental link roads

Mathematical Problems in Engineering 11

000100000200000300000400000500000600000700000800000900001000001100001200

Link

trav

el tim

e

0 10 15 20 25 30 35 40 45 505G-H (SVM)

000100

000200

000300

000400

000500

000600

000700

000800

Link

trav

el tim

e

0 10 15 20 25 30 35 40 45 505H-J (RF)

000200000300000400000500000600000700000800000900001000001100001200

Link

trav

el tim

e

0 5 15 20 25 30 35 40 45 5010E-H (SVM)

000100

000200

000300

000400

000500

000600

000700

000800

Link

trav

el tim

e

0 5 15 20 25 30 35 40 45 5010E-F (RF)

000400000500000600000700000800000900001000001100001200001300001400001500001600001700001800001900002000002100002200

Link

trav

el tim

e

0 5 15 20 25 30 35 40 45 5010B-D (SVM)

000200

000300

000400

000500

000600

000700

000800

000900

001000

Link

trav

el tim

e

0 10 15 20 25 30 35 40 45 505B-E (RF)

Raw valueWithout meteorological featuresMeteorological features

Raw valueWithout meteorological featuresMeteorological features

Figure 8 Comparison forecast results including and excluding meteorological features

For temporary roads the average accuracy increasesby 1930

(2) LTTP models established using the SVM and RFalgorithms are better than those established using thekNN approach There is no large difference betweenthe SVM and RF results although the RF algorithmrequires less space and time complexity than the SVMalgorithm

(3) This paper is original in that it considers the effectof meteorological features on LTTP The results show

that considering the effect of meteorological featureson LTTP increases the prediction accuracy by 513

(4) The differences between LTTP and RTTP are alsodiscussed and the former has a higher predictionaccuracy The MAPE decreases by 1182 for theLTTP method

Some work is already underway to incorporate the MLprediction models into the OPATDS of the FWOM whichwill be helpful in improving the dispatching efficiency of theOPTs

12 Mathematical Problems in Engineering

Node J

Load G

Node E

Load F

Dump ANode B

Load D

Load C

Node H

Fixed roadsTemporary roads

Figure 9 The location of the route A-G in the FWOM roadmap

Raw valuesRTTP (RF)

RTTP (SVM)LTTP

5 10 15 20 25 30 35 40 45 500Route A-G

000600000800001000001200001400001600001800002000002200

Truc

k tr

avel

tim

e

Figure 10 Prediction results for RTTP (RF) RTTP (SVM) andLTTP

Data Availability

The data used to support the findings of this study areavailable from the corresponding author upon request

Conflicts of Interest

The authors declare no conflicts of interest

Authorsrsquo Contributions

Xiaoyu Sun as the principal investigator provided the dataused to train the ML models Hang Zhang performed theexperiments andwrote the paper Fengliang Tian contributedthe programming Lei Yang proofread the manuscript

Acknowledgments

This work was funded by the National Natural ScienceFoundation of China (no 51674063) and the NationalKey Research and Development Program of China (no2016YFC0801608)

References

[1] J Czaplicki Shovel-Truck Systems CRC Press 2008[2] J M Czaplicki ldquoModelling and analysis of the exploitation

process of a shovel-truck systemrdquo in Shovel-Truck Systems pp79ndash89 CRC Press 2008

[3] S G Ercelebi and A Bascetin ldquoOptimization of shovel-trucksystem for surface miningrdquo Journal of the Southern AfricanInstitute of Mining and Metallurgy vol 109 no 7 pp 433ndash4392009

[4] R Mena E Zio F Kristjanpoller and A Arata ldquoAvailability-based simulation and optimization modeling framework foropen-pit mine truck allocation under dynamic constraintsrdquoInternational Journal of Mining Science and Technology vol 23no 1 pp 113ndash119 2013

[5] F Soumis J Ethier and J Elbrond ldquoTruck dispatching inan open pit minerdquo International Journal of Surface MiningReclamation and Environment vol 3 no 2 pp 115ndash119 1989

[6] A Y F Fadin Komarudin and A O Moeis ldquoSimulation-optimization truck dispatch problem using look - ahead algo-rithm in open pit minesrdquo International Journal of GEOMATEvol 13 no 36 pp 80ndash86 2017

[7] Y Tan and S Takakuwa ldquoA practical simulation approachfor an effective truck dispatching system of open pit minesusing VBArdquo in Proceedings of the 2016 Winter SimulationConference WSC 2016 pp 2394ndash2405 IEEE Washington DCUSA December 2016

[8] J Li R Bai J Mao and W Li ldquoForecast of applied effect fortruck real-time dispatch system in open-pit mine based onCSUSSrdquo in Proceedings of the 2010 International Conference onE-Product E-Service and E-Entertainment ICEEE2010 pp 1ndash4IEEE Henan China November 2010

[9] S P Alarie and M Gamache ldquoOverview of solution strategiesused in truck dispatching systems for open pit minesrdquo Interna-tional Journal of Surface Mining Reclamation and Environmentvol 16 no 1 pp 59ndash76 2002

[10] B Kolonja D R Kalasky and J M Mutmansky ldquoOptimizationof dispatching criteria for open-pit truck haulage system designusingmultiple comparisons with the best and common random

Mathematical Problems in Engineering 13

numbersrdquo in Proceedings of the 25th Conference on Winter Sim-ulation WSC 1993 pp 393ndash401 ACM Los Angeles CaliforniaUSA December 1993

[11] Q Wang Y Zhang C Chen and W Xu ldquoOpen-pit mine truckreal-time dispatching principle under macroscopic controlrdquo inProceedings of the 1st International Conference on InnovativeComputing Information and Control 2006 ICICICrsquo06 pp 702ndash705 IEEE Beijing China September 2006

[12] Y Choi ldquoSimulation of Shovel-Truck Haulage Systems byConsidering Truck Dispatch Methodsrdquo Journal of the KoreanSociety of Mineral and Energy Resources Engineers vol 50 no4 p 543 2013

[13] E Topal and S Ramazan ldquoMining truck scheduling withstochastic maintenance costrdquo Journal of Coal Science andEngineering vol 18 no 3 pp 313ndash319 2012

[14] P Chaowasakoo H Seppala H Koivo and Q Zhou ldquoDigi-talization of mine operations Scenarios to benefit in real-timetruck dispatchingrdquo International Journal of Mining Science andTechnology vol 27 no 2 pp 229ndash236 2017

[15] Q Sun ldquoRoad running time statistics method in truck schedul-ingrdquo Opencast Coal Mining Technology vol 01 pp 35ndash37 1998

[16] R Bai J Li and J Xu ldquoReal-time dynamic forecast of truck linktravel timerdquo Journal of Liaoning Technical University vol 1 pp12ndash14 2005

[17] L Jiangang ldquoReal-time dynamic forecasts of truck link traveltime based on fuzzy neural networkrdquo Journal of the China CoalSociety vol 6 pp 796ndash800 2005

[18] E K Chanda and S Gardiner ldquoA comparative study of truckcycle time prediction methods in open-pit miningrdquo Engineer-ing Construction and Architectural Management vol 17 no 5pp 446ndash460 2010

[19] D J Edwards and I J Griffiths ldquoArtificial intelligence approachto calculation of hydraulic excavator cycle time and outputrdquoMining Technology vol 109 no 1 pp 23ndash29 2013

[20] K Erarslan ldquoModelling performance and retarder chart of off-highway trucks by cubic splines for cycle time estimationrdquoMining Technology vol 114 pp 161ndash166 2013

[21] X Xue W Sun and R Liang ldquoA new method of real-timedynamic forecast of truck link travel time in open minesrdquoJournal of the China Coal Society vol 37 no 8 pp 1418ndash14222012

[22] X Meng Research on scheduling services of open-pit mine basedon real-time travel time prediction China University of Miningand Technology 2014

[23] V Shalamanov V Pershin S Shabaev and D Boiko ldquoJustifi-cation of the Optimal Granulometric Composition of CrushedRocks for Open-Pit Mine Road Surfacingrdquo in Proceedings of the1st International InnovativeMining Symposium 2017 KemerovoRussia April 2017

[24] M Hofmann and M OrsquoMahony ldquoThe impact of adverseweather conditions on urban bus performance measuresrdquoin Proceedings of the 8th International IEEE Conference onIntelligent Transportation Systems pp 431ndash436 IEEE ViennaAustria September 2005

[25] T H Maze M Agarwal and G Burchett ldquoWhether weathermatters to traffic demand traffic safety and traffic operationsand flowrdquoTransportation Research Record no 1948 pp 170ndash1762006

[26] S A Silvester I S Lowndes and D M Hargreaves ldquoAcomputational study of particulate emissions from an openpit quarry under neutral atmospheric conditionsrdquo AtmosphericEnvironment vol 43 no 40 pp 6415ndash6424 2009

[27] I Tsapakis T Cheng and A Bolbol ldquoImpact of weather condi-tions on macroscopic urban travel timesrdquo Journal of TransportGeography vol 28 pp 204ndash211 2013

[28] TheMinistry of Land and Resources ldquoPRCThe basic situationof mineral resources in fushunrdquo httpwwwmlrgovcnkczyglkczydjtj201208t20120813 1130832htm

[29] G F Cooper and E Herskovits ldquoA Bayesian method forthe induction of probabilistic networks from datardquo MachineLearning vol 9 no 4 pp 309ndash347 1992

[30] C Yunqiang Z X Sean and T S Huang ldquoOne-class svm forlearning in image retrievalrdquo in In Proceedings 2001 InternationalConference on Image Processing (Cat No01CH37205) pp 34ndash372001

[31] T K Ho ldquoIn Random decision forestsrdquo in Proceedings of 3rdInternational Conference on Document Analysis and Recogni-tion IEEE 1995

[32] D G Kleinbaum and M Klein ldquoAnalysis of Matched DataUsing Logistic Regressionrdquo in Logistic Regression pp 389ndash428Springer New York NY USA 2010

[33] N S Altman ldquoAn introduction to kernel and nearest-neighbornonparametric regressionrdquo The American Statistician vol 46no 3 pp 175ndash185 1992

[34] S R Eddy ldquoProfile hiddenMarkovmodelsrdquo Bioinformatics vol14 no 9 pp 755ndash763 1998

[35] J R Koza F H Bennett D Andre and M A Keane ldquoAuto-mated design of both the topology and sizing of analog electricalcircuits using genetic programmingrdquo in In Artificial intelligencein design rsquo96 pp 151ndash170 Springer Netherlands 1996

[36] T Oladipupo ldquoIntroduction to machine learningrdquo in In Newadvances in machine learning InTech 2010

[37] H Mannila ldquoData mining machine learning statistics anddatabasesrdquo in Proceedings of the 8th International Conferenceon Scientific and Statistical Data Base Management IEEEStockholm Sweden Sweden 2002

[38] M Troc and O Unold ldquoSelf-adaptation of parameters in alearning classifier system ensemble machinerdquo InternationalJournal of Applied Mathematics and Computer Science vol 20no 1 pp 157ndash174 2010

[39] T Hastie R Tibshirani and J Friedman The Elements ofStatistical Learning Springer-Verlag New York NY USA 2009

[40] N J Nilsson ldquoArtificial intelligence A modern approachrdquoArtificial Intelligence vol 82 no 1-2 pp 369ndash380 1996

[41] I Kavakiotis O Tsave A Salifoglou N Maglaveras I Vla-havas and I Chouvarda ldquoMachine Learning and Data MiningMethods in Diabetes Researchrdquo Computational and StructuralBiotechnology Journal vol 15 pp 104ndash116 2017

[42] M Mohri A Rostamizadeh and A Talwalkar Foundations ofmachine learning MIT press 2012

[43] Y Freund and R E Schapire ldquoA decision-theoretic generaliza-tion of on-line learning and an application to boostingrdquo Journalof Computer and System Sciences vol 55 no 1 part 2 pp 119ndash139 1997

[44] R S Michalski J G Carbonell and T M Mitchell ldquoMachinelearning 1983rdquo

[45] O Kramer ldquoK-nearest neighborsrdquo in Dimensionality reductionwith unsupervised nearest neighbors vol 51 pp 13ndash23 SpringerBerlin Heidelberg Germany 2013

[46] C Cortes and V Vapnik ldquoSupport-vector networksrdquo MachineLearning vol 20 no 3 pp 273ndash297 1995

8 Mathematical Problems in Engineering

Table 5 LTTP evaluation based on the different ML models

Link road Road type Evaluation kNN SVM RF

B-E

Fixed

MAD 591119864 minus 04 509119864 minus 04 456E minus 04MAPE 178119864 + 01 158119864 + 01 144E + 01

E-H MAD 944119864 minus 04 332E minus 04 637119864 minus 04MAPE 249119864 + 01 957E + 00 181119864 + 01

H-J MAD 516119864 minus 04 355119864 minus 04 354E minus 04MAPE 214119864 + 01 159119864 + 01 148E + 01

B-D

Temporary

MAD 171119864 minus 03 544E minus 04 670119864 minus 04MAPE 275119864 + 01 809E + 00 990119864 + 00

E-F MAD 959119864 minus 04 805119864 minus 04 563E minus 04MAPE 313119864 + 01 294119864 + 01 182E + 01

G-H MAD 118119864 minus 03 735E minus 04 785119864 minus 04MAPE 342119864 + 01 194E + 01 238119864 + 01

4

Rece

nt h

istor

ical

dat

a

2

Data predicted

Calculatingthe average time

(i) Same link road (ii) Same load status(iii) Same truck type

3001357

001421

001409BELAZB-E

001357

Empty

Empty

BELAZB-E

001821LoadB-E MT-86

001421EmptyB-E BELAZ

001715B-E EmptyMT-86

1

Figure 6 The flow chart of traditional averaging methods

Table 6 Summary of the optimal ML prediction models for eachlink road

Road Type Optimal ML modelB-E

FixedRF

E-H SVMH-J RFB-D

TemporarySVM

E-F RFG-H SVM

Table 7 1198772 values of the different ML models for each link road

Road SVM KNN RF Optimal ML modelB-E 028 016 041 SVME-H 083 016 067 SVMH-J 072 013 056 SVMB-D 089 023 07 SVME-F 054 024 073 RFG-H 061 019 062 RF

from the traditional averaging methods are summarized inTable 8

Smaller MAD and MAPE values mean better predictionperformance of the traditional averaging methods and the

smallest records are highlighted in Table 8The predicted val-ues obtained from the optimal ML method and a traditionalaverage method for each link road are given in Table 9 thedecrease in the MAPE is also shown

Table 9 shows that the tested ML models are superiorto the traditional averaging method in the context of LTTPbecause the former has smaller MAPEs An average increaseof 1579 in prediction accuracy is achieved in all experimen-tal link roads in which increases of 1254 and 1930 forthree fixed and three temporary roads respectively are alsoobtained

33 Discussion of Meteorological Features This study alsoconsidered the influence of meteorological features on theLTTP of an open-pit mine The data were obtained froma CMA monitoring station including 5 variables pressurewind speed temperature relative humidity and precipita-tion

The Pearson correlation coefficient (PCC) an evaluationmethod developed by Pearson [59] was used to evaluate thelinear correlation between two variables The expression ofthe PPC is as follows

120588119883119884 = cov (119883 119884)120590119883120590119884 (5)

Mathematical Problems in Engineering 9

Table 8 Results obtained from the traditional averaging methods

Road Evaluation Traditional averaging methods10 records 20 records 30 records 40 records 50 records

B-E MAD 102119864 minus 03 949119864 minus 04 917119864 minus 04 918119864 minus 04 904E minus 04MAPE 306119864 + 01 281119864 + 01 266119864 + 01 264119864 + 01 258E + 01

E-H MAD 122119864 minus 03 113119864 minus 03 109119864 minus 03 109119864 minus 03 107E minus 03MAPE 329119864 + 01 300119864 + 01 284119864 + 01 281119864 + 01 273E + 01

H-J MAD 629119864 minus 04 609119864 minus 04 587119864 minus 04 581119864 minus 04 580E minus 04MAPE 254119864 + 01 247119864 + 01 236119864 + 01 234119864 + 01 233E + 01

B-D MAD 215119864 minus 03 183E minus 03 246119864 minus 03 236119864 minus 03 205119864 minus 03MAPE 317119864 + 01 269E + 01 386119864 + 01 362119864 + 01 325119864 + 01

E-F MAD 116119864 minus 03 110E minus 03 114119864 minus 03 115119864 minus 03 116119864 minus 03MAPE 391119864 + 01 363E + 01 381119864 + 01 390119864 + 01 395119864 + 01

G-H MAD 129E minus 03 138119864 minus 03 136119864 minus 03 132119864 minus 03 130119864 minus 03MAPE 404E + 01 412119864 + 01 391119864 + 01 370119864 + 01 357119864 + 01

Table 9 Comparison between the optimal ML model and the optimal averaging method

Road Type Optimal average method (MAPE) Optimal ML model (MAPE) MAPE decrease AverageB-E

Fixed258119864 + 01 144119864 + 01 1140

1254E-H 273119864 + 01 957119864 + 00 1773H-J 233119864 + 01 148119864 + 01 850B-D

Temporary269119864 + 01 809119864 + 00 1881

1930E-F 363119864 + 01 182119864 + 01 1810G-H 404119864 + 01 194119864 + 01 2100Average 1579

Table 10 Prediction results after including meteorological data

Type Road Methods Meteorological features MAD MAPE MAPE decrease (no-yes)

Temporary

B-E RF No 690119864 minus 04 207119864 + 01 630Yes 456119864 minus 04 144119864 + 01

E-H SVM No 341119864 minus 04 169119864 + 01 728Yes 332119864 minus 04 957119864 + 00

H-J RF No 416119864 minus 04 186119864 + 01 380Yes 354119864 minus 04 148119864 + 01

Fixed

B-D SVM No 635119864 minus 04 122119864 + 01 408Yes 544119864 minus 04 809119864 + 00

E-F RF No 660119864 minus 04 217119864 + 01 350Yes 563119864 minus 04 182119864 + 01

G-H SVM No 842119864 minus 04 252119864 + 01 580Yes 735119864 minus 04 194119864 + 01

Average 513

where cov(119883 119884) is the covariance 120590119883 is the standard devia-tion of119883 and 120590119884 is the standard deviation of 119884

The PPC values of different variables are shown inFigure 7 including the 5 meteorological variables and trucktravel time A high PCC value indicates a closer relationshipbetween the two variables

Following controlled experiments the effect of meteo-rological features was investigated by adding or removingindividual features We selected the optimal ML model for

each link road The raw (observation) values and predictedresults withwithout meteorological features are shown inFigure 8

The results of the controlled experiments are shownin Table 10 the calculated decrease in the MAPE is alsoshown The results considering meteorological features arebetter than those withoutmeteorological featuresTheMAPEdecreased by 513 on average for all link roads after addingthe meteorological data

10 Mathematical Problems in Engineering

Pressure08

Wind speed04

Temperature

00

Relative humidity

Precipitation

Travel time

minus04

minus08

Pres

sure

Win

d sp

eed

Tem

pera

ture

Relat

ive h

umid

ity

Prec

ipita

tion

Trav

el tim

e

1

1

1

1

1

1

minus048 minus048

minus048

minus048

064

064

minus0041 minus0019

minus0019

005

005

minus0088

minus0088

minus082

minus082

047

012

012

047 minus064 014

014

0049

0049

minus0041

minus0054

minus0054

0045

0045

minus064

Figure 7 The PCC heat map of meteorological features

Table 11 Evaluation of LTTP based on different ML models

Link road Road type Evaluation kNN SVM RF

A-B Fixed MAD 495119864 minus 04 328119864 minus 04 299E minus 04MAPE 469119864 + 01 340119864 + 01 336E + 01

34 Discussion of LTTP and RTTP The above experimentsused the link rather than the route to predict the travel timeof OPTs However the differences between LTTP and RTTPneed to be further discussed In the ensuing discussion thelongest route between dump point A and load point G isselected as shown in Figure 9

The A-G route consists of 4 links A-B B-E E-H and H-G Among them the optimal ML prediction models of B-EE-H andH-G are SVM RF and SVM respectivelyThe sameexperimental procedure as used in Section 31 was used toobtain the optimal MLmodel for A-B and Table 11 shows theMAD and MAPE values of the three ML methods It can beseen that the RF model is the best ML method for link A-B

The SVM and RF methods are used to predict the RTTPof A-G because those two models have a good predictionperformance Thus the experiments are summarized asfollows

(i) RTTP (SVM) using the SVM algorithm to train theTTP model for the route A-G

(ii) RTTP (RF) using the RF algorithm to train the TTPmodel for the route A-G

(iii) LTTP using the optimalMLmodel for each link thatis A-B (RF) B-E (SVM) E-H (RF) and H-G (SVM)and the truck travel time of A-G is the sum of eachLTTP result

Raw values and predicted results of the above threeexperiments are shown in Figure 10 while the evaluated

Table 12 Evaluation of the results between LTTP and RTTP

Method Model Evaluation Values

RTTP SVM MAD 155119864 minus 03MAPE 208119864 + 01

RTTP RF MAD 178119864 minus 03MAPE 235119864 + 01

LTTP Assemble MAD 834E minus 04MAPE 898E + 00

results of those experiments are shown in Table 12 Both theMAD and MAPE values of the LTTP approach are smallerthan the two RTTP methods Thus using the link as theprediction unit is better than using the route

4 Conclusions

The link roads of an open-pit mine are divided into fixedand temporary roads in this paper Three ML algorithmsthat is kNN SVM and RF are used for the LTTP of OPTsThe experimental results not only reflect the self-adaptive andself-feedback characteristics of the ML algorithms but alsodemonstrate the practicality of themethod for road segmentsThe conclusions based on the results are as follows

(1) LTTP models based on ML are more efficient andaccurate than traditional averaging methods Anoverall average increase of 1579 in the predictionaccuracy is obtained for six experimental link roads

Mathematical Problems in Engineering 11

000100000200000300000400000500000600000700000800000900001000001100001200

Link

trav

el tim

e

0 10 15 20 25 30 35 40 45 505G-H (SVM)

000100

000200

000300

000400

000500

000600

000700

000800

Link

trav

el tim

e

0 10 15 20 25 30 35 40 45 505H-J (RF)

000200000300000400000500000600000700000800000900001000001100001200

Link

trav

el tim

e

0 5 15 20 25 30 35 40 45 5010E-H (SVM)

000100

000200

000300

000400

000500

000600

000700

000800

Link

trav

el tim

e

0 5 15 20 25 30 35 40 45 5010E-F (RF)

000400000500000600000700000800000900001000001100001200001300001400001500001600001700001800001900002000002100002200

Link

trav

el tim

e

0 5 15 20 25 30 35 40 45 5010B-D (SVM)

000200

000300

000400

000500

000600

000700

000800

000900

001000

Link

trav

el tim

e

0 10 15 20 25 30 35 40 45 505B-E (RF)

Raw valueWithout meteorological featuresMeteorological features

Raw valueWithout meteorological featuresMeteorological features

Figure 8 Comparison forecast results including and excluding meteorological features

For temporary roads the average accuracy increasesby 1930

(2) LTTP models established using the SVM and RFalgorithms are better than those established using thekNN approach There is no large difference betweenthe SVM and RF results although the RF algorithmrequires less space and time complexity than the SVMalgorithm

(3) This paper is original in that it considers the effectof meteorological features on LTTP The results show

that considering the effect of meteorological featureson LTTP increases the prediction accuracy by 513

(4) The differences between LTTP and RTTP are alsodiscussed and the former has a higher predictionaccuracy The MAPE decreases by 1182 for theLTTP method

Some work is already underway to incorporate the MLprediction models into the OPATDS of the FWOM whichwill be helpful in improving the dispatching efficiency of theOPTs

12 Mathematical Problems in Engineering

Node J

Load G

Node E

Load F

Dump ANode B

Load D

Load C

Node H

Fixed roadsTemporary roads

Figure 9 The location of the route A-G in the FWOM roadmap

Raw valuesRTTP (RF)

RTTP (SVM)LTTP

5 10 15 20 25 30 35 40 45 500Route A-G

000600000800001000001200001400001600001800002000002200

Truc

k tr

avel

tim

e

Figure 10 Prediction results for RTTP (RF) RTTP (SVM) andLTTP

Data Availability

The data used to support the findings of this study areavailable from the corresponding author upon request

Conflicts of Interest

The authors declare no conflicts of interest

Authorsrsquo Contributions

Xiaoyu Sun as the principal investigator provided the dataused to train the ML models Hang Zhang performed theexperiments andwrote the paper Fengliang Tian contributedthe programming Lei Yang proofread the manuscript

Acknowledgments

This work was funded by the National Natural ScienceFoundation of China (no 51674063) and the NationalKey Research and Development Program of China (no2016YFC0801608)

References

[1] J Czaplicki Shovel-Truck Systems CRC Press 2008[2] J M Czaplicki ldquoModelling and analysis of the exploitation

process of a shovel-truck systemrdquo in Shovel-Truck Systems pp79ndash89 CRC Press 2008

[3] S G Ercelebi and A Bascetin ldquoOptimization of shovel-trucksystem for surface miningrdquo Journal of the Southern AfricanInstitute of Mining and Metallurgy vol 109 no 7 pp 433ndash4392009

[4] R Mena E Zio F Kristjanpoller and A Arata ldquoAvailability-based simulation and optimization modeling framework foropen-pit mine truck allocation under dynamic constraintsrdquoInternational Journal of Mining Science and Technology vol 23no 1 pp 113ndash119 2013

[5] F Soumis J Ethier and J Elbrond ldquoTruck dispatching inan open pit minerdquo International Journal of Surface MiningReclamation and Environment vol 3 no 2 pp 115ndash119 1989

[6] A Y F Fadin Komarudin and A O Moeis ldquoSimulation-optimization truck dispatch problem using look - ahead algo-rithm in open pit minesrdquo International Journal of GEOMATEvol 13 no 36 pp 80ndash86 2017

[7] Y Tan and S Takakuwa ldquoA practical simulation approachfor an effective truck dispatching system of open pit minesusing VBArdquo in Proceedings of the 2016 Winter SimulationConference WSC 2016 pp 2394ndash2405 IEEE Washington DCUSA December 2016

[8] J Li R Bai J Mao and W Li ldquoForecast of applied effect fortruck real-time dispatch system in open-pit mine based onCSUSSrdquo in Proceedings of the 2010 International Conference onE-Product E-Service and E-Entertainment ICEEE2010 pp 1ndash4IEEE Henan China November 2010

[9] S P Alarie and M Gamache ldquoOverview of solution strategiesused in truck dispatching systems for open pit minesrdquo Interna-tional Journal of Surface Mining Reclamation and Environmentvol 16 no 1 pp 59ndash76 2002

[10] B Kolonja D R Kalasky and J M Mutmansky ldquoOptimizationof dispatching criteria for open-pit truck haulage system designusingmultiple comparisons with the best and common random

Mathematical Problems in Engineering 13

numbersrdquo in Proceedings of the 25th Conference on Winter Sim-ulation WSC 1993 pp 393ndash401 ACM Los Angeles CaliforniaUSA December 1993

[11] Q Wang Y Zhang C Chen and W Xu ldquoOpen-pit mine truckreal-time dispatching principle under macroscopic controlrdquo inProceedings of the 1st International Conference on InnovativeComputing Information and Control 2006 ICICICrsquo06 pp 702ndash705 IEEE Beijing China September 2006

[12] Y Choi ldquoSimulation of Shovel-Truck Haulage Systems byConsidering Truck Dispatch Methodsrdquo Journal of the KoreanSociety of Mineral and Energy Resources Engineers vol 50 no4 p 543 2013

[13] E Topal and S Ramazan ldquoMining truck scheduling withstochastic maintenance costrdquo Journal of Coal Science andEngineering vol 18 no 3 pp 313ndash319 2012

[14] P Chaowasakoo H Seppala H Koivo and Q Zhou ldquoDigi-talization of mine operations Scenarios to benefit in real-timetruck dispatchingrdquo International Journal of Mining Science andTechnology vol 27 no 2 pp 229ndash236 2017

[15] Q Sun ldquoRoad running time statistics method in truck schedul-ingrdquo Opencast Coal Mining Technology vol 01 pp 35ndash37 1998

[16] R Bai J Li and J Xu ldquoReal-time dynamic forecast of truck linktravel timerdquo Journal of Liaoning Technical University vol 1 pp12ndash14 2005

[17] L Jiangang ldquoReal-time dynamic forecasts of truck link traveltime based on fuzzy neural networkrdquo Journal of the China CoalSociety vol 6 pp 796ndash800 2005

[18] E K Chanda and S Gardiner ldquoA comparative study of truckcycle time prediction methods in open-pit miningrdquo Engineer-ing Construction and Architectural Management vol 17 no 5pp 446ndash460 2010

[19] D J Edwards and I J Griffiths ldquoArtificial intelligence approachto calculation of hydraulic excavator cycle time and outputrdquoMining Technology vol 109 no 1 pp 23ndash29 2013

[20] K Erarslan ldquoModelling performance and retarder chart of off-highway trucks by cubic splines for cycle time estimationrdquoMining Technology vol 114 pp 161ndash166 2013

[21] X Xue W Sun and R Liang ldquoA new method of real-timedynamic forecast of truck link travel time in open minesrdquoJournal of the China Coal Society vol 37 no 8 pp 1418ndash14222012

[22] X Meng Research on scheduling services of open-pit mine basedon real-time travel time prediction China University of Miningand Technology 2014

[23] V Shalamanov V Pershin S Shabaev and D Boiko ldquoJustifi-cation of the Optimal Granulometric Composition of CrushedRocks for Open-Pit Mine Road Surfacingrdquo in Proceedings of the1st International InnovativeMining Symposium 2017 KemerovoRussia April 2017

[24] M Hofmann and M OrsquoMahony ldquoThe impact of adverseweather conditions on urban bus performance measuresrdquoin Proceedings of the 8th International IEEE Conference onIntelligent Transportation Systems pp 431ndash436 IEEE ViennaAustria September 2005

[25] T H Maze M Agarwal and G Burchett ldquoWhether weathermatters to traffic demand traffic safety and traffic operationsand flowrdquoTransportation Research Record no 1948 pp 170ndash1762006

[26] S A Silvester I S Lowndes and D M Hargreaves ldquoAcomputational study of particulate emissions from an openpit quarry under neutral atmospheric conditionsrdquo AtmosphericEnvironment vol 43 no 40 pp 6415ndash6424 2009

[27] I Tsapakis T Cheng and A Bolbol ldquoImpact of weather condi-tions on macroscopic urban travel timesrdquo Journal of TransportGeography vol 28 pp 204ndash211 2013

[28] TheMinistry of Land and Resources ldquoPRCThe basic situationof mineral resources in fushunrdquo httpwwwmlrgovcnkczyglkczydjtj201208t20120813 1130832htm

[29] G F Cooper and E Herskovits ldquoA Bayesian method forthe induction of probabilistic networks from datardquo MachineLearning vol 9 no 4 pp 309ndash347 1992

[30] C Yunqiang Z X Sean and T S Huang ldquoOne-class svm forlearning in image retrievalrdquo in In Proceedings 2001 InternationalConference on Image Processing (Cat No01CH37205) pp 34ndash372001

[31] T K Ho ldquoIn Random decision forestsrdquo in Proceedings of 3rdInternational Conference on Document Analysis and Recogni-tion IEEE 1995

[32] D G Kleinbaum and M Klein ldquoAnalysis of Matched DataUsing Logistic Regressionrdquo in Logistic Regression pp 389ndash428Springer New York NY USA 2010

[33] N S Altman ldquoAn introduction to kernel and nearest-neighbornonparametric regressionrdquo The American Statistician vol 46no 3 pp 175ndash185 1992

[34] S R Eddy ldquoProfile hiddenMarkovmodelsrdquo Bioinformatics vol14 no 9 pp 755ndash763 1998

[35] J R Koza F H Bennett D Andre and M A Keane ldquoAuto-mated design of both the topology and sizing of analog electricalcircuits using genetic programmingrdquo in In Artificial intelligencein design rsquo96 pp 151ndash170 Springer Netherlands 1996

[36] T Oladipupo ldquoIntroduction to machine learningrdquo in In Newadvances in machine learning InTech 2010

[37] H Mannila ldquoData mining machine learning statistics anddatabasesrdquo in Proceedings of the 8th International Conferenceon Scientific and Statistical Data Base Management IEEEStockholm Sweden Sweden 2002

[38] M Troc and O Unold ldquoSelf-adaptation of parameters in alearning classifier system ensemble machinerdquo InternationalJournal of Applied Mathematics and Computer Science vol 20no 1 pp 157ndash174 2010

[39] T Hastie R Tibshirani and J Friedman The Elements ofStatistical Learning Springer-Verlag New York NY USA 2009

[40] N J Nilsson ldquoArtificial intelligence A modern approachrdquoArtificial Intelligence vol 82 no 1-2 pp 369ndash380 1996

[41] I Kavakiotis O Tsave A Salifoglou N Maglaveras I Vla-havas and I Chouvarda ldquoMachine Learning and Data MiningMethods in Diabetes Researchrdquo Computational and StructuralBiotechnology Journal vol 15 pp 104ndash116 2017

[42] M Mohri A Rostamizadeh and A Talwalkar Foundations ofmachine learning MIT press 2012

[43] Y Freund and R E Schapire ldquoA decision-theoretic generaliza-tion of on-line learning and an application to boostingrdquo Journalof Computer and System Sciences vol 55 no 1 part 2 pp 119ndash139 1997

[44] R S Michalski J G Carbonell and T M Mitchell ldquoMachinelearning 1983rdquo

[45] O Kramer ldquoK-nearest neighborsrdquo in Dimensionality reductionwith unsupervised nearest neighbors vol 51 pp 13ndash23 SpringerBerlin Heidelberg Germany 2013

[46] C Cortes and V Vapnik ldquoSupport-vector networksrdquo MachineLearning vol 20 no 3 pp 273ndash297 1995

Mathematical Problems in Engineering 9

Table 8 Results obtained from the traditional averaging methods

Road Evaluation Traditional averaging methods10 records 20 records 30 records 40 records 50 records

B-E MAD 102119864 minus 03 949119864 minus 04 917119864 minus 04 918119864 minus 04 904E minus 04MAPE 306119864 + 01 281119864 + 01 266119864 + 01 264119864 + 01 258E + 01

E-H MAD 122119864 minus 03 113119864 minus 03 109119864 minus 03 109119864 minus 03 107E minus 03MAPE 329119864 + 01 300119864 + 01 284119864 + 01 281119864 + 01 273E + 01

H-J MAD 629119864 minus 04 609119864 minus 04 587119864 minus 04 581119864 minus 04 580E minus 04MAPE 254119864 + 01 247119864 + 01 236119864 + 01 234119864 + 01 233E + 01

B-D MAD 215119864 minus 03 183E minus 03 246119864 minus 03 236119864 minus 03 205119864 minus 03MAPE 317119864 + 01 269E + 01 386119864 + 01 362119864 + 01 325119864 + 01

E-F MAD 116119864 minus 03 110E minus 03 114119864 minus 03 115119864 minus 03 116119864 minus 03MAPE 391119864 + 01 363E + 01 381119864 + 01 390119864 + 01 395119864 + 01

G-H MAD 129E minus 03 138119864 minus 03 136119864 minus 03 132119864 minus 03 130119864 minus 03MAPE 404E + 01 412119864 + 01 391119864 + 01 370119864 + 01 357119864 + 01

Table 9 Comparison between the optimal ML model and the optimal averaging method

Road Type Optimal average method (MAPE) Optimal ML model (MAPE) MAPE decrease AverageB-E

Fixed258119864 + 01 144119864 + 01 1140

1254E-H 273119864 + 01 957119864 + 00 1773H-J 233119864 + 01 148119864 + 01 850B-D

Temporary269119864 + 01 809119864 + 00 1881

1930E-F 363119864 + 01 182119864 + 01 1810G-H 404119864 + 01 194119864 + 01 2100Average 1579

Table 10 Prediction results after including meteorological data

Type Road Methods Meteorological features MAD MAPE MAPE decrease (no-yes)

Temporary

B-E RF No 690119864 minus 04 207119864 + 01 630Yes 456119864 minus 04 144119864 + 01

E-H SVM No 341119864 minus 04 169119864 + 01 728Yes 332119864 minus 04 957119864 + 00

H-J RF No 416119864 minus 04 186119864 + 01 380Yes 354119864 minus 04 148119864 + 01

Fixed

B-D SVM No 635119864 minus 04 122119864 + 01 408Yes 544119864 minus 04 809119864 + 00

E-F RF No 660119864 minus 04 217119864 + 01 350Yes 563119864 minus 04 182119864 + 01

G-H SVM No 842119864 minus 04 252119864 + 01 580Yes 735119864 minus 04 194119864 + 01

Average 513

where cov(119883 119884) is the covariance 120590119883 is the standard devia-tion of119883 and 120590119884 is the standard deviation of 119884

The PPC values of different variables are shown inFigure 7 including the 5 meteorological variables and trucktravel time A high PCC value indicates a closer relationshipbetween the two variables

Following controlled experiments the effect of meteo-rological features was investigated by adding or removingindividual features We selected the optimal ML model for

each link road The raw (observation) values and predictedresults withwithout meteorological features are shown inFigure 8

The results of the controlled experiments are shownin Table 10 the calculated decrease in the MAPE is alsoshown The results considering meteorological features arebetter than those withoutmeteorological featuresTheMAPEdecreased by 513 on average for all link roads after addingthe meteorological data

10 Mathematical Problems in Engineering

Pressure08

Wind speed04

Temperature

00

Relative humidity

Precipitation

Travel time

minus04

minus08

Pres

sure

Win

d sp

eed

Tem

pera

ture

Relat

ive h

umid

ity

Prec

ipita

tion

Trav

el tim

e

1

1

1

1

1

1

minus048 minus048

minus048

minus048

064

064

minus0041 minus0019

minus0019

005

005

minus0088

minus0088

minus082

minus082

047

012

012

047 minus064 014

014

0049

0049

minus0041

minus0054

minus0054

0045

0045

minus064

Figure 7 The PCC heat map of meteorological features

Table 11 Evaluation of LTTP based on different ML models

Link road Road type Evaluation kNN SVM RF

A-B Fixed MAD 495119864 minus 04 328119864 minus 04 299E minus 04MAPE 469119864 + 01 340119864 + 01 336E + 01

34 Discussion of LTTP and RTTP The above experimentsused the link rather than the route to predict the travel timeof OPTs However the differences between LTTP and RTTPneed to be further discussed In the ensuing discussion thelongest route between dump point A and load point G isselected as shown in Figure 9

The A-G route consists of 4 links A-B B-E E-H and H-G Among them the optimal ML prediction models of B-EE-H andH-G are SVM RF and SVM respectivelyThe sameexperimental procedure as used in Section 31 was used toobtain the optimal MLmodel for A-B and Table 11 shows theMAD and MAPE values of the three ML methods It can beseen that the RF model is the best ML method for link A-B

The SVM and RF methods are used to predict the RTTPof A-G because those two models have a good predictionperformance Thus the experiments are summarized asfollows

(i) RTTP (SVM) using the SVM algorithm to train theTTP model for the route A-G

(ii) RTTP (RF) using the RF algorithm to train the TTPmodel for the route A-G

(iii) LTTP using the optimalMLmodel for each link thatis A-B (RF) B-E (SVM) E-H (RF) and H-G (SVM)and the truck travel time of A-G is the sum of eachLTTP result

Raw values and predicted results of the above threeexperiments are shown in Figure 10 while the evaluated

Table 12 Evaluation of the results between LTTP and RTTP

Method Model Evaluation Values

RTTP SVM MAD 155119864 minus 03MAPE 208119864 + 01

RTTP RF MAD 178119864 minus 03MAPE 235119864 + 01

LTTP Assemble MAD 834E minus 04MAPE 898E + 00

results of those experiments are shown in Table 12 Both theMAD and MAPE values of the LTTP approach are smallerthan the two RTTP methods Thus using the link as theprediction unit is better than using the route

4 Conclusions

The link roads of an open-pit mine are divided into fixedand temporary roads in this paper Three ML algorithmsthat is kNN SVM and RF are used for the LTTP of OPTsThe experimental results not only reflect the self-adaptive andself-feedback characteristics of the ML algorithms but alsodemonstrate the practicality of themethod for road segmentsThe conclusions based on the results are as follows

(1) LTTP models based on ML are more efficient andaccurate than traditional averaging methods Anoverall average increase of 1579 in the predictionaccuracy is obtained for six experimental link roads

Mathematical Problems in Engineering 11

000100000200000300000400000500000600000700000800000900001000001100001200

Link

trav

el tim

e

0 10 15 20 25 30 35 40 45 505G-H (SVM)

000100

000200

000300

000400

000500

000600

000700

000800

Link

trav

el tim

e

0 10 15 20 25 30 35 40 45 505H-J (RF)

000200000300000400000500000600000700000800000900001000001100001200

Link

trav

el tim

e

0 5 15 20 25 30 35 40 45 5010E-H (SVM)

000100

000200

000300

000400

000500

000600

000700

000800

Link

trav

el tim

e

0 5 15 20 25 30 35 40 45 5010E-F (RF)

000400000500000600000700000800000900001000001100001200001300001400001500001600001700001800001900002000002100002200

Link

trav

el tim

e

0 5 15 20 25 30 35 40 45 5010B-D (SVM)

000200

000300

000400

000500

000600

000700

000800

000900

001000

Link

trav

el tim

e

0 10 15 20 25 30 35 40 45 505B-E (RF)

Raw valueWithout meteorological featuresMeteorological features

Raw valueWithout meteorological featuresMeteorological features

Figure 8 Comparison forecast results including and excluding meteorological features

For temporary roads the average accuracy increasesby 1930

(2) LTTP models established using the SVM and RFalgorithms are better than those established using thekNN approach There is no large difference betweenthe SVM and RF results although the RF algorithmrequires less space and time complexity than the SVMalgorithm

(3) This paper is original in that it considers the effectof meteorological features on LTTP The results show

that considering the effect of meteorological featureson LTTP increases the prediction accuracy by 513

(4) The differences between LTTP and RTTP are alsodiscussed and the former has a higher predictionaccuracy The MAPE decreases by 1182 for theLTTP method

Some work is already underway to incorporate the MLprediction models into the OPATDS of the FWOM whichwill be helpful in improving the dispatching efficiency of theOPTs

12 Mathematical Problems in Engineering

Node J

Load G

Node E

Load F

Dump ANode B

Load D

Load C

Node H

Fixed roadsTemporary roads

Figure 9 The location of the route A-G in the FWOM roadmap

Raw valuesRTTP (RF)

RTTP (SVM)LTTP

5 10 15 20 25 30 35 40 45 500Route A-G

000600000800001000001200001400001600001800002000002200

Truc

k tr

avel

tim

e

Figure 10 Prediction results for RTTP (RF) RTTP (SVM) andLTTP

Data Availability

The data used to support the findings of this study areavailable from the corresponding author upon request

Conflicts of Interest

The authors declare no conflicts of interest

Authorsrsquo Contributions

Xiaoyu Sun as the principal investigator provided the dataused to train the ML models Hang Zhang performed theexperiments andwrote the paper Fengliang Tian contributedthe programming Lei Yang proofread the manuscript

Acknowledgments

This work was funded by the National Natural ScienceFoundation of China (no 51674063) and the NationalKey Research and Development Program of China (no2016YFC0801608)

References

[1] J Czaplicki Shovel-Truck Systems CRC Press 2008[2] J M Czaplicki ldquoModelling and analysis of the exploitation

process of a shovel-truck systemrdquo in Shovel-Truck Systems pp79ndash89 CRC Press 2008

[3] S G Ercelebi and A Bascetin ldquoOptimization of shovel-trucksystem for surface miningrdquo Journal of the Southern AfricanInstitute of Mining and Metallurgy vol 109 no 7 pp 433ndash4392009

[4] R Mena E Zio F Kristjanpoller and A Arata ldquoAvailability-based simulation and optimization modeling framework foropen-pit mine truck allocation under dynamic constraintsrdquoInternational Journal of Mining Science and Technology vol 23no 1 pp 113ndash119 2013

[5] F Soumis J Ethier and J Elbrond ldquoTruck dispatching inan open pit minerdquo International Journal of Surface MiningReclamation and Environment vol 3 no 2 pp 115ndash119 1989

[6] A Y F Fadin Komarudin and A O Moeis ldquoSimulation-optimization truck dispatch problem using look - ahead algo-rithm in open pit minesrdquo International Journal of GEOMATEvol 13 no 36 pp 80ndash86 2017

[7] Y Tan and S Takakuwa ldquoA practical simulation approachfor an effective truck dispatching system of open pit minesusing VBArdquo in Proceedings of the 2016 Winter SimulationConference WSC 2016 pp 2394ndash2405 IEEE Washington DCUSA December 2016

[8] J Li R Bai J Mao and W Li ldquoForecast of applied effect fortruck real-time dispatch system in open-pit mine based onCSUSSrdquo in Proceedings of the 2010 International Conference onE-Product E-Service and E-Entertainment ICEEE2010 pp 1ndash4IEEE Henan China November 2010

[9] S P Alarie and M Gamache ldquoOverview of solution strategiesused in truck dispatching systems for open pit minesrdquo Interna-tional Journal of Surface Mining Reclamation and Environmentvol 16 no 1 pp 59ndash76 2002

[10] B Kolonja D R Kalasky and J M Mutmansky ldquoOptimizationof dispatching criteria for open-pit truck haulage system designusingmultiple comparisons with the best and common random

Mathematical Problems in Engineering 13

numbersrdquo in Proceedings of the 25th Conference on Winter Sim-ulation WSC 1993 pp 393ndash401 ACM Los Angeles CaliforniaUSA December 1993

[11] Q Wang Y Zhang C Chen and W Xu ldquoOpen-pit mine truckreal-time dispatching principle under macroscopic controlrdquo inProceedings of the 1st International Conference on InnovativeComputing Information and Control 2006 ICICICrsquo06 pp 702ndash705 IEEE Beijing China September 2006

[12] Y Choi ldquoSimulation of Shovel-Truck Haulage Systems byConsidering Truck Dispatch Methodsrdquo Journal of the KoreanSociety of Mineral and Energy Resources Engineers vol 50 no4 p 543 2013

[13] E Topal and S Ramazan ldquoMining truck scheduling withstochastic maintenance costrdquo Journal of Coal Science andEngineering vol 18 no 3 pp 313ndash319 2012

[14] P Chaowasakoo H Seppala H Koivo and Q Zhou ldquoDigi-talization of mine operations Scenarios to benefit in real-timetruck dispatchingrdquo International Journal of Mining Science andTechnology vol 27 no 2 pp 229ndash236 2017

[15] Q Sun ldquoRoad running time statistics method in truck schedul-ingrdquo Opencast Coal Mining Technology vol 01 pp 35ndash37 1998

[16] R Bai J Li and J Xu ldquoReal-time dynamic forecast of truck linktravel timerdquo Journal of Liaoning Technical University vol 1 pp12ndash14 2005

[17] L Jiangang ldquoReal-time dynamic forecasts of truck link traveltime based on fuzzy neural networkrdquo Journal of the China CoalSociety vol 6 pp 796ndash800 2005

[18] E K Chanda and S Gardiner ldquoA comparative study of truckcycle time prediction methods in open-pit miningrdquo Engineer-ing Construction and Architectural Management vol 17 no 5pp 446ndash460 2010

[19] D J Edwards and I J Griffiths ldquoArtificial intelligence approachto calculation of hydraulic excavator cycle time and outputrdquoMining Technology vol 109 no 1 pp 23ndash29 2013

[20] K Erarslan ldquoModelling performance and retarder chart of off-highway trucks by cubic splines for cycle time estimationrdquoMining Technology vol 114 pp 161ndash166 2013

[21] X Xue W Sun and R Liang ldquoA new method of real-timedynamic forecast of truck link travel time in open minesrdquoJournal of the China Coal Society vol 37 no 8 pp 1418ndash14222012

[22] X Meng Research on scheduling services of open-pit mine basedon real-time travel time prediction China University of Miningand Technology 2014

[23] V Shalamanov V Pershin S Shabaev and D Boiko ldquoJustifi-cation of the Optimal Granulometric Composition of CrushedRocks for Open-Pit Mine Road Surfacingrdquo in Proceedings of the1st International InnovativeMining Symposium 2017 KemerovoRussia April 2017

[24] M Hofmann and M OrsquoMahony ldquoThe impact of adverseweather conditions on urban bus performance measuresrdquoin Proceedings of the 8th International IEEE Conference onIntelligent Transportation Systems pp 431ndash436 IEEE ViennaAustria September 2005

[25] T H Maze M Agarwal and G Burchett ldquoWhether weathermatters to traffic demand traffic safety and traffic operationsand flowrdquoTransportation Research Record no 1948 pp 170ndash1762006

[26] S A Silvester I S Lowndes and D M Hargreaves ldquoAcomputational study of particulate emissions from an openpit quarry under neutral atmospheric conditionsrdquo AtmosphericEnvironment vol 43 no 40 pp 6415ndash6424 2009

[27] I Tsapakis T Cheng and A Bolbol ldquoImpact of weather condi-tions on macroscopic urban travel timesrdquo Journal of TransportGeography vol 28 pp 204ndash211 2013

[28] TheMinistry of Land and Resources ldquoPRCThe basic situationof mineral resources in fushunrdquo httpwwwmlrgovcnkczyglkczydjtj201208t20120813 1130832htm

[29] G F Cooper and E Herskovits ldquoA Bayesian method forthe induction of probabilistic networks from datardquo MachineLearning vol 9 no 4 pp 309ndash347 1992

[30] C Yunqiang Z X Sean and T S Huang ldquoOne-class svm forlearning in image retrievalrdquo in In Proceedings 2001 InternationalConference on Image Processing (Cat No01CH37205) pp 34ndash372001

[31] T K Ho ldquoIn Random decision forestsrdquo in Proceedings of 3rdInternational Conference on Document Analysis and Recogni-tion IEEE 1995

[32] D G Kleinbaum and M Klein ldquoAnalysis of Matched DataUsing Logistic Regressionrdquo in Logistic Regression pp 389ndash428Springer New York NY USA 2010

[33] N S Altman ldquoAn introduction to kernel and nearest-neighbornonparametric regressionrdquo The American Statistician vol 46no 3 pp 175ndash185 1992

[34] S R Eddy ldquoProfile hiddenMarkovmodelsrdquo Bioinformatics vol14 no 9 pp 755ndash763 1998

[35] J R Koza F H Bennett D Andre and M A Keane ldquoAuto-mated design of both the topology and sizing of analog electricalcircuits using genetic programmingrdquo in In Artificial intelligencein design rsquo96 pp 151ndash170 Springer Netherlands 1996

[36] T Oladipupo ldquoIntroduction to machine learningrdquo in In Newadvances in machine learning InTech 2010

[37] H Mannila ldquoData mining machine learning statistics anddatabasesrdquo in Proceedings of the 8th International Conferenceon Scientific and Statistical Data Base Management IEEEStockholm Sweden Sweden 2002

[38] M Troc and O Unold ldquoSelf-adaptation of parameters in alearning classifier system ensemble machinerdquo InternationalJournal of Applied Mathematics and Computer Science vol 20no 1 pp 157ndash174 2010

[39] T Hastie R Tibshirani and J Friedman The Elements ofStatistical Learning Springer-Verlag New York NY USA 2009

[40] N J Nilsson ldquoArtificial intelligence A modern approachrdquoArtificial Intelligence vol 82 no 1-2 pp 369ndash380 1996

[41] I Kavakiotis O Tsave A Salifoglou N Maglaveras I Vla-havas and I Chouvarda ldquoMachine Learning and Data MiningMethods in Diabetes Researchrdquo Computational and StructuralBiotechnology Journal vol 15 pp 104ndash116 2017

[42] M Mohri A Rostamizadeh and A Talwalkar Foundations ofmachine learning MIT press 2012

[43] Y Freund and R E Schapire ldquoA decision-theoretic generaliza-tion of on-line learning and an application to boostingrdquo Journalof Computer and System Sciences vol 55 no 1 part 2 pp 119ndash139 1997

[44] R S Michalski J G Carbonell and T M Mitchell ldquoMachinelearning 1983rdquo

[45] O Kramer ldquoK-nearest neighborsrdquo in Dimensionality reductionwith unsupervised nearest neighbors vol 51 pp 13ndash23 SpringerBerlin Heidelberg Germany 2013

[46] C Cortes and V Vapnik ldquoSupport-vector networksrdquo MachineLearning vol 20 no 3 pp 273ndash297 1995

10 Mathematical Problems in Engineering

Pressure08

Wind speed04

Temperature

00

Relative humidity

Precipitation

Travel time

minus04

minus08

Pres

sure

Win

d sp

eed

Tem

pera

ture

Relat

ive h

umid

ity

Prec

ipita

tion

Trav

el tim

e

1

1

1

1

1

1

minus048 minus048

minus048

minus048

064

064

minus0041 minus0019

minus0019

005

005

minus0088

minus0088

minus082

minus082

047

012

012

047 minus064 014

014

0049

0049

minus0041

minus0054

minus0054

0045

0045

minus064

Figure 7 The PCC heat map of meteorological features

Table 11 Evaluation of LTTP based on different ML models

Link road Road type Evaluation kNN SVM RF

A-B Fixed MAD 495119864 minus 04 328119864 minus 04 299E minus 04MAPE 469119864 + 01 340119864 + 01 336E + 01

34 Discussion of LTTP and RTTP The above experimentsused the link rather than the route to predict the travel timeof OPTs However the differences between LTTP and RTTPneed to be further discussed In the ensuing discussion thelongest route between dump point A and load point G isselected as shown in Figure 9

The A-G route consists of 4 links A-B B-E E-H and H-G Among them the optimal ML prediction models of B-EE-H andH-G are SVM RF and SVM respectivelyThe sameexperimental procedure as used in Section 31 was used toobtain the optimal MLmodel for A-B and Table 11 shows theMAD and MAPE values of the three ML methods It can beseen that the RF model is the best ML method for link A-B

The SVM and RF methods are used to predict the RTTPof A-G because those two models have a good predictionperformance Thus the experiments are summarized asfollows

(i) RTTP (SVM) using the SVM algorithm to train theTTP model for the route A-G

(ii) RTTP (RF) using the RF algorithm to train the TTPmodel for the route A-G

(iii) LTTP using the optimalMLmodel for each link thatis A-B (RF) B-E (SVM) E-H (RF) and H-G (SVM)and the truck travel time of A-G is the sum of eachLTTP result

Raw values and predicted results of the above threeexperiments are shown in Figure 10 while the evaluated

Table 12 Evaluation of the results between LTTP and RTTP

Method Model Evaluation Values

RTTP SVM MAD 155119864 minus 03MAPE 208119864 + 01

RTTP RF MAD 178119864 minus 03MAPE 235119864 + 01

LTTP Assemble MAD 834E minus 04MAPE 898E + 00

results of those experiments are shown in Table 12 Both theMAD and MAPE values of the LTTP approach are smallerthan the two RTTP methods Thus using the link as theprediction unit is better than using the route

4 Conclusions

The link roads of an open-pit mine are divided into fixedand temporary roads in this paper Three ML algorithmsthat is kNN SVM and RF are used for the LTTP of OPTsThe experimental results not only reflect the self-adaptive andself-feedback characteristics of the ML algorithms but alsodemonstrate the practicality of themethod for road segmentsThe conclusions based on the results are as follows

(1) LTTP models based on ML are more efficient andaccurate than traditional averaging methods Anoverall average increase of 1579 in the predictionaccuracy is obtained for six experimental link roads

Mathematical Problems in Engineering 11

000100000200000300000400000500000600000700000800000900001000001100001200

Link

trav

el tim

e

0 10 15 20 25 30 35 40 45 505G-H (SVM)

000100

000200

000300

000400

000500

000600

000700

000800

Link

trav

el tim

e

0 10 15 20 25 30 35 40 45 505H-J (RF)

000200000300000400000500000600000700000800000900001000001100001200

Link

trav

el tim

e

0 5 15 20 25 30 35 40 45 5010E-H (SVM)

000100

000200

000300

000400

000500

000600

000700

000800

Link

trav

el tim

e

0 5 15 20 25 30 35 40 45 5010E-F (RF)

000400000500000600000700000800000900001000001100001200001300001400001500001600001700001800001900002000002100002200

Link

trav

el tim

e

0 5 15 20 25 30 35 40 45 5010B-D (SVM)

000200

000300

000400

000500

000600

000700

000800

000900

001000

Link

trav

el tim

e

0 10 15 20 25 30 35 40 45 505B-E (RF)

Raw valueWithout meteorological featuresMeteorological features

Raw valueWithout meteorological featuresMeteorological features

Figure 8 Comparison forecast results including and excluding meteorological features

For temporary roads the average accuracy increasesby 1930

(2) LTTP models established using the SVM and RFalgorithms are better than those established using thekNN approach There is no large difference betweenthe SVM and RF results although the RF algorithmrequires less space and time complexity than the SVMalgorithm

(3) This paper is original in that it considers the effectof meteorological features on LTTP The results show

that considering the effect of meteorological featureson LTTP increases the prediction accuracy by 513

(4) The differences between LTTP and RTTP are alsodiscussed and the former has a higher predictionaccuracy The MAPE decreases by 1182 for theLTTP method

Some work is already underway to incorporate the MLprediction models into the OPATDS of the FWOM whichwill be helpful in improving the dispatching efficiency of theOPTs

12 Mathematical Problems in Engineering

Node J

Load G

Node E

Load F

Dump ANode B

Load D

Load C

Node H

Fixed roadsTemporary roads

Figure 9 The location of the route A-G in the FWOM roadmap

Raw valuesRTTP (RF)

RTTP (SVM)LTTP

5 10 15 20 25 30 35 40 45 500Route A-G

000600000800001000001200001400001600001800002000002200

Truc

k tr

avel

tim

e

Figure 10 Prediction results for RTTP (RF) RTTP (SVM) andLTTP

Data Availability

The data used to support the findings of this study areavailable from the corresponding author upon request

Conflicts of Interest

The authors declare no conflicts of interest

Authorsrsquo Contributions

Xiaoyu Sun as the principal investigator provided the dataused to train the ML models Hang Zhang performed theexperiments andwrote the paper Fengliang Tian contributedthe programming Lei Yang proofread the manuscript

Acknowledgments

This work was funded by the National Natural ScienceFoundation of China (no 51674063) and the NationalKey Research and Development Program of China (no2016YFC0801608)

References

[1] J Czaplicki Shovel-Truck Systems CRC Press 2008[2] J M Czaplicki ldquoModelling and analysis of the exploitation

process of a shovel-truck systemrdquo in Shovel-Truck Systems pp79ndash89 CRC Press 2008

[3] S G Ercelebi and A Bascetin ldquoOptimization of shovel-trucksystem for surface miningrdquo Journal of the Southern AfricanInstitute of Mining and Metallurgy vol 109 no 7 pp 433ndash4392009

[4] R Mena E Zio F Kristjanpoller and A Arata ldquoAvailability-based simulation and optimization modeling framework foropen-pit mine truck allocation under dynamic constraintsrdquoInternational Journal of Mining Science and Technology vol 23no 1 pp 113ndash119 2013

[5] F Soumis J Ethier and J Elbrond ldquoTruck dispatching inan open pit minerdquo International Journal of Surface MiningReclamation and Environment vol 3 no 2 pp 115ndash119 1989

[6] A Y F Fadin Komarudin and A O Moeis ldquoSimulation-optimization truck dispatch problem using look - ahead algo-rithm in open pit minesrdquo International Journal of GEOMATEvol 13 no 36 pp 80ndash86 2017

[7] Y Tan and S Takakuwa ldquoA practical simulation approachfor an effective truck dispatching system of open pit minesusing VBArdquo in Proceedings of the 2016 Winter SimulationConference WSC 2016 pp 2394ndash2405 IEEE Washington DCUSA December 2016

[8] J Li R Bai J Mao and W Li ldquoForecast of applied effect fortruck real-time dispatch system in open-pit mine based onCSUSSrdquo in Proceedings of the 2010 International Conference onE-Product E-Service and E-Entertainment ICEEE2010 pp 1ndash4IEEE Henan China November 2010

[9] S P Alarie and M Gamache ldquoOverview of solution strategiesused in truck dispatching systems for open pit minesrdquo Interna-tional Journal of Surface Mining Reclamation and Environmentvol 16 no 1 pp 59ndash76 2002

[10] B Kolonja D R Kalasky and J M Mutmansky ldquoOptimizationof dispatching criteria for open-pit truck haulage system designusingmultiple comparisons with the best and common random

Mathematical Problems in Engineering 13

numbersrdquo in Proceedings of the 25th Conference on Winter Sim-ulation WSC 1993 pp 393ndash401 ACM Los Angeles CaliforniaUSA December 1993

[11] Q Wang Y Zhang C Chen and W Xu ldquoOpen-pit mine truckreal-time dispatching principle under macroscopic controlrdquo inProceedings of the 1st International Conference on InnovativeComputing Information and Control 2006 ICICICrsquo06 pp 702ndash705 IEEE Beijing China September 2006

[12] Y Choi ldquoSimulation of Shovel-Truck Haulage Systems byConsidering Truck Dispatch Methodsrdquo Journal of the KoreanSociety of Mineral and Energy Resources Engineers vol 50 no4 p 543 2013

[13] E Topal and S Ramazan ldquoMining truck scheduling withstochastic maintenance costrdquo Journal of Coal Science andEngineering vol 18 no 3 pp 313ndash319 2012

[14] P Chaowasakoo H Seppala H Koivo and Q Zhou ldquoDigi-talization of mine operations Scenarios to benefit in real-timetruck dispatchingrdquo International Journal of Mining Science andTechnology vol 27 no 2 pp 229ndash236 2017

[15] Q Sun ldquoRoad running time statistics method in truck schedul-ingrdquo Opencast Coal Mining Technology vol 01 pp 35ndash37 1998

[16] R Bai J Li and J Xu ldquoReal-time dynamic forecast of truck linktravel timerdquo Journal of Liaoning Technical University vol 1 pp12ndash14 2005

[17] L Jiangang ldquoReal-time dynamic forecasts of truck link traveltime based on fuzzy neural networkrdquo Journal of the China CoalSociety vol 6 pp 796ndash800 2005

[18] E K Chanda and S Gardiner ldquoA comparative study of truckcycle time prediction methods in open-pit miningrdquo Engineer-ing Construction and Architectural Management vol 17 no 5pp 446ndash460 2010

[19] D J Edwards and I J Griffiths ldquoArtificial intelligence approachto calculation of hydraulic excavator cycle time and outputrdquoMining Technology vol 109 no 1 pp 23ndash29 2013

[20] K Erarslan ldquoModelling performance and retarder chart of off-highway trucks by cubic splines for cycle time estimationrdquoMining Technology vol 114 pp 161ndash166 2013

[21] X Xue W Sun and R Liang ldquoA new method of real-timedynamic forecast of truck link travel time in open minesrdquoJournal of the China Coal Society vol 37 no 8 pp 1418ndash14222012

[22] X Meng Research on scheduling services of open-pit mine basedon real-time travel time prediction China University of Miningand Technology 2014

[23] V Shalamanov V Pershin S Shabaev and D Boiko ldquoJustifi-cation of the Optimal Granulometric Composition of CrushedRocks for Open-Pit Mine Road Surfacingrdquo in Proceedings of the1st International InnovativeMining Symposium 2017 KemerovoRussia April 2017

[24] M Hofmann and M OrsquoMahony ldquoThe impact of adverseweather conditions on urban bus performance measuresrdquoin Proceedings of the 8th International IEEE Conference onIntelligent Transportation Systems pp 431ndash436 IEEE ViennaAustria September 2005

[25] T H Maze M Agarwal and G Burchett ldquoWhether weathermatters to traffic demand traffic safety and traffic operationsand flowrdquoTransportation Research Record no 1948 pp 170ndash1762006

[26] S A Silvester I S Lowndes and D M Hargreaves ldquoAcomputational study of particulate emissions from an openpit quarry under neutral atmospheric conditionsrdquo AtmosphericEnvironment vol 43 no 40 pp 6415ndash6424 2009

[27] I Tsapakis T Cheng and A Bolbol ldquoImpact of weather condi-tions on macroscopic urban travel timesrdquo Journal of TransportGeography vol 28 pp 204ndash211 2013

[28] TheMinistry of Land and Resources ldquoPRCThe basic situationof mineral resources in fushunrdquo httpwwwmlrgovcnkczyglkczydjtj201208t20120813 1130832htm

[29] G F Cooper and E Herskovits ldquoA Bayesian method forthe induction of probabilistic networks from datardquo MachineLearning vol 9 no 4 pp 309ndash347 1992

[30] C Yunqiang Z X Sean and T S Huang ldquoOne-class svm forlearning in image retrievalrdquo in In Proceedings 2001 InternationalConference on Image Processing (Cat No01CH37205) pp 34ndash372001

[31] T K Ho ldquoIn Random decision forestsrdquo in Proceedings of 3rdInternational Conference on Document Analysis and Recogni-tion IEEE 1995

[32] D G Kleinbaum and M Klein ldquoAnalysis of Matched DataUsing Logistic Regressionrdquo in Logistic Regression pp 389ndash428Springer New York NY USA 2010

[33] N S Altman ldquoAn introduction to kernel and nearest-neighbornonparametric regressionrdquo The American Statistician vol 46no 3 pp 175ndash185 1992

[34] S R Eddy ldquoProfile hiddenMarkovmodelsrdquo Bioinformatics vol14 no 9 pp 755ndash763 1998

[35] J R Koza F H Bennett D Andre and M A Keane ldquoAuto-mated design of both the topology and sizing of analog electricalcircuits using genetic programmingrdquo in In Artificial intelligencein design rsquo96 pp 151ndash170 Springer Netherlands 1996

[36] T Oladipupo ldquoIntroduction to machine learningrdquo in In Newadvances in machine learning InTech 2010

[37] H Mannila ldquoData mining machine learning statistics anddatabasesrdquo in Proceedings of the 8th International Conferenceon Scientific and Statistical Data Base Management IEEEStockholm Sweden Sweden 2002

[38] M Troc and O Unold ldquoSelf-adaptation of parameters in alearning classifier system ensemble machinerdquo InternationalJournal of Applied Mathematics and Computer Science vol 20no 1 pp 157ndash174 2010

[39] T Hastie R Tibshirani and J Friedman The Elements ofStatistical Learning Springer-Verlag New York NY USA 2009

[40] N J Nilsson ldquoArtificial intelligence A modern approachrdquoArtificial Intelligence vol 82 no 1-2 pp 369ndash380 1996

[41] I Kavakiotis O Tsave A Salifoglou N Maglaveras I Vla-havas and I Chouvarda ldquoMachine Learning and Data MiningMethods in Diabetes Researchrdquo Computational and StructuralBiotechnology Journal vol 15 pp 104ndash116 2017

[42] M Mohri A Rostamizadeh and A Talwalkar Foundations ofmachine learning MIT press 2012

[43] Y Freund and R E Schapire ldquoA decision-theoretic generaliza-tion of on-line learning and an application to boostingrdquo Journalof Computer and System Sciences vol 55 no 1 part 2 pp 119ndash139 1997

[44] R S Michalski J G Carbonell and T M Mitchell ldquoMachinelearning 1983rdquo

[45] O Kramer ldquoK-nearest neighborsrdquo in Dimensionality reductionwith unsupervised nearest neighbors vol 51 pp 13ndash23 SpringerBerlin Heidelberg Germany 2013

[46] C Cortes and V Vapnik ldquoSupport-vector networksrdquo MachineLearning vol 20 no 3 pp 273ndash297 1995

Mathematical Problems in Engineering 11

000100000200000300000400000500000600000700000800000900001000001100001200

Link

trav

el tim

e

0 10 15 20 25 30 35 40 45 505G-H (SVM)

000100

000200

000300

000400

000500

000600

000700

000800

Link

trav

el tim

e

0 10 15 20 25 30 35 40 45 505H-J (RF)

000200000300000400000500000600000700000800000900001000001100001200

Link

trav

el tim

e

0 5 15 20 25 30 35 40 45 5010E-H (SVM)

000100

000200

000300

000400

000500

000600

000700

000800

Link

trav

el tim

e

0 5 15 20 25 30 35 40 45 5010E-F (RF)

000400000500000600000700000800000900001000001100001200001300001400001500001600001700001800001900002000002100002200

Link

trav

el tim

e

0 5 15 20 25 30 35 40 45 5010B-D (SVM)

000200

000300

000400

000500

000600

000700

000800

000900

001000

Link

trav

el tim

e

0 10 15 20 25 30 35 40 45 505B-E (RF)

Raw valueWithout meteorological featuresMeteorological features

Raw valueWithout meteorological featuresMeteorological features

Figure 8 Comparison forecast results including and excluding meteorological features

For temporary roads the average accuracy increasesby 1930

(2) LTTP models established using the SVM and RFalgorithms are better than those established using thekNN approach There is no large difference betweenthe SVM and RF results although the RF algorithmrequires less space and time complexity than the SVMalgorithm

(3) This paper is original in that it considers the effectof meteorological features on LTTP The results show

that considering the effect of meteorological featureson LTTP increases the prediction accuracy by 513

(4) The differences between LTTP and RTTP are alsodiscussed and the former has a higher predictionaccuracy The MAPE decreases by 1182 for theLTTP method

Some work is already underway to incorporate the MLprediction models into the OPATDS of the FWOM whichwill be helpful in improving the dispatching efficiency of theOPTs

12 Mathematical Problems in Engineering

Node J

Load G

Node E

Load F

Dump ANode B

Load D

Load C

Node H

Fixed roadsTemporary roads

Figure 9 The location of the route A-G in the FWOM roadmap

Raw valuesRTTP (RF)

RTTP (SVM)LTTP

5 10 15 20 25 30 35 40 45 500Route A-G

000600000800001000001200001400001600001800002000002200

Truc

k tr

avel

tim

e

Figure 10 Prediction results for RTTP (RF) RTTP (SVM) andLTTP

Data Availability

The data used to support the findings of this study areavailable from the corresponding author upon request

Conflicts of Interest

The authors declare no conflicts of interest

Authorsrsquo Contributions

Xiaoyu Sun as the principal investigator provided the dataused to train the ML models Hang Zhang performed theexperiments andwrote the paper Fengliang Tian contributedthe programming Lei Yang proofread the manuscript

Acknowledgments

This work was funded by the National Natural ScienceFoundation of China (no 51674063) and the NationalKey Research and Development Program of China (no2016YFC0801608)

References

[1] J Czaplicki Shovel-Truck Systems CRC Press 2008[2] J M Czaplicki ldquoModelling and analysis of the exploitation

process of a shovel-truck systemrdquo in Shovel-Truck Systems pp79ndash89 CRC Press 2008

[3] S G Ercelebi and A Bascetin ldquoOptimization of shovel-trucksystem for surface miningrdquo Journal of the Southern AfricanInstitute of Mining and Metallurgy vol 109 no 7 pp 433ndash4392009

[4] R Mena E Zio F Kristjanpoller and A Arata ldquoAvailability-based simulation and optimization modeling framework foropen-pit mine truck allocation under dynamic constraintsrdquoInternational Journal of Mining Science and Technology vol 23no 1 pp 113ndash119 2013

[5] F Soumis J Ethier and J Elbrond ldquoTruck dispatching inan open pit minerdquo International Journal of Surface MiningReclamation and Environment vol 3 no 2 pp 115ndash119 1989

[6] A Y F Fadin Komarudin and A O Moeis ldquoSimulation-optimization truck dispatch problem using look - ahead algo-rithm in open pit minesrdquo International Journal of GEOMATEvol 13 no 36 pp 80ndash86 2017

[7] Y Tan and S Takakuwa ldquoA practical simulation approachfor an effective truck dispatching system of open pit minesusing VBArdquo in Proceedings of the 2016 Winter SimulationConference WSC 2016 pp 2394ndash2405 IEEE Washington DCUSA December 2016

[8] J Li R Bai J Mao and W Li ldquoForecast of applied effect fortruck real-time dispatch system in open-pit mine based onCSUSSrdquo in Proceedings of the 2010 International Conference onE-Product E-Service and E-Entertainment ICEEE2010 pp 1ndash4IEEE Henan China November 2010

[9] S P Alarie and M Gamache ldquoOverview of solution strategiesused in truck dispatching systems for open pit minesrdquo Interna-tional Journal of Surface Mining Reclamation and Environmentvol 16 no 1 pp 59ndash76 2002

[10] B Kolonja D R Kalasky and J M Mutmansky ldquoOptimizationof dispatching criteria for open-pit truck haulage system designusingmultiple comparisons with the best and common random

Mathematical Problems in Engineering 13

numbersrdquo in Proceedings of the 25th Conference on Winter Sim-ulation WSC 1993 pp 393ndash401 ACM Los Angeles CaliforniaUSA December 1993

[11] Q Wang Y Zhang C Chen and W Xu ldquoOpen-pit mine truckreal-time dispatching principle under macroscopic controlrdquo inProceedings of the 1st International Conference on InnovativeComputing Information and Control 2006 ICICICrsquo06 pp 702ndash705 IEEE Beijing China September 2006

[12] Y Choi ldquoSimulation of Shovel-Truck Haulage Systems byConsidering Truck Dispatch Methodsrdquo Journal of the KoreanSociety of Mineral and Energy Resources Engineers vol 50 no4 p 543 2013

[13] E Topal and S Ramazan ldquoMining truck scheduling withstochastic maintenance costrdquo Journal of Coal Science andEngineering vol 18 no 3 pp 313ndash319 2012

[14] P Chaowasakoo H Seppala H Koivo and Q Zhou ldquoDigi-talization of mine operations Scenarios to benefit in real-timetruck dispatchingrdquo International Journal of Mining Science andTechnology vol 27 no 2 pp 229ndash236 2017

[15] Q Sun ldquoRoad running time statistics method in truck schedul-ingrdquo Opencast Coal Mining Technology vol 01 pp 35ndash37 1998

[16] R Bai J Li and J Xu ldquoReal-time dynamic forecast of truck linktravel timerdquo Journal of Liaoning Technical University vol 1 pp12ndash14 2005

[17] L Jiangang ldquoReal-time dynamic forecasts of truck link traveltime based on fuzzy neural networkrdquo Journal of the China CoalSociety vol 6 pp 796ndash800 2005

[18] E K Chanda and S Gardiner ldquoA comparative study of truckcycle time prediction methods in open-pit miningrdquo Engineer-ing Construction and Architectural Management vol 17 no 5pp 446ndash460 2010

[19] D J Edwards and I J Griffiths ldquoArtificial intelligence approachto calculation of hydraulic excavator cycle time and outputrdquoMining Technology vol 109 no 1 pp 23ndash29 2013

[20] K Erarslan ldquoModelling performance and retarder chart of off-highway trucks by cubic splines for cycle time estimationrdquoMining Technology vol 114 pp 161ndash166 2013

[21] X Xue W Sun and R Liang ldquoA new method of real-timedynamic forecast of truck link travel time in open minesrdquoJournal of the China Coal Society vol 37 no 8 pp 1418ndash14222012

[22] X Meng Research on scheduling services of open-pit mine basedon real-time travel time prediction China University of Miningand Technology 2014

[23] V Shalamanov V Pershin S Shabaev and D Boiko ldquoJustifi-cation of the Optimal Granulometric Composition of CrushedRocks for Open-Pit Mine Road Surfacingrdquo in Proceedings of the1st International InnovativeMining Symposium 2017 KemerovoRussia April 2017

[24] M Hofmann and M OrsquoMahony ldquoThe impact of adverseweather conditions on urban bus performance measuresrdquoin Proceedings of the 8th International IEEE Conference onIntelligent Transportation Systems pp 431ndash436 IEEE ViennaAustria September 2005

[25] T H Maze M Agarwal and G Burchett ldquoWhether weathermatters to traffic demand traffic safety and traffic operationsand flowrdquoTransportation Research Record no 1948 pp 170ndash1762006

[26] S A Silvester I S Lowndes and D M Hargreaves ldquoAcomputational study of particulate emissions from an openpit quarry under neutral atmospheric conditionsrdquo AtmosphericEnvironment vol 43 no 40 pp 6415ndash6424 2009

[27] I Tsapakis T Cheng and A Bolbol ldquoImpact of weather condi-tions on macroscopic urban travel timesrdquo Journal of TransportGeography vol 28 pp 204ndash211 2013

[28] TheMinistry of Land and Resources ldquoPRCThe basic situationof mineral resources in fushunrdquo httpwwwmlrgovcnkczyglkczydjtj201208t20120813 1130832htm

[29] G F Cooper and E Herskovits ldquoA Bayesian method forthe induction of probabilistic networks from datardquo MachineLearning vol 9 no 4 pp 309ndash347 1992

[30] C Yunqiang Z X Sean and T S Huang ldquoOne-class svm forlearning in image retrievalrdquo in In Proceedings 2001 InternationalConference on Image Processing (Cat No01CH37205) pp 34ndash372001

[31] T K Ho ldquoIn Random decision forestsrdquo in Proceedings of 3rdInternational Conference on Document Analysis and Recogni-tion IEEE 1995

[32] D G Kleinbaum and M Klein ldquoAnalysis of Matched DataUsing Logistic Regressionrdquo in Logistic Regression pp 389ndash428Springer New York NY USA 2010

[33] N S Altman ldquoAn introduction to kernel and nearest-neighbornonparametric regressionrdquo The American Statistician vol 46no 3 pp 175ndash185 1992

[34] S R Eddy ldquoProfile hiddenMarkovmodelsrdquo Bioinformatics vol14 no 9 pp 755ndash763 1998

[35] J R Koza F H Bennett D Andre and M A Keane ldquoAuto-mated design of both the topology and sizing of analog electricalcircuits using genetic programmingrdquo in In Artificial intelligencein design rsquo96 pp 151ndash170 Springer Netherlands 1996

[36] T Oladipupo ldquoIntroduction to machine learningrdquo in In Newadvances in machine learning InTech 2010

[37] H Mannila ldquoData mining machine learning statistics anddatabasesrdquo in Proceedings of the 8th International Conferenceon Scientific and Statistical Data Base Management IEEEStockholm Sweden Sweden 2002

[38] M Troc and O Unold ldquoSelf-adaptation of parameters in alearning classifier system ensemble machinerdquo InternationalJournal of Applied Mathematics and Computer Science vol 20no 1 pp 157ndash174 2010

[39] T Hastie R Tibshirani and J Friedman The Elements ofStatistical Learning Springer-Verlag New York NY USA 2009

[40] N J Nilsson ldquoArtificial intelligence A modern approachrdquoArtificial Intelligence vol 82 no 1-2 pp 369ndash380 1996

[41] I Kavakiotis O Tsave A Salifoglou N Maglaveras I Vla-havas and I Chouvarda ldquoMachine Learning and Data MiningMethods in Diabetes Researchrdquo Computational and StructuralBiotechnology Journal vol 15 pp 104ndash116 2017

[42] M Mohri A Rostamizadeh and A Talwalkar Foundations ofmachine learning MIT press 2012

[43] Y Freund and R E Schapire ldquoA decision-theoretic generaliza-tion of on-line learning and an application to boostingrdquo Journalof Computer and System Sciences vol 55 no 1 part 2 pp 119ndash139 1997

[44] R S Michalski J G Carbonell and T M Mitchell ldquoMachinelearning 1983rdquo

[45] O Kramer ldquoK-nearest neighborsrdquo in Dimensionality reductionwith unsupervised nearest neighbors vol 51 pp 13ndash23 SpringerBerlin Heidelberg Germany 2013

[46] C Cortes and V Vapnik ldquoSupport-vector networksrdquo MachineLearning vol 20 no 3 pp 273ndash297 1995

12 Mathematical Problems in Engineering

Node J

Load G

Node E

Load F

Dump ANode B

Load D

Load C

Node H

Fixed roadsTemporary roads

Figure 9 The location of the route A-G in the FWOM roadmap

Raw valuesRTTP (RF)

RTTP (SVM)LTTP

5 10 15 20 25 30 35 40 45 500Route A-G

000600000800001000001200001400001600001800002000002200

Truc

k tr

avel

tim

e

Figure 10 Prediction results for RTTP (RF) RTTP (SVM) andLTTP

Data Availability

The data used to support the findings of this study areavailable from the corresponding author upon request

Conflicts of Interest

The authors declare no conflicts of interest

Authorsrsquo Contributions

Xiaoyu Sun as the principal investigator provided the dataused to train the ML models Hang Zhang performed theexperiments andwrote the paper Fengliang Tian contributedthe programming Lei Yang proofread the manuscript

Acknowledgments

This work was funded by the National Natural ScienceFoundation of China (no 51674063) and the NationalKey Research and Development Program of China (no2016YFC0801608)

References

[1] J Czaplicki Shovel-Truck Systems CRC Press 2008[2] J M Czaplicki ldquoModelling and analysis of the exploitation

process of a shovel-truck systemrdquo in Shovel-Truck Systems pp79ndash89 CRC Press 2008

[3] S G Ercelebi and A Bascetin ldquoOptimization of shovel-trucksystem for surface miningrdquo Journal of the Southern AfricanInstitute of Mining and Metallurgy vol 109 no 7 pp 433ndash4392009

[4] R Mena E Zio F Kristjanpoller and A Arata ldquoAvailability-based simulation and optimization modeling framework foropen-pit mine truck allocation under dynamic constraintsrdquoInternational Journal of Mining Science and Technology vol 23no 1 pp 113ndash119 2013

[5] F Soumis J Ethier and J Elbrond ldquoTruck dispatching inan open pit minerdquo International Journal of Surface MiningReclamation and Environment vol 3 no 2 pp 115ndash119 1989

[6] A Y F Fadin Komarudin and A O Moeis ldquoSimulation-optimization truck dispatch problem using look - ahead algo-rithm in open pit minesrdquo International Journal of GEOMATEvol 13 no 36 pp 80ndash86 2017

[7] Y Tan and S Takakuwa ldquoA practical simulation approachfor an effective truck dispatching system of open pit minesusing VBArdquo in Proceedings of the 2016 Winter SimulationConference WSC 2016 pp 2394ndash2405 IEEE Washington DCUSA December 2016

[8] J Li R Bai J Mao and W Li ldquoForecast of applied effect fortruck real-time dispatch system in open-pit mine based onCSUSSrdquo in Proceedings of the 2010 International Conference onE-Product E-Service and E-Entertainment ICEEE2010 pp 1ndash4IEEE Henan China November 2010

[9] S P Alarie and M Gamache ldquoOverview of solution strategiesused in truck dispatching systems for open pit minesrdquo Interna-tional Journal of Surface Mining Reclamation and Environmentvol 16 no 1 pp 59ndash76 2002

[10] B Kolonja D R Kalasky and J M Mutmansky ldquoOptimizationof dispatching criteria for open-pit truck haulage system designusingmultiple comparisons with the best and common random

Mathematical Problems in Engineering 13

numbersrdquo in Proceedings of the 25th Conference on Winter Sim-ulation WSC 1993 pp 393ndash401 ACM Los Angeles CaliforniaUSA December 1993

[11] Q Wang Y Zhang C Chen and W Xu ldquoOpen-pit mine truckreal-time dispatching principle under macroscopic controlrdquo inProceedings of the 1st International Conference on InnovativeComputing Information and Control 2006 ICICICrsquo06 pp 702ndash705 IEEE Beijing China September 2006

[12] Y Choi ldquoSimulation of Shovel-Truck Haulage Systems byConsidering Truck Dispatch Methodsrdquo Journal of the KoreanSociety of Mineral and Energy Resources Engineers vol 50 no4 p 543 2013

[13] E Topal and S Ramazan ldquoMining truck scheduling withstochastic maintenance costrdquo Journal of Coal Science andEngineering vol 18 no 3 pp 313ndash319 2012

[14] P Chaowasakoo H Seppala H Koivo and Q Zhou ldquoDigi-talization of mine operations Scenarios to benefit in real-timetruck dispatchingrdquo International Journal of Mining Science andTechnology vol 27 no 2 pp 229ndash236 2017

[15] Q Sun ldquoRoad running time statistics method in truck schedul-ingrdquo Opencast Coal Mining Technology vol 01 pp 35ndash37 1998

[16] R Bai J Li and J Xu ldquoReal-time dynamic forecast of truck linktravel timerdquo Journal of Liaoning Technical University vol 1 pp12ndash14 2005

[17] L Jiangang ldquoReal-time dynamic forecasts of truck link traveltime based on fuzzy neural networkrdquo Journal of the China CoalSociety vol 6 pp 796ndash800 2005

[18] E K Chanda and S Gardiner ldquoA comparative study of truckcycle time prediction methods in open-pit miningrdquo Engineer-ing Construction and Architectural Management vol 17 no 5pp 446ndash460 2010

[19] D J Edwards and I J Griffiths ldquoArtificial intelligence approachto calculation of hydraulic excavator cycle time and outputrdquoMining Technology vol 109 no 1 pp 23ndash29 2013

[20] K Erarslan ldquoModelling performance and retarder chart of off-highway trucks by cubic splines for cycle time estimationrdquoMining Technology vol 114 pp 161ndash166 2013

[21] X Xue W Sun and R Liang ldquoA new method of real-timedynamic forecast of truck link travel time in open minesrdquoJournal of the China Coal Society vol 37 no 8 pp 1418ndash14222012

[22] X Meng Research on scheduling services of open-pit mine basedon real-time travel time prediction China University of Miningand Technology 2014

[23] V Shalamanov V Pershin S Shabaev and D Boiko ldquoJustifi-cation of the Optimal Granulometric Composition of CrushedRocks for Open-Pit Mine Road Surfacingrdquo in Proceedings of the1st International InnovativeMining Symposium 2017 KemerovoRussia April 2017

[24] M Hofmann and M OrsquoMahony ldquoThe impact of adverseweather conditions on urban bus performance measuresrdquoin Proceedings of the 8th International IEEE Conference onIntelligent Transportation Systems pp 431ndash436 IEEE ViennaAustria September 2005

[25] T H Maze M Agarwal and G Burchett ldquoWhether weathermatters to traffic demand traffic safety and traffic operationsand flowrdquoTransportation Research Record no 1948 pp 170ndash1762006

[26] S A Silvester I S Lowndes and D M Hargreaves ldquoAcomputational study of particulate emissions from an openpit quarry under neutral atmospheric conditionsrdquo AtmosphericEnvironment vol 43 no 40 pp 6415ndash6424 2009

[27] I Tsapakis T Cheng and A Bolbol ldquoImpact of weather condi-tions on macroscopic urban travel timesrdquo Journal of TransportGeography vol 28 pp 204ndash211 2013

[28] TheMinistry of Land and Resources ldquoPRCThe basic situationof mineral resources in fushunrdquo httpwwwmlrgovcnkczyglkczydjtj201208t20120813 1130832htm

[29] G F Cooper and E Herskovits ldquoA Bayesian method forthe induction of probabilistic networks from datardquo MachineLearning vol 9 no 4 pp 309ndash347 1992

[30] C Yunqiang Z X Sean and T S Huang ldquoOne-class svm forlearning in image retrievalrdquo in In Proceedings 2001 InternationalConference on Image Processing (Cat No01CH37205) pp 34ndash372001

[31] T K Ho ldquoIn Random decision forestsrdquo in Proceedings of 3rdInternational Conference on Document Analysis and Recogni-tion IEEE 1995

[32] D G Kleinbaum and M Klein ldquoAnalysis of Matched DataUsing Logistic Regressionrdquo in Logistic Regression pp 389ndash428Springer New York NY USA 2010

[33] N S Altman ldquoAn introduction to kernel and nearest-neighbornonparametric regressionrdquo The American Statistician vol 46no 3 pp 175ndash185 1992

[34] S R Eddy ldquoProfile hiddenMarkovmodelsrdquo Bioinformatics vol14 no 9 pp 755ndash763 1998

[35] J R Koza F H Bennett D Andre and M A Keane ldquoAuto-mated design of both the topology and sizing of analog electricalcircuits using genetic programmingrdquo in In Artificial intelligencein design rsquo96 pp 151ndash170 Springer Netherlands 1996

[36] T Oladipupo ldquoIntroduction to machine learningrdquo in In Newadvances in machine learning InTech 2010

[37] H Mannila ldquoData mining machine learning statistics anddatabasesrdquo in Proceedings of the 8th International Conferenceon Scientific and Statistical Data Base Management IEEEStockholm Sweden Sweden 2002

[38] M Troc and O Unold ldquoSelf-adaptation of parameters in alearning classifier system ensemble machinerdquo InternationalJournal of Applied Mathematics and Computer Science vol 20no 1 pp 157ndash174 2010

[39] T Hastie R Tibshirani and J Friedman The Elements ofStatistical Learning Springer-Verlag New York NY USA 2009

[40] N J Nilsson ldquoArtificial intelligence A modern approachrdquoArtificial Intelligence vol 82 no 1-2 pp 369ndash380 1996

[41] I Kavakiotis O Tsave A Salifoglou N Maglaveras I Vla-havas and I Chouvarda ldquoMachine Learning and Data MiningMethods in Diabetes Researchrdquo Computational and StructuralBiotechnology Journal vol 15 pp 104ndash116 2017

[42] M Mohri A Rostamizadeh and A Talwalkar Foundations ofmachine learning MIT press 2012

[43] Y Freund and R E Schapire ldquoA decision-theoretic generaliza-tion of on-line learning and an application to boostingrdquo Journalof Computer and System Sciences vol 55 no 1 part 2 pp 119ndash139 1997

[44] R S Michalski J G Carbonell and T M Mitchell ldquoMachinelearning 1983rdquo

[45] O Kramer ldquoK-nearest neighborsrdquo in Dimensionality reductionwith unsupervised nearest neighbors vol 51 pp 13ndash23 SpringerBerlin Heidelberg Germany 2013

[46] C Cortes and V Vapnik ldquoSupport-vector networksrdquo MachineLearning vol 20 no 3 pp 273ndash297 1995

Mathematical Problems in Engineering 13

numbersrdquo in Proceedings of the 25th Conference on Winter Sim-ulation WSC 1993 pp 393ndash401 ACM Los Angeles CaliforniaUSA December 1993

[11] Q Wang Y Zhang C Chen and W Xu ldquoOpen-pit mine truckreal-time dispatching principle under macroscopic controlrdquo inProceedings of the 1st International Conference on InnovativeComputing Information and Control 2006 ICICICrsquo06 pp 702ndash705 IEEE Beijing China September 2006

[12] Y Choi ldquoSimulation of Shovel-Truck Haulage Systems byConsidering Truck Dispatch Methodsrdquo Journal of the KoreanSociety of Mineral and Energy Resources Engineers vol 50 no4 p 543 2013

[13] E Topal and S Ramazan ldquoMining truck scheduling withstochastic maintenance costrdquo Journal of Coal Science andEngineering vol 18 no 3 pp 313ndash319 2012

[14] P Chaowasakoo H Seppala H Koivo and Q Zhou ldquoDigi-talization of mine operations Scenarios to benefit in real-timetruck dispatchingrdquo International Journal of Mining Science andTechnology vol 27 no 2 pp 229ndash236 2017

[15] Q Sun ldquoRoad running time statistics method in truck schedul-ingrdquo Opencast Coal Mining Technology vol 01 pp 35ndash37 1998

[16] R Bai J Li and J Xu ldquoReal-time dynamic forecast of truck linktravel timerdquo Journal of Liaoning Technical University vol 1 pp12ndash14 2005

[17] L Jiangang ldquoReal-time dynamic forecasts of truck link traveltime based on fuzzy neural networkrdquo Journal of the China CoalSociety vol 6 pp 796ndash800 2005

[18] E K Chanda and S Gardiner ldquoA comparative study of truckcycle time prediction methods in open-pit miningrdquo Engineer-ing Construction and Architectural Management vol 17 no 5pp 446ndash460 2010

[19] D J Edwards and I J Griffiths ldquoArtificial intelligence approachto calculation of hydraulic excavator cycle time and outputrdquoMining Technology vol 109 no 1 pp 23ndash29 2013

[20] K Erarslan ldquoModelling performance and retarder chart of off-highway trucks by cubic splines for cycle time estimationrdquoMining Technology vol 114 pp 161ndash166 2013

[21] X Xue W Sun and R Liang ldquoA new method of real-timedynamic forecast of truck link travel time in open minesrdquoJournal of the China Coal Society vol 37 no 8 pp 1418ndash14222012

[22] X Meng Research on scheduling services of open-pit mine basedon real-time travel time prediction China University of Miningand Technology 2014

[23] V Shalamanov V Pershin S Shabaev and D Boiko ldquoJustifi-cation of the Optimal Granulometric Composition of CrushedRocks for Open-Pit Mine Road Surfacingrdquo in Proceedings of the1st International InnovativeMining Symposium 2017 KemerovoRussia April 2017

[24] M Hofmann and M OrsquoMahony ldquoThe impact of adverseweather conditions on urban bus performance measuresrdquoin Proceedings of the 8th International IEEE Conference onIntelligent Transportation Systems pp 431ndash436 IEEE ViennaAustria September 2005

[25] T H Maze M Agarwal and G Burchett ldquoWhether weathermatters to traffic demand traffic safety and traffic operationsand flowrdquoTransportation Research Record no 1948 pp 170ndash1762006

[26] S A Silvester I S Lowndes and D M Hargreaves ldquoAcomputational study of particulate emissions from an openpit quarry under neutral atmospheric conditionsrdquo AtmosphericEnvironment vol 43 no 40 pp 6415ndash6424 2009

[27] I Tsapakis T Cheng and A Bolbol ldquoImpact of weather condi-tions on macroscopic urban travel timesrdquo Journal of TransportGeography vol 28 pp 204ndash211 2013

[28] TheMinistry of Land and Resources ldquoPRCThe basic situationof mineral resources in fushunrdquo httpwwwmlrgovcnkczyglkczydjtj201208t20120813 1130832htm

[29] G F Cooper and E Herskovits ldquoA Bayesian method forthe induction of probabilistic networks from datardquo MachineLearning vol 9 no 4 pp 309ndash347 1992

[30] C Yunqiang Z X Sean and T S Huang ldquoOne-class svm forlearning in image retrievalrdquo in In Proceedings 2001 InternationalConference on Image Processing (Cat No01CH37205) pp 34ndash372001

[31] T K Ho ldquoIn Random decision forestsrdquo in Proceedings of 3rdInternational Conference on Document Analysis and Recogni-tion IEEE 1995

[32] D G Kleinbaum and M Klein ldquoAnalysis of Matched DataUsing Logistic Regressionrdquo in Logistic Regression pp 389ndash428Springer New York NY USA 2010

[33] N S Altman ldquoAn introduction to kernel and nearest-neighbornonparametric regressionrdquo The American Statistician vol 46no 3 pp 175ndash185 1992

[34] S R Eddy ldquoProfile hiddenMarkovmodelsrdquo Bioinformatics vol14 no 9 pp 755ndash763 1998

[35] J R Koza F H Bennett D Andre and M A Keane ldquoAuto-mated design of both the topology and sizing of analog electricalcircuits using genetic programmingrdquo in In Artificial intelligencein design rsquo96 pp 151ndash170 Springer Netherlands 1996

[36] T Oladipupo ldquoIntroduction to machine learningrdquo in In Newadvances in machine learning InTech 2010

[37] H Mannila ldquoData mining machine learning statistics anddatabasesrdquo in Proceedings of the 8th International Conferenceon Scientific and Statistical Data Base Management IEEEStockholm Sweden Sweden 2002

[38] M Troc and O Unold ldquoSelf-adaptation of parameters in alearning classifier system ensemble machinerdquo InternationalJournal of Applied Mathematics and Computer Science vol 20no 1 pp 157ndash174 2010

[39] T Hastie R Tibshirani and J Friedman The Elements ofStatistical Learning Springer-Verlag New York NY USA 2009

[40] N J Nilsson ldquoArtificial intelligence A modern approachrdquoArtificial Intelligence vol 82 no 1-2 pp 369ndash380 1996

[41] I Kavakiotis O Tsave A Salifoglou N Maglaveras I Vla-havas and I Chouvarda ldquoMachine Learning and Data MiningMethods in Diabetes Researchrdquo Computational and StructuralBiotechnology Journal vol 15 pp 104ndash116 2017

[42] M Mohri A Rostamizadeh and A Talwalkar Foundations ofmachine learning MIT press 2012

[43] Y Freund and R E Schapire ldquoA decision-theoretic generaliza-tion of on-line learning and an application to boostingrdquo Journalof Computer and System Sciences vol 55 no 1 part 2 pp 119ndash139 1997

[44] R S Michalski J G Carbonell and T M Mitchell ldquoMachinelearning 1983rdquo

[45] O Kramer ldquoK-nearest neighborsrdquo in Dimensionality reductionwith unsupervised nearest neighbors vol 51 pp 13ndash23 SpringerBerlin Heidelberg Germany 2013

[46] C Cortes and V Vapnik ldquoSupport-vector networksrdquo MachineLearning vol 20 no 3 pp 273ndash297 1995

14 Mathematical Problems in Engineering

[47] C Campbell and Y Ying ldquoLearning with support vectormachinesrdquo Synthesis Lectures on Artificial Intelligence andMachine Learning vol 10 pp 1ndash95 2011

[48] A J Smola and B Scholkopf ldquoA tutorial on support vectorregressionrdquo Statistics and Computing vol 14 no 3 pp 199ndash2222004

[49] L Breiman ldquoBagging predictorsrdquoMachine Learning vol 24 no2 pp 123ndash140 1996

[50] G Tsoumakas I Katakis and I Vlahavas ldquoMining multi-labeldatardquo in In Data mining and knowledge discovery handbook pp667ndash685 2009

[51] J Asamer and M Reinthaler ldquoEstimation of road capacity andfree flow speed for urban roads under adverse weather condi-tionsrdquo in Proceedings of the 13th International IEEE Conferenceon Intelligent Transportation Systems (ITSC 2010) pp 812ndash818IEEE Funchal Portugal September 2010

[52] F Nelli ldquoMachine learning with scikit-learnrdquo in In Python DataAnalytics pp 237ndash264 Apress 2015

[53] O Kramer ldquoScikit-Learnrdquo in Machine Learning for EvolutionStrategies pp 45ndash53 Springer International Publishing 2016

[54] HKonno andHYamazaki ldquoMean-absolute deviation portfoliooptimization model and its applications to tokyo stock marketrdquoManagement Science vol 37 pp 519ndash531 1991

[55] E R Ziegel E L Lehmann and G Casella ldquoTheory of PointEstimationrdquo Technometrics vol 41 no 3 p 274 1999

[56] R J Hyndman and A B Koehler ldquoAnother look at measures offorecast accuracyrdquo International Journal of Forecasting vol 22no 4 pp 679ndash688 2006

[57] Minitab ldquoWhat are mape mad and msdrdquo httpsupportmin-itabcomen-usminitab17topic-librarymodeling-statisticstime-seriestime-series-modelswhat-are-mape-mad-and-msd

[58] StatTrek ldquoCoefficient of determinationrdquo httpstattrekcomstatisticsdictionaryaspxdefinition=coefficient of determina-tion

[59] K Pearson ldquoNote on regression and inheritance in the caseof two parentsrdquo Proceedings of The Royal Society of London(1854ndash1905) vol 58 pp 240ndash242 1895

Hindawiwwwhindawicom Volume 2018

MathematicsJournal of

Hindawiwwwhindawicom Volume 2018

Mathematical Problems in Engineering

Applied MathematicsJournal of

Hindawiwwwhindawicom Volume 2018

Probability and StatisticsHindawiwwwhindawicom Volume 2018

Journal of

Hindawiwwwhindawicom Volume 2018

Mathematical PhysicsAdvances in

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Function SpacesAbstract and Applied AnalysisHindawiwwwhindawicom Volume 2018

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Hindawi Publishing Corporation httpwwwhindawicom Volume 2013Hindawiwwwhindawicom

The Scientific World Journal

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Hindawiwwwhindawicom Volume 2018Volume 2018

Numerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisNumerical AnalysisAdvances inAdvances in Discrete Dynamics in

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