MultiobjectiveConstructionOptimizationModelBasedon …downloads.hindawi.com/journals/ace/2019/5153082.pdf · 2019-07-30 · MATLAB 2016b. After running the optimization, the results

Research ArticleMultiobjective Construction Optimization Model Based onQuantum Genetic Algorithm

Wei He and Yichao Shi

College of Civil Engineering and Mechanics Yanshan University Qinhuangdao 066004 Hebei China

Correspondence should be addressed to Wei He heweiysueducn

Received 16 March 2019 Accepted 23 May 2019 Published 1 July 2019

Academic Editor Tayfun Dede

Copyright copy 2019 Wei He and Yichao Shi is is an open access article distributed under the Creative Commons AttributionLicense which permits unrestricted use distribution and reproduction in any medium provided the original work isproperly cited

It is critical for the construction party to meet the established economic and social demand for the construction project with theshortest construction period and the lowest cost In this study the construction characteristics of the project were analyzed Inaddition the multiconstraint and multitarget construction optimization model with minimum period and cost was establishedbased on the quantum genetic algorithm In order to improve the adaptability of the quantum genetic algorithm for themultiobjective model the encoding form quantum revolving door and genetic flow of the algorithm were reconstructedMATLAB 2016b was used as the simulation platform and the implementation of the algorithm was improved according to thecharacteristics of the variables in the construction project including period and cost Finally the optimization of the algorithmwas verified and analyzed by an engineering example e results showed that using the multiobjective quantum genetic al-gorithm the optimal durationcost can be achieved and the most reasonable and effective control decision scheme for theconstruction management can be provided through the Pareto solution set

1 Introduction

With the development of the world economy more andmore attention has been paid to the duration and cost ofprojects [1] Large construction projects have large capitalinvestment and long construction cycle [2] In order tominimize the duration and cost of the project it is critical todesign an effective construction organization plan [3] epurpose of the construction plan is to obtain a short con-struction period and a low cost Researchers have focused onthe studies to optimize the period and cost of constructionHowever in the optimization algorithm there is an in-evitable conflict between schedule and cost [4] ereforeoptimization is also known as striking a balance betweenduration and cost [5] e optimization balance means thatunder the constraints of personnel machinery and mate-rials managers can reasonably allocate resources to achievetheminimum combination of time and cost by appropriatelyincreasing the costtime of subprojects under the samecircumstances [6]

Traditional balance strategy includes the critical pathmethod integer programming method and enumerationmethod However due to the expansion of the constructionproject scale nowadays the computational complexity hasbeen growing exponentially [7] us it is difficult for thesemethods to meet the computing requirements of large-scaleconstruction projects [8] It is very urgent to find an al-gorithm that can find a quick accurate and effective op-timization balance of period and cost ie shortenedconstruction period and reduced cost without breaking thearchitectural design and function In recent years theheuristic algorithm with global search ability has been usedto solve optimization problems including the Jaya algo-rithm [9 10] particle swarm algorithm [11] colony al-gorithm [12] simulated annealing algorithm [13] harmonysearch algorithm logic [14] and other hybrid algorithms[15 16] In general the balance between duration and costwhich is the focus of long-term research in project man-agement can be investigated using these existing methodsBased on the results by Boussad et al [17] in terms of

HindawiAdvances in Civil EngineeringVolume 2019 Article ID 5153082 8 pageshttpsdoiorg10115520195153082

design ability and application effect genetic algorithm wasundoubtedly the best solution among many complexheuristic algorithms Based on the in-depth studies ofgenetic algorithm the combination of genetic algorithmand other methods has also been developed Gulbin [18]considered the influence of environmental factors on theoperation of the algorithm and designed the genetic al-gorithm for nondominant sequencing Jia et al [19] appliedthe fuzzy set theory based on the operation of geneticalgorithm considered the uncertain conditions of con-struction and proposed a multiobjective method to opti-mize the duration cost and quality of the constructionproject Mungle et al [20] designed the fuzzy clusteringgenetic algorithm to solve the problem of multiobjectiveoptimization for highway projects Xie et al [21] used thepretreatment method and cost improvement process to thegenetic algorithm and established the optimization modelof multimode resource-limited projects under variantconstraints However these methods have inevitable lim-itations for large-scale projects with the requirements ofhigh precision and high timeliness erefore the com-putational model and algorithm for the optimization oflarge-scale construction projects need to be improved

In theory the problems which are solvable with geneticalgorithm can also be solved by quantum genetic algorithm(QGA) [22 23]us the QGA should be feasible in the fieldof genetic algorithm such as the multiobjective optimizationof both period and cost In addition as an alternative cal-culation method [24] quantum computing has a strong dataanalysis and processing ability for the large dataset [25ndash28]erefore in this study the QGA was used to solve theperiodcost trade-off problems and developed an optimi-zation model In the optimization model the genetic al-gorithm was used as the basis the parallelism of quantumcomputing was integrated with the genetic algorithm thequantum vector state expression was introduced into thegenetic coding and the chromosome evolution and renewalwere achieved through the quantum revolving door In thispaper the construction period-cost optimizationmodel withthe quantum genetic algorithm was established to improvethe search efficiency on the basis of global search and reducethe application error of the Pareto solution e experi-mental results proved that the proposed method had a betterperformance ratio than the traditional genetic algorithm

2 Problem Description

In the engineering construction management the periodand the cost of the construction project are two main ob-jectives to be controlled However there is a restrictiverelationship between both objectives that is gaining oneobjective is at the expense of another For example thereduction of time leads to an inevitable increase of cost[29 30] us the timecost optimization of the construc-tion project is also considered a multiconstraint hybridoptimization problem [31] On the contrary the networkplan of a project is composed of several subprocesses whichare logically arranged and there are several alternatives foreach of the subprocesses Different labor and construction

machinery schemes can lead to different time and cost of theprocess For instance the project duration direct cost andindirect cost can be affected by different schemes us thetimecost optimization problem is also considered a mul-tivariable problem In general before solving the multi-objective optimization problem [32] functional expressionsare needed to show the relationship between each objectiveTable 1 lists the symbol interpretation

21 Objective 01 Time e total time of the project is cal-culated by summing up the duration of each subprocess eduration of the subproject is marked with an intermediatevariable ldquoxrdquo e selected subprocess requires that the workcan and must start immediately when the previous work isfinished without restrictions of resources or other processese restrictions on the time parameter of each process satisfythe logical relationship between processes e calculationequation and constraint conditions of the control period ofthe construction project are defined as follows

T 1113944 Dij (1)

Dei leD

(j)

i leDni (2)

TleTmax (3)

22 Objective 02 Cost e cost includes direct cost andindirect cost Both costs have different changing rules andneed to be calculated separately Direct cost is the sum of thecosts of personnel construction machinery and materialswhich are directly used in the construction process and themeasures of the project At the same time the cost is in-creased in the emergency construction due to the increase inthe dispatched resources and the construction difficulty andthe extension of working hours of both personnel andmachinery Indirect costs are not directly included in theproject Instead they refer to other expenses that must bepaid for the preparation organization and management ofconstruction and production including enterprise man-agement fees and policy fees e value of the indirect costscan be estimated by contract documents or experts ecalculation equation and constraint conditions of the controlcost of the construction project are defined as follows

C min1113944n

i1α(j)

i C(j)

(1i) + α(j)i ΔtC

(j)

(2i)1113966 1113967 (4)

1113944

m

j1α(j)

i 1 (5)

CleCmax (6)

α(j)i1113966 1113967sube 0 1 (7)

where C(1i) is the sum of the product of the unit price andthe work quantity of the process and the measure cost

2 Advances in Civil Engineering

3 Optimization Model Based on QGA

31 QGA QGA is a new evolutionary optimization algo-rithm which integrates quantum computation with geneticalgorithm e QGA has obvious performance advantagesdue to the introduction of quantum concepts such asquantum state quantum revolving gate and probabilityamplitude in quantum computation e QGA has few it-erations high search efficiency and wide applicabilityBesides one chromosome can express the superposition ofmultiple states and thus has a large storage capacity Evenwhen the population is very small the global optimization ofthe algorithm is not affected us the possibility of thealgorithm to fall into a local search is greatly avoidedCompared to the traditional genetic algorithm (GA) theQGA does not rely on the gene updates by genetic operatorssuch as crossover and mutation to achieve the evolution ofthe population Although these genetic operators can changethe probability amplitude to some extent the quantumchromosome already exhibits the population diversity due tothe use of quantum superposition Instead the introductionof genetic operators such as crossover and mutation willreduce the computing speed and performance of the QGA

311 Quantum Bits Bit is the unit of information in binarynumber In traditional calculation there are only two basicstates ie ldquo0rdquo and ldquo1rdquo After the introduction of thequantum concept the bit state becomes a vector unit in atwo-dimensional complex coordinate Besides 0 and 1 thequantum bit state can also be the linear superposition of thebasic states [33] which is called the superposition state ofquantum bits

|ϕrang α|0rang + β|1rang (8)

Among them ldquo|middotrangrdquo is the Dirac notation to indicate thestate e parameters ɑ and β are the probability of thecorresponding states respectively e probability of |0rang is|α|2 while the probability of |1rang is |β|2 Both probabilitiessatisfy the normalization condition

|α|2

+|β|2

1 (9)

On the basis of binary coding in the genetic algorithmthe quantum bit state |ϕrang is used to code the target and theinitial value e coding rules can be expressed as followsthrough the expression of the quantum superposition state agene can express any quantum bit information In addition

the genome sequence can be formed by the composition ofchromosomes e mth chromosome of the scheme can berepresented as follows

Pnm

αn1

βn1

αn2

βn2

111386811138681113868111386811138681113868111386811138681113868

111386811138681113868111386811138681113868111386811138681113868

middot middot middot


αnjminus1

βnjminus1

1113868111386811138681113868111386811138681113868111386811138681113868

1113868111386811138681113868111386811138681113868111386811138681113868

αnj

βnj

⎡⎢⎣ ⎤⎥⎦ (10)

where n is the number of iterations and j is the quantumnumber (length of the chromosome) e complete quan-tum population containing all the modern chromosomescan be expressed as

P(t) pt1 p

t2 p

tm p

tT1113966 1113967 (11)

312 Quantum Gate e renewal and evolution of thequantum population are conducted through a quantum gatewhich is a quantum device that can realize logical trans-formation within a certain time interval e quantum gateACTS is used for the superposition of the quantum andresults in the phase change of the gene position in thechromosome Finally the probability converges to 0 or 1within a shortest time and the optimal searching solution isachieved e only requirement for quantum gates is

U+lowastU I (12)

where U is the matrix representation of the quantum gateU+ is the conjugate transpose and I is the identity matrixQuantum gates have many forms In this algorithm designthe method of quantum rotation is defined as follows

U(θ) cos θ minussin θ

sin θ cos θ1113890 1113891 (13)

where θ is the rotation angle e chromosome renewalprocess can be expressed as follows

αn+1k

βn+1k

⎡⎣ ⎤⎦ cos θi minussin θi

sin θi cos θi

1113890 1113891αn

k

βnk

1113890 1113891 (14)

where [αnk βn

k]T is the Kth quantum bit of the Nth generationof the chromosome

θi Δθ times sig (15)

where Δθ determines the convergence speed and the searchaccuracy of the algorithm If the amplitude ofΔθ is too smallthe search time is increased or even ldquostagnatesrdquo If theamplitude is too large premature convergence can occurand it is difficult to obtain the optimal solution sig is thecoefficient sign of the rotation angle namely the rotationdirection whose value determines the direction of con-vergence to the optimal solution When ibin (current in-dividual quantum bit value) is equal to ibbest (optimalindividual quantum bit value) sig is 1

2m

radic when ibin and

ibbest are different the values of sig are shown in Table 2

32 Optimization Process

321 Encoding and Population Initialization ere arethree encoding methods in the quantum genetic algorithm

Table 1 Notations

Notations MeaningsD i

j Duration of the jth procedure of the ith subitem

D ei (D n

i )Emergency (normal) construction time of available

construction plan for the ith subitemT Total project timeC Total project costC(1i) Direct cost of activity iC(2i) Indirect cost of activity iΔt Duration of alternativesα(j)

i Probability of selecting plan j in the ith procedure

Advances in Civil Engineering 3

e initial population encoding is quantum bit encoding inwhich N is the length of the encoded quantum bits epseudocode is shown in Figure 1

When the population is rst measured the quantum bitcode is converted into the binary code as shown in Figure 2e binary is decoded into the decimal in the calculation ofthe adaptability of the population

To optimize the construction period and cost of aproject the population can be dened as the set of chro-mosomes (Figure 3) that stores the duration of all sequentialsubitems and the initial population can be expressed asP(t 0) p01 p

02 p

0m p

0T where T is the pop-

ulation size e probability amplitudes of the population2jT are all 1

2

radic which means that in the initial state each

chromosome is in a linear superposition state with the sameprobability of 1

2m

radic

322 Evaluation of Adaptability e individuals in thepopulation can be evaluated by adaptability Higher adapt-ability indicates that the individual is better and has greatersurvival probability On the contrary the individuals withlower adaptability are easier to be eliminatede adaptabilityevaluation function is generally consistent with the objectivefunction Since the two opposite subobjectives ie durationand cost seek for the minimum values in the optimizationmodel equations (1) and (4) can be changed as follows

Value 1 1C

Value 2 1T

(16)

Both the adaptability values in decimal and the non-dominant solution (there was no other solution better thanthis one) were obtained from the calculation

323 Quantum Genetic Operation In the operation theQ(t) state of the population is observed and compared withthe existing optimal solution and then the population withthe quantum revolving gate is updated to obtain Q(t+ 1)e adaptability was calculated If the optimal solution inQ(t+ 1) is better than the currently stored solution thestored solution is replaced In the update process thepopulation number is always constant and the nondominantsolution does not repeat

324 Termination Judgment If the termination condition issatised the set of optimal solutions for the schedule andcost of the subprocess is the output Otherwise Steps 2 and 3

are repeated e owchart of the optimization process isshown in Figure 4

33 Experimental Results and Analysis

331 Algorithm Instance A high-rise building project wasselected as the main project for optimization the con-struction data (Table 3) were collected and the feasibility ofthe experimental model was veried Before optimizationaccording to the construction plan the completion durationof the project was 380 days and the cost was 19749 millionyuan

e parameters of the quantum genetic algorithm areshown in Table 4 is algorithm was implemented byMATLAB 2016b

After running the optimization the results were sum-marized as follows

(1) e periodcost evolution of a project is recordedand shown in Figures 5 and 6 From the gures it isnoted that all the target curves are in a decliningtrend which indicates that the evolution of thequantum genetic algorithm is eective With theincrease in the number of iterations the iterationcurve remains at which suggests that the algorithmis convergent and can achieve the optimal value in

QGAChrom = zeros(P N lowast 2)for i = 1P

for j = 1N lowast 2QGAChrom(i j) = 1sqrt(2)

endend

Figure 1 Code in quantum bit encoding

D1 D2 D3 helliphellip Djndash1 Dj

Figure 3 Diagram of the single chromosome structure

Table 2 Values of sig

ibin ibbest f(jfval)ltf(best)sig

αiβi gt 0 αiβi lt 0 αi 0 βi 0

0 1 True 1 0 0 plusmn10 1 False minus1 1 plusmn1 01 0 True minus1 1 plusmn1 01 0 False 1 minus1 0 plusmn1

Chrombin = zeros(P N)for i = 1P

for j = 1Npick = randif

pick gt (QGAChrom(i j)^2)Chrombit(i j) = 1

elseChrombin(i j) = 0

endend

end

Figure 2 Conversion of the quantum bit code to the binary code


the process of evolution instead of getting into localoptimum

(2) Figure 7 shows the nal solution of the QGA ie thePareto front under the dual constraints of both timelimit and cost According to the Pareto front of theoptimization the project manager can select a set of

feasible processes with exible activity arrangementunder certain constraints of time or constructionperiod (Table 4) to maximize the economic andsocial benets For example when the total con-struction period is 280 days the total cost is at least22882600 yuan e corresponding duration of thesubprocess is shown in Figure 8 in which the 19thactivity is concurrent engineering and does not in-crease the total construction period At this time noother combination method of the subprocesses canbe superior to the scheme shown in Figure 8

Initialization set parameters

Set of feasible solutions

N

Quantum revolving door

Evaluation

Output nondominant solutions

Coding population

Fitness evaluation

Replacement and storage

End condition

Y

Measurement

Figure 4 Optimization process of the quantum genetic algorithm

Table 3 Construction data

No ActivityTime (days) Cost (ten thousand yuan)

Normal Emergency Normal Emergency1 Measurement and actinomycetes 3 1 01 032 Precipitation and support 15 10 46 653 Earthwork 5 2 9 144 Pile foundation 10 6 240 3005 Earthwork backlling 5 2 18 36 Structure of the rst layer 12 7 635 707 Structure of the second or third layer 22 12 58 668 Structure of the fourth oor 10 5 56 64 17 Structure of the 13th oor 10 5 56 6418 Stage acceptance of the main project 3 1 05 1519 Wall masonry and secondary structure 50 30 147 19620 Structure of the 14th oor 10 5 56 64 33 Structure of the 27th oor 10 5 56 6434 Structure of the 28th oor 12 7 64 7035 Structure acceptance 3 2 1 236 Wall masonry and secondary structure 50 30 147 196

Table 4 Parameter values of the QGA

Δθ Population Variable dimension Max iterations001π 80 36 400


4 Conclusions

e trade-o between period and cost in constructionmanagement is a classic problem in the multiobjectiveoptimization with constraints A new model based on thequantum genetic algorithm (QGA) was proposed in thisstudy Firstly in the process of double-objective optimiza-tion the conict between the construction period and thepractical cost was considered and the direct and complexrelationship between the two objectives was analyzed Twomain objective functions were established which provided amathematical basis for the application of the algorithm tothe construction management Secondly a complete opti-mization concept and process of the quantum genetic al-gorithm were developed the quantum coding mode was

explained the quantum revolving door was improved andthe computational ecentciency of the algorithm was improvedin large-scale projects rough the construction example ofa high-rise building project the quantum genetic algorithmwas proved to be able to obtain the optimization resultsunder the condition of small population size and few iter-ation times us the quantum genetic algorithm had theadvantages of short calculation time and strong global op-timization ability Finally the developed model was appliedto a practical construction project e experimental resultsshowed that the QGA can perform multiple optimizationcycles and nd the nonconicting Pareto solution quicklyand accurately to meet the requirements under dierentconstraints in dierent projects with variant activity ar-rangements In addition the QGA can also provide ownersand contractors with more realistic decision-makingschemes conveniently and ecentciently which can maximizethe economic benets In the future the development of

Pareto front

240

260

280

300

320

340

Tim

e

234023202300 2360 238022602240 22802220Cost

Figure 7 Pareto solution set of the multiobjective quantum geneticalgorithm

Schedule

05

101520253035404550

Tim

e

4 7 10 13 16 19 22 25 28 31 341Activity

Figure 8 Process portfolio for 280 days

Cost iteration curve of QGA

Cost

2230

2235

2240

2245

2250

2255

2260

Cost

100 200 300 4000Number of iterations

Figure 5 Iteration curve of the construction period in the mul-tiobjective quantum genetic algorithm

Time

Time iteration curve of QGA

240

245

250

255

260

Tim

e

1000 300 400200Number of iterations

Figure 6 Iteration curve of cost in the multiobjective quantumgenetic algorithm


intelligent algorithms with high efficiency in large-scaleengineering optimization will become the research focus

Data Availability

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

Conflicts of Interest

e authors declare that there are no conflicts of interestregarding the publication of this paper

Acknowledgments

is research was partially supported by the Natural ScienceFoundation of Hebei Province of China under Grant NoE2016203147 Useful suggestions given by Dr Dewei Kongof Yanshan University are also acknowledged

References

[1] M J T Amiri F Haghighi E Eshtehardian and O AbessildquoMulti-project time-cost optimization in critical chain withresource constraintsrdquo KSCE Journal of Civil Engineeringvol 22 no 10 pp 3738ndash3752 2018

[2] Y Zhong Z Chen and Z Zhou ldquoResource allocation modeland strategy research of large-scale construction projectsystem dynamics modeling and simulationrdquo Chinese Journalof Management Science vol 24 no 3 pp 125ndash132 2016

[3] J Zhang ldquoDiscussion on the comprehensive equilibriumoptimization scheme of construction period cost and qualityin project managementrdquo Construction amp Design for Engi-neering vol 2 pp 141ndash143 2017

[4] S Monghasemi M R Nikoo M A K Fasaee andJ Adamowskic ldquoA novel multi criteria decision makingmodel for optimizing time-cost-quality trade-off problems inconstruction projectsrdquo Expert Systems with Applicationsvol 42 no 6 pp 3089ndash3104 2015

[5] A B Senouci and S A Mubarak ldquoMultiobjective optimi-zation model for scheduling of construction projects underextreme weatherrdquo Journal of Civil Engineering and Man-agement vol 22 no 3 pp 373ndash381 2016

[6] I Javier E P Karan and J Farzad ldquoIntegrating BIM and GISto improve the visual monitoring of construction supply chainmanagementrdquo Automation in Construction vol 31 pp 241ndash254 2013

[7] D Agdas D Warne J Osio-Norgaard and F MastersldquoUtility of genetic algorithms for solving large-scale con-struction time-cost trade-off problemsrdquo Journal of Computingin Civil Engineering vol 32 no 1 2018

[8] J Wu M Chen K Ju and S Jiang ldquoConstruction period ofsegmented ship engineering project based on harmonic searchalgorithmmdashcost optimizationrdquo Journal of Finance and Ac-counting vol 6 pp 68ndash70 2015

[9] T Dede ldquoJaya algorithm to solve single objective size opti-mization problem for steel grillage structuresrdquo Steel andComposite Structures vol 26 no 2 pp 163ndash170 2018

[10] M Grzywinski T Dede and Y I Ozdemir ldquoOptimization ofthe braced dome structures by using Jaya algorithm withfrequency constraintsrdquo Steel and Composite Structuresvol 30 pp 47ndash55 2019

[11] L Zhang Y Luan and X Zou ldquoProject dura-tionmdashcostmdashquality balance optimizationrdquo Systems Engi-neering vol 3 pp 85ndash91 2012

[12] A M Adrian A Utamima and K J Wang ldquoA comparativestudy of GA PSO and ACO for solving construction sitelayout optimizationrdquo KSCE Journal of Civil Engineeringvol 19 no 3 pp 520ndash527 2015

[13] M O Suliman V S S Kumar and W Abdulal ldquoOptimi-zation of uncertain construction time-cost trade off problemusing simulated annealing algorithmrdquo in Proceedings of theWorld Congress on Information and Communication Tech-nologies IEEE Trivandrum India October-November 2012

[14] O Giran R Temur and G Bekda ldquoResource constrainedproject scheduling by harmony search algorithmrdquo KSCEJournal of Civil Engineering vol 21 no 2 pp 479ndash487 2017

[15] D-H Tran M-Y Cheng and M-T Cao ldquoHybrid multipleobjective artificial bee colony with differential evolution forthe time-cost-quality tradeoff problemrdquo Knowledge-BasedSystems vol 74 no 1 pp 176ndash186 2015

[16] M Rogalska W Bozejko and Z Hejducki ldquoTimecost op-timization using hybrid evolutionary algorithm in con-struction project schedulingrdquo Automation in Constructionvol 18 no 1 pp 24ndash31 2009

[17] I Boussad J Lepagnot and P Siarry ldquoA survey on opti-mization metaheuristicsrdquo Information Sciences vol 237pp 82ndash117 2013

[18] O D Gulbin ldquoTime Cost and environmental impact analysison construction operation optimization using genetic algo-rithmsrdquo Journal of Management in Engineering vol 28 no 3pp 265ndash272 2012

[19] J Liu Y Liu and Y Shi ldquoMethod of time-cost-qualitytradeoff optimization of construction projectA study basedon fuzzy set theoryrdquo Journal of Beijing Jiaotong University(Social Sciences Edition) vol 16 no 3 pp 30ndash38 2017

[20] S Mungle L Benyoucef Y J Son and M K Tiwari ldquoA fuzzyclustering-based genetic algorithm approach for timendashcostndashquality trade-off problems a case study of highway con-struction projectrdquo Engineering Applications of Artificial In-telligence vol 26 no 8 pp 1953ndash1966 2013

[21] F Xie Z Xu and J Yu ldquoBi-objective optimization for theproject scheduling problem with variable resource availabil-ityrdquo Systems Engineering-Beory amp Practice vol 36 no 3pp 674ndash683 2016

[22] J Yang G Xie Z Zhang and L Guo ldquoQuantum geneticalgorithm and its application in image blind separationrdquoJournal of computer aided design and graphics vol 20 no 1pp 62ndash68 2003

[23] Q Guo and Y Sun ldquoImproved quantum genetic algorithmwith double chains in image denoisingrdquo Journal of HarbinInstitute of Technology vol 48 no 5 pp 140ndash147 2016

[24] N Sanghvi A Shah and V Varadan ldquoe concept and futureof quantum computingrdquo International Journal of ComputerApplications vol 106 no 4 pp 30ndash33 2014

[25] S Wei T Wang R Dong and G Long ldquoQuantum com-putingrdquo Scientia Sinica vol 10 pp 27ndash47 2017

[26] T A Shaikh and R Ali ldquoQuantum computing in big dataanalytics a surveyrdquo in Proceedings of the IEEE InternationalConference on Computer amp Information Technology HelsinkiFinland August 2017

[27] Y Tian W Hu D Bo et al ldquoIQGA a route selection methodbased on quantum genetic algorithm- toward urban trafficmanagement under big data environmentrdquoWorldWideWeb-Internet amp Web Information Systems vol 15 pp 1ndash23 2018


[28] L Zhang H Lv D Tan et al ldquoAdaptive quantum geneticalgorithm for task sequence planning of complex assemblysystemsrdquo Electronics Letters vol 54 no 14 pp 870ndash872 2018

[29] P Ghoddousi E Eshtehardian S Jooybanpour andA Javanmardi ldquoMulti-mode resource-constrained discretetime-cost-resource optimization in project scheduling usingnon-dominated sorting genetic algorithmrdquo Automation inConstruction vol 30 no 30 pp 216ndash227 2013

[30] M-Y Cheng and D-H Tran ldquoOpposition-based multipleobjective differential evolution (OMODE) for optimizingwork shift schedulesrdquo Automation in Construction vol 55pp 1ndash14 2015

[31] D A Wood ldquoGas and oil project time-cost-quality tradeoffintegrated stochastic and fuzzy multi-objective optimizationapplying a memetic nondominated sorting algorithmrdquoJournal of Natural Gas Science and Engineering vol 45pp 143ndash164 2017

[32] C Koo T Hong and S Kim ldquoAn integrated multi-objectiveoptimization model for solving the construction time-costtrade-off problemrdquo Journal of Civil Engineering and Man-agement vol 21 no 3 pp 323ndash333 2015

[33] A V Kozlovskii ldquoFluctuations of the hermitian phase op-erator of electromagnetic field for quantum phase superpo-sitions of coherent statesrdquo Journal of Modern Optics vol 15pp 1ndash10 2018


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design ability and application effect genetic algorithm wasundoubtedly the best solution among many complexheuristic algorithms Based on the in-depth studies ofgenetic algorithm the combination of genetic algorithmand other methods has also been developed Gulbin [18]considered the influence of environmental factors on theoperation of the algorithm and designed the genetic al-gorithm for nondominant sequencing Jia et al [19] appliedthe fuzzy set theory based on the operation of geneticalgorithm considered the uncertain conditions of con-struction and proposed a multiobjective method to opti-mize the duration cost and quality of the constructionproject Mungle et al [20] designed the fuzzy clusteringgenetic algorithm to solve the problem of multiobjectiveoptimization for highway projects Xie et al [21] used thepretreatment method and cost improvement process to thegenetic algorithm and established the optimization modelof multimode resource-limited projects under variantconstraints However these methods have inevitable lim-itations for large-scale projects with the requirements ofhigh precision and high timeliness erefore the com-putational model and algorithm for the optimization oflarge-scale construction projects need to be improved

In theory the problems which are solvable with geneticalgorithm can also be solved by quantum genetic algorithm(QGA) [22 23]us the QGA should be feasible in the fieldof genetic algorithm such as the multiobjective optimizationof both period and cost In addition as an alternative cal-culation method [24] quantum computing has a strong dataanalysis and processing ability for the large dataset [25ndash28]erefore in this study the QGA was used to solve theperiodcost trade-off problems and developed an optimi-zation model In the optimization model the genetic al-gorithm was used as the basis the parallelism of quantumcomputing was integrated with the genetic algorithm thequantum vector state expression was introduced into thegenetic coding and the chromosome evolution and renewalwere achieved through the quantum revolving door In thispaper the construction period-cost optimizationmodel withthe quantum genetic algorithm was established to improvethe search efficiency on the basis of global search and reducethe application error of the Pareto solution e experi-mental results proved that the proposed method had a betterperformance ratio than the traditional genetic algorithm

2 Problem Description

In the engineering construction management the periodand the cost of the construction project are two main ob-jectives to be controlled However there is a restrictiverelationship between both objectives that is gaining oneobjective is at the expense of another For example thereduction of time leads to an inevitable increase of cost[29 30] us the timecost optimization of the construc-tion project is also considered a multiconstraint hybridoptimization problem [31] On the contrary the networkplan of a project is composed of several subprocesses whichare logically arranged and there are several alternatives foreach of the subprocesses Different labor and construction

machinery schemes can lead to different time and cost of theprocess For instance the project duration direct cost andindirect cost can be affected by different schemes us thetimecost optimization problem is also considered a mul-tivariable problem In general before solving the multi-objective optimization problem [32] functional expressionsare needed to show the relationship between each objectiveTable 1 lists the symbol interpretation

21 Objective 01 Time e total time of the project is cal-culated by summing up the duration of each subprocess eduration of the subproject is marked with an intermediatevariable ldquoxrdquo e selected subprocess requires that the workcan and must start immediately when the previous work isfinished without restrictions of resources or other processese restrictions on the time parameter of each process satisfythe logical relationship between processes e calculationequation and constraint conditions of the control period ofthe construction project are defined as follows

T 1113944 Dij (1)

Dei leD

(j)

i leDni (2)

TleTmax (3)

22 Objective 02 Cost e cost includes direct cost andindirect cost Both costs have different changing rules andneed to be calculated separately Direct cost is the sum of thecosts of personnel construction machinery and materialswhich are directly used in the construction process and themeasures of the project At the same time the cost is in-creased in the emergency construction due to the increase inthe dispatched resources and the construction difficulty andthe extension of working hours of both personnel andmachinery Indirect costs are not directly included in theproject Instead they refer to other expenses that must bepaid for the preparation organization and management ofconstruction and production including enterprise man-agement fees and policy fees e value of the indirect costscan be estimated by contract documents or experts ecalculation equation and constraint conditions of the controlcost of the construction project are defined as follows

C min1113944n

i1α(j)

i C(j)

(1i) + α(j)i ΔtC

(j)

(2i)1113966 1113967 (4)

1113944

m

j1α(j)

i 1 (5)

CleCmax (6)

α(j)i1113966 1113967sube 0 1 (7)

where C(1i) is the sum of the product of the unit price andthe work quantity of the process and the measure cost







|α|2

+|β|2

1 (9)



Pnm

αn1

βn1

αn2

βn2

111386811138681113868111386811138681113868111386811138681113868

111386811138681113868111386811138681113868111386811138681113868



αnjminus1

βnjminus1

1113868111386811138681113868111386811138681113868111386811138681113868

1113868111386811138681113868111386811138681113868111386811138681113868

αnj

βnj

⎡⎢⎣ ⎤⎥⎦ (10)


P(t) pt1 p

t2 p

tm p

tT1113966 1113967 (11)


U+lowastU I (12)



sin θ cos θ1113890 1113891 (13)


αn+1k

βn+1k


sin θi cos θi

1113890 1113891αn

k

βnk

1113890 1113891 (14)

where [αnk βn




2m

radic when ibin and




Table 1 Notations



D ei (D n








02 p

0m p



2



2m

radic


Value 1 1C

Value 2 1T

(16)












endend












endend

end








N


Evaluation


Coding population

Fitness evaluation


End condition

Y

Measurement








4 Conclusions



Pareto front

240

260

280

300

320

340

Tim

e

234023202300 2360 238022602240 22802220Cost


Schedule

05

101520253035404550

Tim

e

4 7 10 13 16 19 22 25 28 31 341Activity



Cost

2230

2235

2240

2245

2250

2255

2260

Cost



Time


240

245

250

255

260

Tim

e





Data Availability




Acknowledgments


References






































RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia







|α|2

+|β|2

1 (9)



Pnm

αn1

βn1

αn2

βn2

111386811138681113868111386811138681113868111386811138681113868

111386811138681113868111386811138681113868111386811138681113868



αnjminus1

βnjminus1

1113868111386811138681113868111386811138681113868111386811138681113868

1113868111386811138681113868111386811138681113868111386811138681113868

αnj

βnj

⎡⎢⎣ ⎤⎥⎦ (10)


P(t) pt1 p

t2 p

tm p

tT1113966 1113967 (11)


U+lowastU I (12)



sin θ cos θ1113890 1113891 (13)


αn+1k

βn+1k


sin θi cos θi

1113890 1113891αn

k

βnk

1113890 1113891 (14)

where [αnk βn




2m

radic when ibin and




Table 1 Notations



D ei (D n








02 p

0m p



2



2m

radic


Value 1 1C

Value 2 1T

(16)












endend












endend

end








N


Evaluation


Coding population

Fitness evaluation


End condition

Y

Measurement








4 Conclusions



Pareto front

240

260

280

300

320

340

Tim

e

234023202300 2360 238022602240 22802220Cost


Schedule

05

101520253035404550

Tim

e

4 7 10 13 16 19 22 25 28 31 341Activity



Cost

2230

2235

2240

2245

2250

2255

2260

Cost



Time


240

245

250

255

260

Tim

e





Data Availability




Acknowledgments


References






































RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia





02 p

0m p



2



2m

radic


Value 1 1C

Value 2 1T

(16)












endend












endend

end








N


Evaluation


Coding population

Fitness evaluation


End condition

Y

Measurement








4 Conclusions



Pareto front

240

260

280

300

320

340

Tim

e

234023202300 2360 238022602240 22802220Cost


Schedule

05

101520253035404550

Tim

e

4 7 10 13 16 19 22 25 28 31 341Activity



Cost

2230

2235

2240

2245

2250

2255

2260

Cost



Time


240

245

250

255

260

Tim

e





Data Availability




Acknowledgments


References






































RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia







N


Evaluation


Coding population

Fitness evaluation


End condition

Y

Measurement








4 Conclusions



Pareto front

240

260

280

300

320

340

Tim

e

234023202300 2360 238022602240 22802220Cost


Schedule

05

101520253035404550

Tim

e

4 7 10 13 16 19 22 25 28 31 341Activity



Cost

2230

2235

2240

2245

2250

2255

2260

Cost



Time


240

245

250

255

260

Tim

e





Data Availability




Acknowledgments


References






































RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia


4 Conclusions



Pareto front

240

260

280

300

320

340

Tim

e

234023202300 2360 238022602240 22802220Cost


Schedule

05

101520253035404550

Tim

e

4 7 10 13 16 19 22 25 28 31 341Activity



Cost

2230

2235

2240

2245

2250

2255

2260

Cost



Time


240

245

250

255

260

Tim

e





Data Availability




Acknowledgments


References






































RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia



Data Availability




Acknowledgments


References






































RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia











RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia




RoboticsJournal of




VLSI Design



Shock and Vibration







Journal of



Volume 2018



Volume 2018


Journal of




SensorsJournal of



RotatingMachinery





Propagation






Hindawi


Advances in

Multimedia


Documents

MultiobjectiveConstructionOptimizationModelBasedon …downloads.hindawi.com/journals/ace/2019/5153082.pdf · 2019-07-30 · MATLAB 2016b. After running the optimization, the results