Research ArticleOptimal Operation of the Hybrid Electricity Generation SystemUsing Multiverse Optimization Algorithm

Muhammad Sulaiman 1 Sohail Ahmad1 Javed Iqbal1 Asfandyar Khan 1

and Rahim Khan2

1Department of Mathematics Abdul Wali Khan University Mardan Mardan KP Pakistan2Department of Computer Science Abdul Wali Khan University Mardan Mardan KP Pakistan

Correspondence should be addressed to Muhammad Sulaiman sulaiman513yahoocouk

Received 12 September 2018 Revised 31 January 2019 Accepted 11 February 2019 Published 11 March 2019

Academic Editor Antonino Laudani

Copyright copy 2019Muhammad Sulaiman et al 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

e ongoing load-shedding and energy crises due to mismanagement of energy produced by different sources in Pakistan and in-creasing dependency on those sources which produce energy using expensive fuels have contributed to rise in load shedding and price ofenergy per kilo watt hour In this paper we have presented the linear programmingmodel of 95 energy production systems in PakistanAn improved multiverse optimizer is implemented to generate a dataset of 100000 different solutions which are suggesting to fulfill theoverall demand of energy in the country ranging from 9587MWto 27208MWWe found that if some of the power-generating systemsare down due to some technical problems still we can get our demand by following another solution from the dataset which is partiallyutilizing the particular faulty power system According to different case studies taken in the present study based on the reports aboutthe electricity short falls been published in news from time to time we have presented our solutions respectively for each case It isinteresting to note that it is easy to reduce the load shedding in the country by following the solutions presented in our datasetGraphical analysis is presented to further elaborate our findings By comparing our results with state-of-the-art algorithms it isinteresting to note that an improved multiverse optimizer is better in getting solutions with lower power generation costs

1 Introduction

Propermanagement and finding out optimal solutions to utilizethe available power production sources is an important opti-mization problem in Pakistan which is the main theme of thispaper [1ndash11] According to the reports in [12 13] the demandof the power is increasing exponentially andwhich is causing anincrease in load shedding each year [14] e cause of thisshortage is mismanagement of power production sources

According to a report published by National ElectricPower Regulatory Authority (NEPRA) in 2016 [15] the totalcapacity of 27240MW is installed in the country whereasthe demand rises to 22000MW in summer [16] eseproduction units can produce enough energy if all aremanaged optimally In [17] these production units werenormally producing up to 13240MW with 4760MW ofshortfall In nomenclature we have indicated all the 95installed capacities of electricity production with majority of

them depending on thermal sources [15] In [14] it is re-ported that the gap between demand and production isexpected to increase in the coming years It is further re-ported in the literature [14 18] that urban areas are facing aload shading in summer season as of 10ndash12 hours and inrural areas it is even worse as 16ndash18 hours a day Urbani-zation and rapid increase in population have caused anincrease in the industrial zones [19] and it is worth notingthat the demand of electricity was 16000 (MW) duringsummer of 2012 while the short fall was 8500 (MW) [20]

In this study we have explored a scientific decision-making approach in terms of mathematical programmingfor providing a strategy to utilize the available productionsources of Pakistan to meet the demand of energy in dif-ferent seasons However in [21] a general mechanism waspresented in terms of 5 major energy production types as X1to X5 ey have fixed the per unit price to estimate theoverall mathematical model We have extended the model

HindawiComputational Intelligence and NeuroscienceVolume 2019 Article ID 6192980 12 pageshttpsdoiorg10115520196192980

and included 95 production sources which generateselectricity using different means (oil gas wind hydropowerand coal) We have implemented per unit price according tothe actual price of fuel used to run these sources eproduction capacities of each source are given in Table 1[22] Our model will help to reduce the shortfall by utilizingthe power production sources properly

In the last few years evolutionary algorithms (EAs) areimplemented to solve different real-world optimizationproblems EAs simulate social behavior or natural pro-cedures in order to handle optimization problems with bestsolution Among the popular EAs are the Bat algorithm[23 24] grasshopper optimization algorithm (GOA) [25]and firefly algorithm (FA) [26 27] e efficiency of met-aheuristics is better as compared to classical optimizationtechniques in solving optimization problems with iterationsand random search behavior e main idea behind all EAsis the survival of the fittest which in return increases thefitness of individuals in population EAs are implementedwith different frameworks which includes populationstructure and search equations [28] EAs with differentframeworks generate random populations en all solu-tions are evaluated according to a given objective functione search space is explored and exploited in two phasesEAs get stuck in local optima due to their random searchSeveral papers are published in the literature to overcomethis problem in EAs [29 30]

e multiverse optimization algorithm (MVO) is anature-inspired optimization technique given in [31] ekey idea of MVO is inspired from the theory of multiversesSince its invention it is applied to solve several real-worldproblems In [31] it is shown that MVO obtained verycompetitive results compared with other metaheuristicoptimization algorithms Also Faris et al [32] employed theMVO for training the multilayer perceptions in neuralnetwork e efficiency of their techniques was evaluated ondifferent medical datasets from UCI repository e out-come of their experiments is then compared to differentmetaheuristics namely Particle Swarm Optimization(PSO) Genetic Algorithm (GA) Differential Evolution (DE)Algorithm and Cuckoo Search (CS) It was observed thatMVO was improved in terms of convergence and avoidanceof local optima MVO still lacks behind in accuracy of resultsand convergence speed Fewer studies like Levy-flight-basedMVO [33] and a quantum version of MVO [34] are recentlyproposed to further enhance the capabilities of MVO Ex-perimental results show that they have improved the so-lutions to some extent

Currently as can be seen in the former review there arelimited works on improving the performance of MVO iswork presents a new method of initialization with the MVOalgorithm called improved multiverse optimization algorithm(IMVO) e experimental results on mathematical model ofeconomic dispatch problem of electricity generation system inPakistan and its three case studies show that IMVO is verycompetitive over FA Bat algorithm and GOA

Furthermore we have presented solutions to five casestudies for proper management and production by all the 95energy producers in the country Our model can be

Table 1 Electricity production constraints on each source

Power unit Lower limit Upper limitx1 0 3478x2 0 1000x3 0 1450x4 0 243x5 0 184x6 0 130x7 0 121x8 0 72x9 0 30x10 0 22x11 0 22x12 0 20x13 0 17x14 0 14x15 0 135x16 0 4x17 0 1x18 0 1x19 0 1655x20 0 1350x21 0 850x22 0 244x23 0 195x24 0 174x25 0 150x26 0 132x27 0 59x28 0 39x29 0 35x30 0 17x31 0 247x32 0 100x33 0 100x34 0 1260x35 0 560x36 0 900x37 0 362x38 0 365x39 0 29x40 0 225x41 0 165x42 0 330x43 0 94x44 0 1525x45 0 2265x46 0 157x47 0 110x48 0 179x49 0 165x50 0 188x51 0 2015x52 0 136x53 0 140x54 0 225x55 0 225x56 0 1292x57 0 165x58 0 120x59 0 131x60 0 1638x61 0 232

2 Computational Intelligence and Neuroscience

implemented to reduce the load shedding and distribute theburden of production on respective power production units

is work is organized as follows Section 2 describes theconcept of multiverse optimizer and improvements in itemathematical model for the problem is described in Section3 Experimental settings results and discussions based onnumerical simulations are given in Section 4 Conclusion ofour findings is presented in Section 5

2 An Improved Multiverse Optimizer

e MVO algorithm simulates the theory of multiversewhere three verses play main part in the whole algorithmicprocedure these are white holes black holes and worm-holes is is a population-based algorithm where thepopulation is searched in two phases exploration in whichthe search space is visited very well and exploitation per-forms the search in neighborhood of a solution extensivelyWhite hole and black hole in the theory of multiverses areused as exploration agents and wormhole is acting as ex-ploitation agent in this algorithm In Figure 1 black yellowgreen and pink are the objects which are moving through

the whiteblack hole and white points represent objectswhichmove through the wormholeere are 5 assumptionsthat are applied in MVO to the populationuniverse [31]

(a) e probability of having the white holes is directlyproportional to the inflation rate

(b) Individuals (universes) having higher inflation ratesend objects through white holes with higherprobability

(c) Individuals (universes) having higher inflation ratesend objects through white holes with higherprobability

(d) Individuals (universes) having lower rate of inflationsend objects through black holes with higherprobability

(e) e objects present in all universes are movedrandomly towards the current best individual(universe) through wormholes is random processoccurs without taking into account the inflation rateA sketch of this algorithm is shown in Figure 1

e initialization phase of MVO can be written asfollows

U

x11 middot middot middot xd

1

⋮ ⋱ ⋮

x1n middot middot middot xd

n

⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦ (1)

where U represents the matrix of candidate solutions d isthe dimensions of the problem and n is the number ofuniverses (population of solutions) which can be repre-sented as follows

xji

xj

k r1ltNI Ui( 1113857

xji r1geNI Ui( 1113857

⎧⎪⎨

⎪⎩

⎫⎪⎬

⎪⎭ (2)

where xji is the jth parameter of ith universe Ui denotes the

ith universe NI (Ui) is the scaled inflation rate of the ith

universe r1 isin (01) and xj

k is the jth parameter of kth

universe selected by a roulette wheel selection mechanisme objects are changed among the universes withoutperturbation To maintain the balance between exploration

Universe (1)

Universe (2)

Universe (3)

Universe (n ndash 1)

Universe (n)

Best universecreated so far

Wormhole tunnelWhiteblack hole tunnel

Figure 1 A sketch of MVO [31]

Table 1 Continued

Power unit Lower limit Upper limitx62 0 202x63 0 660x64 0 200x65 0 200x66 0 225x67 0 164x68 0 412x69 0 114x70 0 225x71 0 235x72 0 350x73 0 52x74 0 80x75 0 110x76 0 1335x77 0 126x78 0 990x79 0 137x80 0 325x81 0 325x82 0 340x83 0 425x84 0 150x85 0 50x86 0 50x87 0 49x88 0 50x89 0 52x90 0 50x91 0 56x92 0 30x93 0 49x94 0 50x95 0 50

Computational Intelligence and Neuroscience 3

and exploitation during the searching process in MVO eachuniverse is randomly treated to have wormholes to transportits objects through space In order to ensure the exploitationaround the current best solutions particular wormholetunnels are always established between a universe and thebest universe formed so far which can be representedmathematically as follows

xj

i

XJ + TDR times ubj minus lbj1113872 1113873 times r4 + lbj1113872 1113873 r3 lt 05

XJ minusTDR times ubj minus lbj1113872 1113873 times r4 + lbj1113872 1113873 r3 ge 05

⎧⎪⎨

⎪⎩r2 ltWEP

xj

i r2 geWEP

⎧⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎩

(3)

where Xj is the jth parameter of best universe formed so farTDR (travelling distance rate) and WEP (wormhole exis-tence probability) are coefficients lbj and ubj are the lowerbound and upper bound of jth variable respectively xij isthe jth parameter of ith universe and r2 r3 and r4 are randomnumbers between 0 and 1 WEP and TDR are treated asadaptive formula as follows

WEP Wmin + lWmax minusWmin

L1113874 1113875

TDR 1minusl1p

L1p

(4)

where Wmin is the minimum (in this paper it is set to 02)Wmax is the maximum (in this paper it is set to 1) l is thecurrent iteration L is the maximum iterations and p is theexploitation accuracy over the iterations (in this paper it isset to 6) Higher the value of p the sooner andmore accurateexploitationlocal search is performed [31] It is worth tohighlight that the MVO algorithm depends on number ofiterations number of universes roulette wheel mechanismand universe sorting mechanisme quick sort algorithm isused to sort universe at each iteration and roulette wheelselection is run for each variable in every universe in alliterations Detailed description of MVO can be seen in [31]

3 Our Proposed Initialization Strategy

According to the trend in stochastic techniques randominitialization in each generation is the frequently usedmethod to initialize algorithms without knowing any prioryinformation about the problem in hand e idea of randominitialization is often pushing the algorithm to explore thegiven domain very well while the exploitation around bestsolutions is not carried out by this type of initialization Wehave used an initialization strategy in which IMVO is bal-anced in terms of exploration and exploitation We havedesigned a two-stage initialization strategy in the first stagethe algorithm is initialized randomly for a certain number ofscattered solutions in the whole search domain In stage twoafter the algorithm completes a certain number of iterationsand collects best points in the search domain we initializethe IMVO with population of these best solutions to con-centrate the algorithm on exploitation around the best so-lutions in the space Hence in current studies we haveassigned the function evaluations fixed to solve a problem

in two parts e first part initializes with random pop-ulations and collects the best solutions of each iteration byusing the following equation

Ui Lbi + Ubi minus Lbi( 1113857lowast rand(0 1) (5)

In the second phase the algorithm is directed to searchin the neighborhood of the best solutions obtained in thefirst part and exploits the search space around the pop-ulation of these best solutions

4 Modeling of Electricity Production Cost as aSingle Objective LinearProgramming Problem

In this paper we have presented an optimal mixture ofenergy production system as a linear programming (LP)model consisting of different decision variables representingdifferent electricity production sources of Pakistan seeNomenclature [21] Each variable is bounded and generateselectricity through different fuel types like hydro thermalnuclear wind and solar energies e suggested LP modelincludes different production sources as xi i 1 2 95and ui i 1 2 3 95 represent different costs per kWhfor each source e objective function represents the totalcost (C) incurred to meet the demand of energy in differentsituations Mathematically

minimize cost 111394495

i1uixi (6)

where ui represents the cost per MWh and xi are the dif-ferent sources given in nomenclature e objective of thisstudy is to produce a data set of solutions so that we canselect the required optimal solution fulfilling the givendemand with lowest cost per kWh as compared to othersolutions in the data set For more details about the data setgenerated the reader may refer to [35] e problem is tosearch for best solutions among several candidate solutionsand to meet the required power demand and satisfy con-straints on each variable ese constraints are given inEquation (7) and Table 1 as follows

Total demand constraint

111394495

t1xt ge d (7)

5 Experimental Settings Resultsand Discussion

We have implemented IMVO which is coded in MatlabR2016 [31]emain features of our computer included 8GBRAM with Intelreg Coretrade i7-7500U CPU 27GHz 29GHzwith a 64-bit operating system Windows 10 For a faircomparison the population size was taken as 100 and thenumber of iterations was 100 We have repeated our simu-lations 10 times To elaborate the efficiency of IMVO we haveconsidered three special cases e experimental outcome iscompared with state-of-the-art algorithms firefly algorithm

4 Computational Intelligence and Neuroscience

bat algorithm and grasshopper optimization algorithm as inTables 2 3 and 4 Also we have picked 5 solutions fromoverall 100000 solutions and presented these solutions asdifferent case studies with their respective costs per MWh(Table 5) which are based on the power demand in summersas provided in [20 36ndash38] e power demands and decisionvariables which represent the 95 production sources inPakistan and cost incurred along with the total power pro-duced are given in Table 5 e individual variations of 20best variables required to produce a particular solution in allcase studies are furnished in Table 6 and a weighted com-parison of the 95 energy sources is given in Figure 2 Lookingat these graphs the reader can deduce the importance of eachproduction source of electricity in national grid of thecountry One can deduce which solution to choose if aparticular source is down due to some fault or which sourcesare very impotent and acting as a backbone in generating therequired electricity We have depicted five case studies

graphically as shown in Figure 3 ese graphs are collectiverepresentation of 95 production sources acting to produce acertain demand It is interesting to note that the production ofelectricity from available sources is manageable if propertechniques like IMVO algorithm are implemented to solvethe problem It is worth to note that we have pointed out thetop 20 production sources of electricity in Pakistan accordingto the five case studies listed as in Table 5 ese sources playvital part in the energy production as shown in Table 6 It isobvious that certain sources like x1 are producing higherdemand which are overburdened and could be relaxed byinstalling or expanding alternate sources In Table 7 pricesdepending on different fuel types are listed for a megawatt ofelectricity e convergence plots for these three case studiesare depicted in Figures 4ndash6 It is interesting to note that in allcases with demands of 15000 19000 and 23000megawattsIMVO produced better solutions with lowest costs in millions(Table 2ndash4)

Table 2 Case Study A demand for 15000megawatt where S1 minus S8 represent the collection of sources operating on 8 fuel types

Firefly BAT GOA IMVOPrice in PKR 390831986 252289853 2013324084 1115048004Variable (MW) 150174015 150064398 1500226667 1506746055S1 403519978 289304991 3513562502 4785656S2 140773428 187328453 1072160605 1338551S3 981013264 158209497 624800805 4319034S4 113747918 567079361 3954767659 1476913S5 568488097 850204227 8812308041 5366239S6 921438836 523099019 6841945259 118003S7 393294457 218122192 4421898083 1507902S8 456360696 467863004 198943367 3373776

Table 3 Case Study B demand for 19000megawatt where S1 minus S8 represent collection of sources operating on 8 fuel types

Firefly BAT GOA IMVOPrice in PKR 327227212 236951036 2333069629 1556167319Variable (MW) 190763946 19017236 1902302749 1904411301S1 676141122 492840531 5283899334 3905454S2 239521169 200662552 1695397916 1655S3 146931172 204258471 1671485397 1674898S4 170102742 11029362 1720041194 2433113S5 558369119 101167438 9981020494 816088S6 517009725 15365083 2865642935 4802648S7 489383474 933714342 1374132769 3947306S8 159348169 411244455 9450307236 3397717

Table 4 Case Study C demand for 23000megawatt where S1 minus S8 represent collection of sources operating on 8 fuel types

Firefly BAT GOA IMVOPrice in PKR 350831986 263667565 2766948704 187660591Variable (MW) 230610476 230227254 2304431656 230641461S1 733180841 6292 7333779792 506958882S2 249378785 2618 1725823048 1670682S3 187100046 219 560182213 251706661S4 1756 1756 533408886 246749605S5 768567332 11612 1155322811 978275386S6 110462969 002326828 1089543135 6963726S7 436442721 525 4625011979 448716537S8 381705102 070208538 2900141633 411469586

Computational Intelligence and Neuroscience 5

Table 5 Electricity production of all 95 sources for five case studies

Case Study 1 Case Study 2 Case Study 3 Case Study 4 Case Study 5Price in PKR 112E+ 08 151E+ 08 184E + 08 197E + 08 216E + 08Variables (megawatts) 1500316 19003 2300008 250003 2720836TD (x1) 2379137 156635 2938164 3478 347616MD (x2) 818677 1000 9057829 7634957 98348GBHPP (x3) 5165337 1450 1023352 1347306 1421054WD (x4) 1307975 2104076 1777411 1064834 1815488CB (x5) 3874718 184 7542442 1744151 1638171DKD (x6) 4256789 1163349 1160204 6036495 1274962AKHPP (x7) 2502909 0415286 1190034 3387101 4799439KKHP (x8) 604886 1592544 4172064 72 1927703JagHP (x9) 1417929 30 1285605 8998066 2138508JabHP (x10) 8375935 1057083 1806 9438497 0704657RG (x11) 6866051 3330527 0380166 4987555 9745063DHP (x12) 1428187 1353056 1265834 20 2044366GHD (x13) 605225 0280779 2219217 940119 155921NHP (x14) 6647023 1140453 7595507 6010873 1386329SHP (x15) 1155404 112018 8391618 1116708 13093KHP (x16) 1869716 1137132 1534735 2692804 1023365RKHP (x17) 0905093 1 1 0651626 0854247CHPP (x18) 0864139 0815802 0815802 0965926 0830172GTPP (x19) 1305331 1655 1655 1655 164554MTPP (x20) 6400394 54627 1350 1350 1350JTPP (x21) 1495429 850 850 850 8490554FGTPP (x22) 1489675 1812005 1880609 1031949 217891MGTPP (x23) 4385999 748375 1554596 1458149 1681718MGTPP (x24) 127056 6527735 16615 341201 1109528KGTPP (x25) 1128329 116059 3098832 0567566 1495035LTPP (x26) 4037149 0883692 243518 1205104 1174427FSPP (x27) 3919613 5427258 59 5663659 5509061SGTPP (x28) 0914076 2186785 1466417 2223108 3108445PGTPP (x29) 2730059 1445997 0589928 8484009 2307876PTPP (x30) 1270353 17 6695689 1685053 1195603KGTPS (x31) 9179519 2282708 247 1276751 2468065KPC (x32) 9112861 100 0076503 1621392 1324039GTPS (x33) 2139859 3086809 0608317 4191513 1135833TPS (x34) 1019436 8525889 9217966 1132252 1260CCPP 1 (x35) 3638285 3759421 4858476 5381132 5524153CCPP 2 (x36) 6716314 3599164 5511955 7985884 8991415AES LL (x37) 1248976 362 3301038 3414665 3464409AES PG (x38) 8779272 2897815 365 2441401 3649033AEL (x39) 3047575 29 29 1208485 195939AP (x40) 1465024 1947207 2149626 225 225AGL (x41) 1539627 1074664 1527011 1143378 1135217CHMC PL (x42) 7513341 265198 2733111 2556046 3227874DHA C L (x43) 6873455 0476099 6545028 6296757 7030826EPC (x44) 2340477 98656 3710004 1413346 1520636EPQL (x45) 1307633 2140389 2223562 2265 2262002FKPCL (x46) 952459 157 1512643 278556 1556898FTSM (x47) 5616674 1044668 1008249 7657812 1070448FPCDL (x48) 101152 1643581 1272432 106039 1777063GHLLP (x49) 101702 5626072 1098266 1402346 1576599GEPtvL (x50) 1623922 188 1444615 1795249 1319891GEL (x51) 8193736 8919682 2015 8489962 2015GAEL (x52) 1005592 9235572 5718626 1104825 8202294HCPC (x53) 1113358 5826757 1109772 4347083 1115484HPGC (x54) 1697313 0807693 1923602 1250309 215355HUBCO NPP (x55) 1478875 225 212279 2095134 2235541HUBCOHPP (x56) 1480634 1292 1167515 1292 1292Iptvl (x57) 2153738 1586019 1416202 1642585 1649125JPG (x58) 8413137 120 120 6522738 119424

6 Computational Intelligence and Neuroscience

Table 5 Continued

Case Study 1 Case Study 2 Case Study 3 Case Study 4 Case Study 5KEL (x59) 4350688 4752342 1038332 3058684 1308207KAPCL (x60) 8114451 1223218 118571 1638 1638LPL (x61) 1530046 052402 9467205 1964468 1822104LPTL (x62) 1241896 681917 5095543 1388238 1986912LEPCL (x63) 2556012 5897144 5785459 660 6586634NCP (x64) 1582538 200 9585135 200 1513611NPL (x65) 3248763 200 1684331 1688323 1991059OPCL (x66) 2052865 089022 1327586 6589102 2200356REPGCL (x67) 3020849 1002075 5299079 164 1634477RP (x68) 3271605 2760325 3021523 412 4118322SPC (x69) 7208175 7502883 9121424 1091339 1126283SPPQ (x70) 1010073 225 1240716 21105 221962SESL (x71) 2081023 265598 6600281 2155041 2003566SSEL (x72) 2205401 141361 3211493 3106587 3432993SNPCL (x73) 393573 4414536 0398791 2011775 5189066SE (x74) 7728166 1107506 6637944 2384816 1650386SEPC (x75) 1201473 7111238 401338 4743561 8328035SPGL (x76) 71382 3585756 1086969 8837954 113884TEL (x77) 1102271 2538428 1135676 265028 9401525UchPL (x78) 7352781 2816507 990 990 9897866KANUPP (x79) 504151 9210906 137 1057683 1347101CHASNUPP-1 (x80) 2829386 863647 2758089 325 2687866CHASNUPP-2 (x81) 2002746 2432484 1494219 325 3208773CHASNUPP-3 (x82) 1918579 340 319874 3016324 2140955NPP (x83) 1816426 173693 3748168 3362965 4207756QezSP (x84) 4971705 1069033 7003342 1473463 1267687YEL (x85) 1558682 2334511 4623074 2448091 1286986MWPCL (x86) 4101434 2135616 2794642 3645242 4521504TGL (x87) 9466357 2520002 49 4779046 4790783GAWPL (x88) 1535919 1891722 4514516 1524926 2794244MWEL (x89) 1496827 2199775 52 4787871 4600231FFCEL (x90) 3026861 4268928 50 50 1558795ZEP (x91) 2088768 1437346 4467045 3045881 4017728TWEL (x92) 1528468 121674 30 2952479 2865781HCDPL (x93) 9876255 2000362 4725205 319031 4152962FWEL 1 (x94) 4369201 2980095 4598028 2968556 2261687FWEPL 2 (x95) 6404915 50 6872093 2165334 4028912

0

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10000

12000

14000

16000

1 4 7 10 13 16 19 22 25 28 31 34 37 40 43 46 49 52 55 58 61 64 67 70 73 76 79 82 85 88 91 94

Ener

gy p

rodu

ctio

n in

meg

awat

ts

95 energy sources

Series 1Series 2Series 3

Series 4Series 5

Figure 2 A weighted comparison of the 95 energy sources used in five case studies Series 1ndash5 represent case studies 1ndash5 respectively

Computational Intelligence and Neuroscience 7

0

500

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1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 33 35 37 39 41 43 45 47 49 51 53 55 57 59 61 63 65 67 69 71 73 75 77 79 81 83 85 87 89 91 93 95

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Power production sources

(a)

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16001400

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(b)

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Power production sources

(c)

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100015002000250030003500

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(d)

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100015002000250030003500

1 4 7 10 13 16 19 22 25 28 31 34 37 40 43 46 49 52 55 58 61 64 67 70 73 76 79 82 85 88 91 94

Elec

tric

ity p

rodu

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meg

awat

ts

All power production sources

(e)

Figure 3 Comprehensive plots of five case studies discussed in Table 4 All production sources are plotted against the electricity productionin megawatts (a) Case Study 1 demand of 15003MW (b) Case Study 2 demand of 19003MW (c) Case Study 3 demand of 23000MW(d) Case Study 4 demand of 250003MW (e) Case Study 5 demand of 272083MW

8 Computational Intelligence and Neuroscience

6 Conclusions

In this paper an improved multiverse optimization al-gorithm is implemented for solving a linear programmingmodel for proper management of electricity productionsources in Pakistan To address the proper management ofpower production sources several bound constraintssuch as constraint for total demand and bounds on allvariables are considered e objective function is linearwith 95 decision variables and different coefficients eIMVO algorithm is easy to implement with few param-eters We have found solutions for five different casestudies and analyzed all solutions graphically A link to thedata set of 100000 different solutions is provided in this

paper In our results we have obtained better solutions tomeet the power demand in summer It is recommendedthat current resources can produce the required powerdemand but some of the resources are required to beexpanded in capacity along with installation of newsources In future we intend to include other factors likepower loss in our model

Nomenclature

TD Tarbela Dam (x1)MD Mangla Dam (x2)GBHPP Ghazi Barota Hydropower Project (x3)WD Warsak Dam (x4)CB Chashma Barrage (x5)DKD Duber Khwar Dam (x6)AKPH Allai Khwar Hydropower Plant (x7)KKPL Khan Khwar Hydropower Plant (x8)JHP Jagran Hydropower Plant (x9)

Table 6 Top 20 electricity production sources according to the five case studies

No1

No2

No3

No4

No5

No6

No7

No8

No9

No10

No11

No12

No13

No14

No15

No16

No17

No18

No19

No20

x1 x19 x60 x3 x20 x56 x34 x78 x21 x2 x36 x63 x35 x68 x83 x37 x38 x72 x74 x81

15

145

14

135

13

125

12

115

11

105

Cos

t

0 10 20 30 40 50 60 70 80 90 100Iterations

times108

Figure 4 IMVO convergence graph demand for 15000megawatt

15

155

145

14

135

17

175

16

165

Cos

t

0 10 20 30 40 50 60 70 80 90 100Iterations

times108

Figure 5 IMVO convergence graph demand for 19000megawatt

194

192

19

188

186

184

182

18

178

174

172C

ost

0 10 20 30 40 50 60 70 80 90 100Iterations

times108

Figure 6 IMVO convergence graph demand for 23000megawatt

Table 7 Per megawatt cost of electricity for different fuel types

Fuel type Price in PKR per megawattHydel 2500LNG 9070Furnace oil 11050High-speed diesel 17960Coal 12080Solar 16950Wind 16630Nuclear 6860Regasified liquefied natural gas 11270

Computational Intelligence and Neuroscience 9

JabHP Jabban Hydropower Plant (x10)RB Rasal Barrage (x11)DHP Dargai Power Plant (x12)GZD Gomal Zam Dam (x13)NHP Nandipur Hydropower Plant (x14)SHP Shadiwal Hydropower Plant (x15)KHP Khuram Hydropower Plant (x16)RKHP Renela Khuard Hydropower Plant (x17)CHPP Chatral Hydropower Plant (x18)GTPP Guduu ermal Power Plant (x19)MTPP Muzaffargarh ermal Power Plant (x20)JTPP Jamshoro ermal Power Plant (x21)FGTPP Faisalabad Gas Turbine Power Plant (x22)MGTPP Multan Gas Turbine Power Plant (x23)KGTPP Kotri Gas Turbine Power Plant (x24)LTPP Larkana ermal Power Plant (x25)FSPP Faisalabad Steam Power Plant (x26)SGTPP Shahdra Gas Turbine Power Plant (x27)PGTPP Panjgur Gas Turbine Power Plant (x28)QTPP Quetta ermal Power Plant (x29)PTPP Pasni ermal Power Plant (x30)KPC Korangi Power Complex (x31)KGTPS Korang Gas Turbine Power Plant Station

(x32)GTPS Gas Turbine Power Station (x33)KPS ermal Power Plant (x34)CCPP1 Combined Cycle Power Plant 1 (x35)CCPP2 Combined Cycle Power Plant 2 (x36)AESLL AES Lalpir Limited (x37)AESPG AES Pak Gen (x38)AEL Altern Energy Limited (x39)AP Altes Power (x40)AGL Attock Gen Limited (x41)CMECP CMEC Power Pvt (x42)DHACL DHA Cogen Limited (x43)EPC Eastern Power Company (x44)EPQL Engro Powergen Qaidpur Limited (x45)FKPP Fauji Kabirwala Power Plant (x46)FTSM First-Star Modaraba (x47)FPCDL Foundation power company Daharki

Limited (x48)GHLLP Grang Holding Limited Power Plant (x49)GEPtvl Green Electric Pvt Limited (x50)GEL Gujranwala Energy Limited (x51)DAEL Gul Ahmad Energy Limited (x52)HCPC Habibullah Coastal Power Company (x53)HPGC Halmore Power Generation Company (x54)HUBCONPP HUBCO Narowal Power Plant (x55)HUBCOHPP HUBCO Hub Power Plant (x56)IPtvL Intergen PTV Limited (x57)JPG Japan Power Plant (x58)KEL Kohinor Energy Limited (x59)KAPCL Kot Addu Power Company Limited (x60)LPL Liberty Power Limited (x61)LPTL Liberty Power Tech Limited (x62)LEPCL Lucky Electric Power Company Limited

(x63)NCP Nishat Chunian Power (x64)

NPL Nishat Power Limited (x65)OPCPrvL Orient Power Company (Pvt) Limited (x66)REPGC Radian Energy Power Generation Company

(x67)RPK Rousch Power Khanewal (x68)SPC Saba Power Company (x69)SPPQ Saif Power Plant Qadirabad (x70)SECL Sapphire Electric Company Limited (x71)SSEL Siddiqsons Energy Limited (x72)SNPCL Sindh Nooriabad Power Company (Pvt)

Limited (x73)SE Sitara Energy (x74)SEPC Southern Electric Power Company Limited

(x75)SPGL Star Power Generation Limited (x76)TEL Tapal Energy Limited (x77)UchPL Uch (Uch-I and Uch-II) Power Limited (x78)KANUPP KANUPP (x79)CHASNUPP-1 CHASNUPP-1 (x80)CHASNUPP-2 CHASNUPP-2 (x81)CHASNUPP-3 CHASNUPP-3 (x82)NPP Nandipur Power Project (x83)QeaSP Quaid-e-Azam Solar Park (x84)YEL Yunus Energy Limited (x85)MWPCL Metro Wind Power Co Limited (x86)TGL Tenaga Generai Limited (x87)GAWPL Gul Ahmed Wind Power Limited (x88)MWEL Master Wind Energy Limited (x89)FFCEL FFC Energy Limited Jhimpir (x90)ZEPJ Zorlu Enerji Pakistan Jhimpir (x91)TWEL Tapal Wind Energy Limited (x92)HCDPL HydroChina Dawood Power Limited (x93)FEW-1L Foundation Wind Energy-I Limited (x94)FEW-2PT Foundation Wind Energy-II Private Limited

(x95)

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

Authorsrsquo Contributions

All authors contributed equally to the writing of this paperAnd all authors read and approved the final manuscript

Acknowledgments

is paper was supported by the Department of Mathe-matics and the Office of Research Innovation andCommercialization of Abdul Wali Khan UniversityMardan Pakistan

10 Computational Intelligence and Neuroscience

References

[1] A Kumar and G Shankar ldquoQuasi-oppositional harmonysearch algorithm based optimal dynamic load frequencycontrol of a hybrid tidal-diesel power generation systemrdquo IETGeneration Transmission amp Distribution vol 12 no 5pp 1099ndash1108 2018

[2] M Mehdinejad B Mohammadi-Ivatloo and R Dadashzadeh-Bonab ldquoEnergy production cost minimization in a combinedheat and power generation systems using cuckoo optimizationalgorithmrdquo Energy Efficiency vol 10 no 1 pp 81ndash96 2017

[3] K Y Lee C Y Chung B J Huang et al ldquoA novel algorithmfor single-axis maximum power generation sun trackersrdquoEnergy Conversion and Management vol 149 pp 543ndash5522017

[4] L S M Guedes P de Mendonca Maia A C LisboaD A G Vieira and R R Saldanha ldquoA unit commitmentalgorithm and a compact MILP model for short-term hydro-power generation schedulingrdquo IEEE Transactions on PowerSystems vol 32 no 5 pp 3381ndash3390 2017

[5] F Zaman S M Elsayed T Ray and R A Sarker ldquoEvo-lutionary algorithms for power generation planning withuncertain renewable energyrdquo Energy vol 112 pp 408ndash4192016

[6] M E Nazari and M M Ardehali ldquoOptimal coordination ofrenewable wind and pumped storage with thermal powergeneration for maximizing economic profit with consider-ations for environmental emission based on newly developedheuristic optimization algorithmrdquo Journal of Renewable andSustainable Energy vol 8 no 6 article 065905 2016

[7] S Hemalatha and S Chandramohan ldquoCost optimization ofpower generation systems using bat algorithm for remotehealth facilitiesrdquo Journal of Medical Imaging and Health In-formatics vol 6 no 7 pp 1646ndash1651 2016

[8] E Assareh and M Biglari ldquoA novel approach to capture themaximum power generation from wind turbines using hybridMLP neural network and bees algorithm (HNNBA)rdquo IETEJournal of Research vol 62 no 3 pp 368ndash378 2016

[9] N Nikmehr and S Najafi-Ravadanegh ldquoOptimal operation ofdistributed generations in micro-grids under uncertainties inload and renewable power generation using heuristic algo-rithmrdquo IET Renewable Power Generation vol 9 no 8pp 982ndash990 2015

[10] W Sun J Wang and H Chang ldquoForecasting annual powergeneration using a harmony search algorithm-based jointparameters optimization combination modelrdquo Energiesvol 5 no 10 pp 3948ndash3971 2012

[11] J Jasper ldquoCost optimization of power generation using adifferential evolution algorithm enhanced with neighbour-hood search operationrdquo International Review of ElectricalEngineering (IREE) vol 7 no 5 pp 5854ndash5865 2012

[12] G Ali ldquoFactors affecting public investment in manufacturingsector of Pakistanrdquo European Journal of Economic Studiesvol 13 no 3 pp 122ndash130 2015

[13] D H Husaini and H H Lean ldquoDoes electricity drive thedevelopment of manufacturing sector in Malaysiardquo Frontiersin Energy Research vol 3 p 18 2015

[14] M M Rafique and S Rehman ldquoNational energy scenario ofPakistan-current status future alternatives and institutionalinfrastructure an overviewrdquo Renewable and SustainableEnergy Reviews vol 69 pp 156ndash167 2017

[15] NEPRA State of Industry Report 2016 httpwwwnepraorgpkpublicationsstateofindustryreportsstateofindustryreport2016pdf

[16] Electricity demand surges to 22000 MWwith rise in mercuryin Dawn 2017 httpswwwdawncomnews1339210

[17] J L C Meza M B Yildirim and A S M Masud ldquoAmultiobjective evolutionary programming algorithm andits applications to power generation expansion planningrdquoIEEE Transactions on Systems Man and Cybernetics-PartA Systems and Humans vol 39 no 5 pp 1086ndash10962009

[18] M Asif ldquoSustainable energy options for Pakistanrdquo Renewableand Sustainable Energy Reviews vol 13 no 4 pp 903ndash9092009

[19] S Wasti Economic Survey of Pakistan 2014-15 Governmentof Pakistan Islamabad Pakistan 2015

[20] M Kugelman Pakistanrsquos Energy Crisis National Bureau ofAsian Research Washington DC USA 2013

[21] H Zameer and Y Wang ldquoEnergy production system opti-mization evidence from Pakistanrdquo Renewable and Sustain-able Energy Reviews vol 82 pp 886ndash893 2018

[22] B Zafar ldquoFuel Price Adjustmentrdquo httpstribunecompkstory957503fuel-price-adjustment-regulator-cuts-power-tariff-for-june-and-july

[23] X S Yang ldquoA new metaheuristic bat-inspired algorithmrdquo inNature Inspired Cooperative Strategies for Optimization(NICSO 2010) pp 65ndash74 Springer Berlin Germany 2010

[24] B Zhu W Zhu Z Liu Q Duan and L Cao ldquoA novelquantum-behaved bat algorithm with mean best positiondirected for numerical optimizationrdquo Computational in-telligence and neuroscience vol 2016 Article ID 609748417 pages 2016

[25] S Saremi S Mirjalili and A Lewis ldquoGrasshopper optimi-sation algorithm theory and applicationrdquo Advances in En-gineering Software vol 105 pp 30ndash47 2017

[26] X S Yang ldquoFirefly algorithm stochastic test functions anddesign optimisationrdquo 2010 httparxivorgabs10031409

[27] C F Chao and M H Horng ldquoe construction of supportvector machine classifier using the firefly algorithmrdquo Com-putational Intelligence and Neuroscience vol 2015 Article ID212719 8 pages 2015

[28] F Ozkaynak ldquoA novel method to improve the performance ofchaos based evolutionary algorithmsrdquo Optik vol 126 no 24pp 5434ndash5438 2015

[29] M Sulaiman A Ahmad A Khan and S MuhammadldquoHybridized symbiotic organism search algorithm for theoptimal operation of directional overcurrent relaysrdquo Com-plexity vol 2018 Article ID 4605769 11 pages 2018

[30] M Sulaiman S Muhammad and A Khan ldquoImproved solu-tions for the optimal coordination of docrs using firefly al-gorithmrdquo Complexity vol 2018 Article ID 7039790 15 pages2018

[31] S Mirjalili Waseem S MMirjalili and A Hatamlou ldquoMulti-verse optimizer a nature-inspired algorithm for global op-timizationrdquo Neural Computing and Applications vol 27no 2 pp 495ndash513 2016

[32] H Faris I Aljarah and S Mirjalili ldquoTraining feedforwardneural networks using multi-verse optimizer for binaryclassification problemsrdquo Applied Intelligence vol 45 no 2pp 322ndash332 2016

[33] C Hu Z Li T Zhou A Zhu and C Xu ldquoA multi-verseoptimizer with levy flights for numerical optimization and itsapplication in test scheduling for network-on-chiprdquo PLoSOne vol 11 no 12 Article ID e0167341 2016

[34] G I Sayed A Darwish and A E Hassanien ldquoQuantummultiverse optimization algorithm for optimization

Computational Intelligence and Neuroscience 11

implemented to reduce the load shedding and distribute theburden of production on respective power production units

is work is organized as follows Section 2 describes theconcept of multiverse optimizer and improvements in itemathematical model for the problem is described in Section3 Experimental settings results and discussions based onnumerical simulations are given in Section 4 Conclusion ofour findings is presented in Section 5

2 An Improved Multiverse Optimizer

e MVO algorithm simulates the theory of multiversewhere three verses play main part in the whole algorithmicprocedure these are white holes black holes and worm-holes is is a population-based algorithm where thepopulation is searched in two phases exploration in whichthe search space is visited very well and exploitation per-forms the search in neighborhood of a solution extensivelyWhite hole and black hole in the theory of multiverses areused as exploration agents and wormhole is acting as ex-ploitation agent in this algorithm In Figure 1 black yellowgreen and pink are the objects which are moving through

the whiteblack hole and white points represent objectswhichmove through the wormholeere are 5 assumptionsthat are applied in MVO to the populationuniverse [31]

(a) e probability of having the white holes is directlyproportional to the inflation rate

(b) Individuals (universes) having higher inflation ratesend objects through white holes with higherprobability

(c) Individuals (universes) having higher inflation ratesend objects through white holes with higherprobability

(d) Individuals (universes) having lower rate of inflationsend objects through black holes with higherprobability

(e) e objects present in all universes are movedrandomly towards the current best individual(universe) through wormholes is random processoccurs without taking into account the inflation rateA sketch of this algorithm is shown in Figure 1

e initialization phase of MVO can be written asfollows

U

x11 middot middot middot xd

1

⋮ ⋱ ⋮

x1n middot middot middot xd

n

⎡⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎢⎣

⎤⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎥⎦ (1)

where U represents the matrix of candidate solutions d isthe dimensions of the problem and n is the number ofuniverses (population of solutions) which can be repre-sented as follows

xji

xj

k r1ltNI Ui( 1113857

xji r1geNI Ui( 1113857

⎧⎪⎨

⎪⎩

⎫⎪⎬

⎪⎭ (2)

where xji is the jth parameter of ith universe Ui denotes the

ith universe NI (Ui) is the scaled inflation rate of the ith

universe r1 isin (01) and xj

k is the jth parameter of kth

universe selected by a roulette wheel selection mechanisme objects are changed among the universes withoutperturbation To maintain the balance between exploration

Universe (1)

Universe (2)

Universe (3)

Universe (n ndash 1)

Universe (n)

Best universecreated so far

Wormhole tunnelWhiteblack hole tunnel

Figure 1 A sketch of MVO [31]

Table 1 Continued

Power unit Lower limit Upper limitx62 0 202x63 0 660x64 0 200x65 0 200x66 0 225x67 0 164x68 0 412x69 0 114x70 0 225x71 0 235x72 0 350x73 0 52x74 0 80x75 0 110x76 0 1335x77 0 126x78 0 990x79 0 137x80 0 325x81 0 325x82 0 340x83 0 425x84 0 150x85 0 50x86 0 50x87 0 49x88 0 50x89 0 52x90 0 50x91 0 56x92 0 30x93 0 49x94 0 50x95 0 50

Computational Intelligence and Neuroscience 3

and exploitation during the searching process in MVO eachuniverse is randomly treated to have wormholes to transportits objects through space In order to ensure the exploitationaround the current best solutions particular wormholetunnels are always established between a universe and thebest universe formed so far which can be representedmathematically as follows

xj

i

XJ + TDR times ubj minus lbj1113872 1113873 times r4 + lbj1113872 1113873 r3 lt 05

XJ minusTDR times ubj minus lbj1113872 1113873 times r4 + lbj1113872 1113873 r3 ge 05

⎧⎪⎨

⎪⎩r2 ltWEP

xj

i r2 geWEP

⎧⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎩

(3)

where Xj is the jth parameter of best universe formed so farTDR (travelling distance rate) and WEP (wormhole exis-tence probability) are coefficients lbj and ubj are the lowerbound and upper bound of jth variable respectively xij isthe jth parameter of ith universe and r2 r3 and r4 are randomnumbers between 0 and 1 WEP and TDR are treated asadaptive formula as follows

WEP Wmin + lWmax minusWmin

L1113874 1113875

TDR 1minusl1p

L1p

(4)

where Wmin is the minimum (in this paper it is set to 02)Wmax is the maximum (in this paper it is set to 1) l is thecurrent iteration L is the maximum iterations and p is theexploitation accuracy over the iterations (in this paper it isset to 6) Higher the value of p the sooner andmore accurateexploitationlocal search is performed [31] It is worth tohighlight that the MVO algorithm depends on number ofiterations number of universes roulette wheel mechanismand universe sorting mechanisme quick sort algorithm isused to sort universe at each iteration and roulette wheelselection is run for each variable in every universe in alliterations Detailed description of MVO can be seen in [31]

3 Our Proposed Initialization Strategy

According to the trend in stochastic techniques randominitialization in each generation is the frequently usedmethod to initialize algorithms without knowing any prioryinformation about the problem in hand e idea of randominitialization is often pushing the algorithm to explore thegiven domain very well while the exploitation around bestsolutions is not carried out by this type of initialization Wehave used an initialization strategy in which IMVO is bal-anced in terms of exploration and exploitation We havedesigned a two-stage initialization strategy in the first stagethe algorithm is initialized randomly for a certain number ofscattered solutions in the whole search domain In stage twoafter the algorithm completes a certain number of iterationsand collects best points in the search domain we initializethe IMVO with population of these best solutions to con-centrate the algorithm on exploitation around the best so-lutions in the space Hence in current studies we haveassigned the function evaluations fixed to solve a problem

in two parts e first part initializes with random pop-ulations and collects the best solutions of each iteration byusing the following equation

Ui Lbi + Ubi minus Lbi( 1113857lowast rand(0 1) (5)

In the second phase the algorithm is directed to searchin the neighborhood of the best solutions obtained in thefirst part and exploits the search space around the pop-ulation of these best solutions

4 Modeling of Electricity Production Cost as aSingle Objective LinearProgramming Problem

In this paper we have presented an optimal mixture ofenergy production system as a linear programming (LP)model consisting of different decision variables representingdifferent electricity production sources of Pakistan seeNomenclature [21] Each variable is bounded and generateselectricity through different fuel types like hydro thermalnuclear wind and solar energies e suggested LP modelincludes different production sources as xi i 1 2 95and ui i 1 2 3 95 represent different costs per kWhfor each source e objective function represents the totalcost (C) incurred to meet the demand of energy in differentsituations Mathematically

minimize cost 111394495

i1uixi (6)

where ui represents the cost per MWh and xi are the dif-ferent sources given in nomenclature e objective of thisstudy is to produce a data set of solutions so that we canselect the required optimal solution fulfilling the givendemand with lowest cost per kWh as compared to othersolutions in the data set For more details about the data setgenerated the reader may refer to [35] e problem is tosearch for best solutions among several candidate solutionsand to meet the required power demand and satisfy con-straints on each variable ese constraints are given inEquation (7) and Table 1 as follows

Total demand constraint

111394495

t1xt ge d (7)

5 Experimental Settings Resultsand Discussion

We have implemented IMVO which is coded in MatlabR2016 [31]emain features of our computer included 8GBRAM with Intelreg Coretrade i7-7500U CPU 27GHz 29GHzwith a 64-bit operating system Windows 10 For a faircomparison the population size was taken as 100 and thenumber of iterations was 100 We have repeated our simu-lations 10 times To elaborate the efficiency of IMVO we haveconsidered three special cases e experimental outcome iscompared with state-of-the-art algorithms firefly algorithm

4 Computational Intelligence and Neuroscience

bat algorithm and grasshopper optimization algorithm as inTables 2 3 and 4 Also we have picked 5 solutions fromoverall 100000 solutions and presented these solutions asdifferent case studies with their respective costs per MWh(Table 5) which are based on the power demand in summersas provided in [20 36ndash38] e power demands and decisionvariables which represent the 95 production sources inPakistan and cost incurred along with the total power pro-duced are given in Table 5 e individual variations of 20best variables required to produce a particular solution in allcase studies are furnished in Table 6 and a weighted com-parison of the 95 energy sources is given in Figure 2 Lookingat these graphs the reader can deduce the importance of eachproduction source of electricity in national grid of thecountry One can deduce which solution to choose if aparticular source is down due to some fault or which sourcesare very impotent and acting as a backbone in generating therequired electricity We have depicted five case studies

graphically as shown in Figure 3 ese graphs are collectiverepresentation of 95 production sources acting to produce acertain demand It is interesting to note that the production ofelectricity from available sources is manageable if propertechniques like IMVO algorithm are implemented to solvethe problem It is worth to note that we have pointed out thetop 20 production sources of electricity in Pakistan accordingto the five case studies listed as in Table 5 ese sources playvital part in the energy production as shown in Table 6 It isobvious that certain sources like x1 are producing higherdemand which are overburdened and could be relaxed byinstalling or expanding alternate sources In Table 7 pricesdepending on different fuel types are listed for a megawatt ofelectricity e convergence plots for these three case studiesare depicted in Figures 4ndash6 It is interesting to note that in allcases with demands of 15000 19000 and 23000megawattsIMVO produced better solutions with lowest costs in millions(Table 2ndash4)

Table 2 Case Study A demand for 15000megawatt where S1 minus S8 represent the collection of sources operating on 8 fuel types

Firefly BAT GOA IMVOPrice in PKR 390831986 252289853 2013324084 1115048004Variable (MW) 150174015 150064398 1500226667 1506746055S1 403519978 289304991 3513562502 4785656S2 140773428 187328453 1072160605 1338551S3 981013264 158209497 624800805 4319034S4 113747918 567079361 3954767659 1476913S5 568488097 850204227 8812308041 5366239S6 921438836 523099019 6841945259 118003S7 393294457 218122192 4421898083 1507902S8 456360696 467863004 198943367 3373776

Table 3 Case Study B demand for 19000megawatt where S1 minus S8 represent collection of sources operating on 8 fuel types

Firefly BAT GOA IMVOPrice in PKR 327227212 236951036 2333069629 1556167319Variable (MW) 190763946 19017236 1902302749 1904411301S1 676141122 492840531 5283899334 3905454S2 239521169 200662552 1695397916 1655S3 146931172 204258471 1671485397 1674898S4 170102742 11029362 1720041194 2433113S5 558369119 101167438 9981020494 816088S6 517009725 15365083 2865642935 4802648S7 489383474 933714342 1374132769 3947306S8 159348169 411244455 9450307236 3397717

Table 4 Case Study C demand for 23000megawatt where S1 minus S8 represent collection of sources operating on 8 fuel types

Firefly BAT GOA IMVOPrice in PKR 350831986 263667565 2766948704 187660591Variable (MW) 230610476 230227254 2304431656 230641461S1 733180841 6292 7333779792 506958882S2 249378785 2618 1725823048 1670682S3 187100046 219 560182213 251706661S4 1756 1756 533408886 246749605S5 768567332 11612 1155322811 978275386S6 110462969 002326828 1089543135 6963726S7 436442721 525 4625011979 448716537S8 381705102 070208538 2900141633 411469586

Computational Intelligence and Neuroscience 5

Table 5 Electricity production of all 95 sources for five case studies

Case Study 1 Case Study 2 Case Study 3 Case Study 4 Case Study 5Price in PKR 112E+ 08 151E+ 08 184E + 08 197E + 08 216E + 08Variables (megawatts) 1500316 19003 2300008 250003 2720836TD (x1) 2379137 156635 2938164 3478 347616MD (x2) 818677 1000 9057829 7634957 98348GBHPP (x3) 5165337 1450 1023352 1347306 1421054WD (x4) 1307975 2104076 1777411 1064834 1815488CB (x5) 3874718 184 7542442 1744151 1638171DKD (x6) 4256789 1163349 1160204 6036495 1274962AKHPP (x7) 2502909 0415286 1190034 3387101 4799439KKHP (x8) 604886 1592544 4172064 72 1927703JagHP (x9) 1417929 30 1285605 8998066 2138508JabHP (x10) 8375935 1057083 1806 9438497 0704657RG (x11) 6866051 3330527 0380166 4987555 9745063DHP (x12) 1428187 1353056 1265834 20 2044366GHD (x13) 605225 0280779 2219217 940119 155921NHP (x14) 6647023 1140453 7595507 6010873 1386329SHP (x15) 1155404 112018 8391618 1116708 13093KHP (x16) 1869716 1137132 1534735 2692804 1023365RKHP (x17) 0905093 1 1 0651626 0854247CHPP (x18) 0864139 0815802 0815802 0965926 0830172GTPP (x19) 1305331 1655 1655 1655 164554MTPP (x20) 6400394 54627 1350 1350 1350JTPP (x21) 1495429 850 850 850 8490554FGTPP (x22) 1489675 1812005 1880609 1031949 217891MGTPP (x23) 4385999 748375 1554596 1458149 1681718MGTPP (x24) 127056 6527735 16615 341201 1109528KGTPP (x25) 1128329 116059 3098832 0567566 1495035LTPP (x26) 4037149 0883692 243518 1205104 1174427FSPP (x27) 3919613 5427258 59 5663659 5509061SGTPP (x28) 0914076 2186785 1466417 2223108 3108445PGTPP (x29) 2730059 1445997 0589928 8484009 2307876PTPP (x30) 1270353 17 6695689 1685053 1195603KGTPS (x31) 9179519 2282708 247 1276751 2468065KPC (x32) 9112861 100 0076503 1621392 1324039GTPS (x33) 2139859 3086809 0608317 4191513 1135833TPS (x34) 1019436 8525889 9217966 1132252 1260CCPP 1 (x35) 3638285 3759421 4858476 5381132 5524153CCPP 2 (x36) 6716314 3599164 5511955 7985884 8991415AES LL (x37) 1248976 362 3301038 3414665 3464409AES PG (x38) 8779272 2897815 365 2441401 3649033AEL (x39) 3047575 29 29 1208485 195939AP (x40) 1465024 1947207 2149626 225 225AGL (x41) 1539627 1074664 1527011 1143378 1135217CHMC PL (x42) 7513341 265198 2733111 2556046 3227874DHA C L (x43) 6873455 0476099 6545028 6296757 7030826EPC (x44) 2340477 98656 3710004 1413346 1520636EPQL (x45) 1307633 2140389 2223562 2265 2262002FKPCL (x46) 952459 157 1512643 278556 1556898FTSM (x47) 5616674 1044668 1008249 7657812 1070448FPCDL (x48) 101152 1643581 1272432 106039 1777063GHLLP (x49) 101702 5626072 1098266 1402346 1576599GEPtvL (x50) 1623922 188 1444615 1795249 1319891GEL (x51) 8193736 8919682 2015 8489962 2015GAEL (x52) 1005592 9235572 5718626 1104825 8202294HCPC (x53) 1113358 5826757 1109772 4347083 1115484HPGC (x54) 1697313 0807693 1923602 1250309 215355HUBCO NPP (x55) 1478875 225 212279 2095134 2235541HUBCOHPP (x56) 1480634 1292 1167515 1292 1292Iptvl (x57) 2153738 1586019 1416202 1642585 1649125JPG (x58) 8413137 120 120 6522738 119424

6 Computational Intelligence and Neuroscience

Table 5 Continued

Case Study 1 Case Study 2 Case Study 3 Case Study 4 Case Study 5KEL (x59) 4350688 4752342 1038332 3058684 1308207KAPCL (x60) 8114451 1223218 118571 1638 1638LPL (x61) 1530046 052402 9467205 1964468 1822104LPTL (x62) 1241896 681917 5095543 1388238 1986912LEPCL (x63) 2556012 5897144 5785459 660 6586634NCP (x64) 1582538 200 9585135 200 1513611NPL (x65) 3248763 200 1684331 1688323 1991059OPCL (x66) 2052865 089022 1327586 6589102 2200356REPGCL (x67) 3020849 1002075 5299079 164 1634477RP (x68) 3271605 2760325 3021523 412 4118322SPC (x69) 7208175 7502883 9121424 1091339 1126283SPPQ (x70) 1010073 225 1240716 21105 221962SESL (x71) 2081023 265598 6600281 2155041 2003566SSEL (x72) 2205401 141361 3211493 3106587 3432993SNPCL (x73) 393573 4414536 0398791 2011775 5189066SE (x74) 7728166 1107506 6637944 2384816 1650386SEPC (x75) 1201473 7111238 401338 4743561 8328035SPGL (x76) 71382 3585756 1086969 8837954 113884TEL (x77) 1102271 2538428 1135676 265028 9401525UchPL (x78) 7352781 2816507 990 990 9897866KANUPP (x79) 504151 9210906 137 1057683 1347101CHASNUPP-1 (x80) 2829386 863647 2758089 325 2687866CHASNUPP-2 (x81) 2002746 2432484 1494219 325 3208773CHASNUPP-3 (x82) 1918579 340 319874 3016324 2140955NPP (x83) 1816426 173693 3748168 3362965 4207756QezSP (x84) 4971705 1069033 7003342 1473463 1267687YEL (x85) 1558682 2334511 4623074 2448091 1286986MWPCL (x86) 4101434 2135616 2794642 3645242 4521504TGL (x87) 9466357 2520002 49 4779046 4790783GAWPL (x88) 1535919 1891722 4514516 1524926 2794244MWEL (x89) 1496827 2199775 52 4787871 4600231FFCEL (x90) 3026861 4268928 50 50 1558795ZEP (x91) 2088768 1437346 4467045 3045881 4017728TWEL (x92) 1528468 121674 30 2952479 2865781HCDPL (x93) 9876255 2000362 4725205 319031 4152962FWEL 1 (x94) 4369201 2980095 4598028 2968556 2261687FWEPL 2 (x95) 6404915 50 6872093 2165334 4028912

0

2000

4000

6000

8000

10000

12000

14000

16000

1 4 7 10 13 16 19 22 25 28 31 34 37 40 43 46 49 52 55 58 61 64 67 70 73 76 79 82 85 88 91 94

Ener

gy p

rodu

ctio

n in

meg

awat

ts

95 energy sources

Series 1Series 2Series 3

Series 4Series 5

Figure 2 A weighted comparison of the 95 energy sources used in five case studies Series 1ndash5 represent case studies 1ndash5 respectively

Computational Intelligence and Neuroscience 7

0

500

1000

1500

2000

2500

1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 33 35 37 39 41 43 45 47 49 51 53 55 57 59 61 63 65 67 69 71 73 75 77 79 81 83 85 87 89 91 93 95

Elec

tric

ity p

rodu

ctio

nin

meg

awat

ts

Power production sources

(a)

0

400200

600

1000800

1200

16001400

1800

1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 33 35 37 39 41 43 45 47 49 51 53 55 57 59 61 63 65 67 69 71 73 75 77 79 81 83 85 87 89 91 93 95

Elec

tric

ity p

rodu

ctio

nin

meg

awat

ts

Power production sources

(b)

0

500

1000

1500

2000

2500

3000

1 4 7 10 13 16 19 22 25 28 31 34 37 40 43 46 49 52 55 58 61 64 67 70 73 76 79 82 85 88 91 94

Elec

tric

ity p

rodu

ctio

nin

meg

awat

ts

Power production sources

(c)

0500

100015002000250030003500

1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 33 35 37 39 41 43 45 47 49 51 53 55 57 59 61 63 65 67 69 71 73 75 77 79 81 83 85 87 89 91 93 95

Elec

tric

ity p

rodu

ctio

nin

meg

awat

ts

Power production sources

(d)

0500

100015002000250030003500

1 4 7 10 13 16 19 22 25 28 31 34 37 40 43 46 49 52 55 58 61 64 67 70 73 76 79 82 85 88 91 94

Elec

tric

ity p

rodu

ctio

nin

meg

awat

ts

All power production sources

(e)

Figure 3 Comprehensive plots of five case studies discussed in Table 4 All production sources are plotted against the electricity productionin megawatts (a) Case Study 1 demand of 15003MW (b) Case Study 2 demand of 19003MW (c) Case Study 3 demand of 23000MW(d) Case Study 4 demand of 250003MW (e) Case Study 5 demand of 272083MW

8 Computational Intelligence and Neuroscience

6 Conclusions

In this paper an improved multiverse optimization al-gorithm is implemented for solving a linear programmingmodel for proper management of electricity productionsources in Pakistan To address the proper management ofpower production sources several bound constraintssuch as constraint for total demand and bounds on allvariables are considered e objective function is linearwith 95 decision variables and different coefficients eIMVO algorithm is easy to implement with few param-eters We have found solutions for five different casestudies and analyzed all solutions graphically A link to thedata set of 100000 different solutions is provided in this

paper In our results we have obtained better solutions tomeet the power demand in summer It is recommendedthat current resources can produce the required powerdemand but some of the resources are required to beexpanded in capacity along with installation of newsources In future we intend to include other factors likepower loss in our model

Nomenclature

TD Tarbela Dam (x1)MD Mangla Dam (x2)GBHPP Ghazi Barota Hydropower Project (x3)WD Warsak Dam (x4)CB Chashma Barrage (x5)DKD Duber Khwar Dam (x6)AKPH Allai Khwar Hydropower Plant (x7)KKPL Khan Khwar Hydropower Plant (x8)JHP Jagran Hydropower Plant (x9)

Table 6 Top 20 electricity production sources according to the five case studies

No1

No2

No3

No4

No5

No6

No7

No8

No9

No10

No11

No12

No13

No14

No15

No16

No17

No18

No19

No20

x1 x19 x60 x3 x20 x56 x34 x78 x21 x2 x36 x63 x35 x68 x83 x37 x38 x72 x74 x81

15

145

14

135

13

125

12

115

11

105

Cos

t

0 10 20 30 40 50 60 70 80 90 100Iterations

times108

Figure 4 IMVO convergence graph demand for 15000megawatt

15

155

145

14

135

17

175

16

165

Cos

t

0 10 20 30 40 50 60 70 80 90 100Iterations

times108

Figure 5 IMVO convergence graph demand for 19000megawatt

194

192

19

188

186

184

182

18

178

174

172C

ost

0 10 20 30 40 50 60 70 80 90 100Iterations

times108

Figure 6 IMVO convergence graph demand for 23000megawatt

Table 7 Per megawatt cost of electricity for different fuel types

Fuel type Price in PKR per megawattHydel 2500LNG 9070Furnace oil 11050High-speed diesel 17960Coal 12080Solar 16950Wind 16630Nuclear 6860Regasified liquefied natural gas 11270

Computational Intelligence and Neuroscience 9

JabHP Jabban Hydropower Plant (x10)RB Rasal Barrage (x11)DHP Dargai Power Plant (x12)GZD Gomal Zam Dam (x13)NHP Nandipur Hydropower Plant (x14)SHP Shadiwal Hydropower Plant (x15)KHP Khuram Hydropower Plant (x16)RKHP Renela Khuard Hydropower Plant (x17)CHPP Chatral Hydropower Plant (x18)GTPP Guduu ermal Power Plant (x19)MTPP Muzaffargarh ermal Power Plant (x20)JTPP Jamshoro ermal Power Plant (x21)FGTPP Faisalabad Gas Turbine Power Plant (x22)MGTPP Multan Gas Turbine Power Plant (x23)KGTPP Kotri Gas Turbine Power Plant (x24)LTPP Larkana ermal Power Plant (x25)FSPP Faisalabad Steam Power Plant (x26)SGTPP Shahdra Gas Turbine Power Plant (x27)PGTPP Panjgur Gas Turbine Power Plant (x28)QTPP Quetta ermal Power Plant (x29)PTPP Pasni ermal Power Plant (x30)KPC Korangi Power Complex (x31)KGTPS Korang Gas Turbine Power Plant Station

(x32)GTPS Gas Turbine Power Station (x33)KPS ermal Power Plant (x34)CCPP1 Combined Cycle Power Plant 1 (x35)CCPP2 Combined Cycle Power Plant 2 (x36)AESLL AES Lalpir Limited (x37)AESPG AES Pak Gen (x38)AEL Altern Energy Limited (x39)AP Altes Power (x40)AGL Attock Gen Limited (x41)CMECP CMEC Power Pvt (x42)DHACL DHA Cogen Limited (x43)EPC Eastern Power Company (x44)EPQL Engro Powergen Qaidpur Limited (x45)FKPP Fauji Kabirwala Power Plant (x46)FTSM First-Star Modaraba (x47)FPCDL Foundation power company Daharki

Limited (x48)GHLLP Grang Holding Limited Power Plant (x49)GEPtvl Green Electric Pvt Limited (x50)GEL Gujranwala Energy Limited (x51)DAEL Gul Ahmad Energy Limited (x52)HCPC Habibullah Coastal Power Company (x53)HPGC Halmore Power Generation Company (x54)HUBCONPP HUBCO Narowal Power Plant (x55)HUBCOHPP HUBCO Hub Power Plant (x56)IPtvL Intergen PTV Limited (x57)JPG Japan Power Plant (x58)KEL Kohinor Energy Limited (x59)KAPCL Kot Addu Power Company Limited (x60)LPL Liberty Power Limited (x61)LPTL Liberty Power Tech Limited (x62)LEPCL Lucky Electric Power Company Limited

(x63)NCP Nishat Chunian Power (x64)

NPL Nishat Power Limited (x65)OPCPrvL Orient Power Company (Pvt) Limited (x66)REPGC Radian Energy Power Generation Company

(x67)RPK Rousch Power Khanewal (x68)SPC Saba Power Company (x69)SPPQ Saif Power Plant Qadirabad (x70)SECL Sapphire Electric Company Limited (x71)SSEL Siddiqsons Energy Limited (x72)SNPCL Sindh Nooriabad Power Company (Pvt)

Limited (x73)SE Sitara Energy (x74)SEPC Southern Electric Power Company Limited

(x75)SPGL Star Power Generation Limited (x76)TEL Tapal Energy Limited (x77)UchPL Uch (Uch-I and Uch-II) Power Limited (x78)KANUPP KANUPP (x79)CHASNUPP-1 CHASNUPP-1 (x80)CHASNUPP-2 CHASNUPP-2 (x81)CHASNUPP-3 CHASNUPP-3 (x82)NPP Nandipur Power Project (x83)QeaSP Quaid-e-Azam Solar Park (x84)YEL Yunus Energy Limited (x85)MWPCL Metro Wind Power Co Limited (x86)TGL Tenaga Generai Limited (x87)GAWPL Gul Ahmed Wind Power Limited (x88)MWEL Master Wind Energy Limited (x89)FFCEL FFC Energy Limited Jhimpir (x90)ZEPJ Zorlu Enerji Pakistan Jhimpir (x91)TWEL Tapal Wind Energy Limited (x92)HCDPL HydroChina Dawood Power Limited (x93)FEW-1L Foundation Wind Energy-I Limited (x94)FEW-2PT Foundation Wind Energy-II Private Limited

(x95)

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

Authorsrsquo Contributions

All authors contributed equally to the writing of this paperAnd all authors read and approved the final manuscript

Acknowledgments

is paper was supported by the Department of Mathe-matics and the Office of Research Innovation andCommercialization of Abdul Wali Khan UniversityMardan Pakistan

10 Computational Intelligence and Neuroscience

References

[1] A Kumar and G Shankar ldquoQuasi-oppositional harmonysearch algorithm based optimal dynamic load frequencycontrol of a hybrid tidal-diesel power generation systemrdquo IETGeneration Transmission amp Distribution vol 12 no 5pp 1099ndash1108 2018

[2] M Mehdinejad B Mohammadi-Ivatloo and R Dadashzadeh-Bonab ldquoEnergy production cost minimization in a combinedheat and power generation systems using cuckoo optimizationalgorithmrdquo Energy Efficiency vol 10 no 1 pp 81ndash96 2017

[3] K Y Lee C Y Chung B J Huang et al ldquoA novel algorithmfor single-axis maximum power generation sun trackersrdquoEnergy Conversion and Management vol 149 pp 543ndash5522017

[4] L S M Guedes P de Mendonca Maia A C LisboaD A G Vieira and R R Saldanha ldquoA unit commitmentalgorithm and a compact MILP model for short-term hydro-power generation schedulingrdquo IEEE Transactions on PowerSystems vol 32 no 5 pp 3381ndash3390 2017

[5] F Zaman S M Elsayed T Ray and R A Sarker ldquoEvo-lutionary algorithms for power generation planning withuncertain renewable energyrdquo Energy vol 112 pp 408ndash4192016

[6] M E Nazari and M M Ardehali ldquoOptimal coordination ofrenewable wind and pumped storage with thermal powergeneration for maximizing economic profit with consider-ations for environmental emission based on newly developedheuristic optimization algorithmrdquo Journal of Renewable andSustainable Energy vol 8 no 6 article 065905 2016

[7] S Hemalatha and S Chandramohan ldquoCost optimization ofpower generation systems using bat algorithm for remotehealth facilitiesrdquo Journal of Medical Imaging and Health In-formatics vol 6 no 7 pp 1646ndash1651 2016

[8] E Assareh and M Biglari ldquoA novel approach to capture themaximum power generation from wind turbines using hybridMLP neural network and bees algorithm (HNNBA)rdquo IETEJournal of Research vol 62 no 3 pp 368ndash378 2016

[9] N Nikmehr and S Najafi-Ravadanegh ldquoOptimal operation ofdistributed generations in micro-grids under uncertainties inload and renewable power generation using heuristic algo-rithmrdquo IET Renewable Power Generation vol 9 no 8pp 982ndash990 2015

[10] W Sun J Wang and H Chang ldquoForecasting annual powergeneration using a harmony search algorithm-based jointparameters optimization combination modelrdquo Energiesvol 5 no 10 pp 3948ndash3971 2012

[11] J Jasper ldquoCost optimization of power generation using adifferential evolution algorithm enhanced with neighbour-hood search operationrdquo International Review of ElectricalEngineering (IREE) vol 7 no 5 pp 5854ndash5865 2012

[12] G Ali ldquoFactors affecting public investment in manufacturingsector of Pakistanrdquo European Journal of Economic Studiesvol 13 no 3 pp 122ndash130 2015

[13] D H Husaini and H H Lean ldquoDoes electricity drive thedevelopment of manufacturing sector in Malaysiardquo Frontiersin Energy Research vol 3 p 18 2015

[14] M M Rafique and S Rehman ldquoNational energy scenario ofPakistan-current status future alternatives and institutionalinfrastructure an overviewrdquo Renewable and SustainableEnergy Reviews vol 69 pp 156ndash167 2017

[15] NEPRA State of Industry Report 2016 httpwwwnepraorgpkpublicationsstateofindustryreportsstateofindustryreport2016pdf

[16] Electricity demand surges to 22000 MWwith rise in mercuryin Dawn 2017 httpswwwdawncomnews1339210

[17] J L C Meza M B Yildirim and A S M Masud ldquoAmultiobjective evolutionary programming algorithm andits applications to power generation expansion planningrdquoIEEE Transactions on Systems Man and Cybernetics-PartA Systems and Humans vol 39 no 5 pp 1086ndash10962009

[18] M Asif ldquoSustainable energy options for Pakistanrdquo Renewableand Sustainable Energy Reviews vol 13 no 4 pp 903ndash9092009

[19] S Wasti Economic Survey of Pakistan 2014-15 Governmentof Pakistan Islamabad Pakistan 2015

[20] M Kugelman Pakistanrsquos Energy Crisis National Bureau ofAsian Research Washington DC USA 2013

[21] H Zameer and Y Wang ldquoEnergy production system opti-mization evidence from Pakistanrdquo Renewable and Sustain-able Energy Reviews vol 82 pp 886ndash893 2018

[22] B Zafar ldquoFuel Price Adjustmentrdquo httpstribunecompkstory957503fuel-price-adjustment-regulator-cuts-power-tariff-for-june-and-july

[23] X S Yang ldquoA new metaheuristic bat-inspired algorithmrdquo inNature Inspired Cooperative Strategies for Optimization(NICSO 2010) pp 65ndash74 Springer Berlin Germany 2010

[24] B Zhu W Zhu Z Liu Q Duan and L Cao ldquoA novelquantum-behaved bat algorithm with mean best positiondirected for numerical optimizationrdquo Computational in-telligence and neuroscience vol 2016 Article ID 609748417 pages 2016

[25] S Saremi S Mirjalili and A Lewis ldquoGrasshopper optimi-sation algorithm theory and applicationrdquo Advances in En-gineering Software vol 105 pp 30ndash47 2017

[26] X S Yang ldquoFirefly algorithm stochastic test functions anddesign optimisationrdquo 2010 httparxivorgabs10031409

[27] C F Chao and M H Horng ldquoe construction of supportvector machine classifier using the firefly algorithmrdquo Com-putational Intelligence and Neuroscience vol 2015 Article ID212719 8 pages 2015

[28] F Ozkaynak ldquoA novel method to improve the performance ofchaos based evolutionary algorithmsrdquo Optik vol 126 no 24pp 5434ndash5438 2015

[29] M Sulaiman A Ahmad A Khan and S MuhammadldquoHybridized symbiotic organism search algorithm for theoptimal operation of directional overcurrent relaysrdquo Com-plexity vol 2018 Article ID 4605769 11 pages 2018

[30] M Sulaiman S Muhammad and A Khan ldquoImproved solu-tions for the optimal coordination of docrs using firefly al-gorithmrdquo Complexity vol 2018 Article ID 7039790 15 pages2018

[31] S Mirjalili Waseem S MMirjalili and A Hatamlou ldquoMulti-verse optimizer a nature-inspired algorithm for global op-timizationrdquo Neural Computing and Applications vol 27no 2 pp 495ndash513 2016

[32] H Faris I Aljarah and S Mirjalili ldquoTraining feedforwardneural networks using multi-verse optimizer for binaryclassification problemsrdquo Applied Intelligence vol 45 no 2pp 322ndash332 2016

[33] C Hu Z Li T Zhou A Zhu and C Xu ldquoA multi-verseoptimizer with levy flights for numerical optimization and itsapplication in test scheduling for network-on-chiprdquo PLoSOne vol 11 no 12 Article ID e0167341 2016

[34] G I Sayed A Darwish and A E Hassanien ldquoQuantummultiverse optimization algorithm for optimization

Computational Intelligence and Neuroscience 11

and exploitation during the searching process in MVO eachuniverse is randomly treated to have wormholes to transportits objects through space In order to ensure the exploitationaround the current best solutions particular wormholetunnels are always established between a universe and thebest universe formed so far which can be representedmathematically as follows

xj

i

XJ + TDR times ubj minus lbj1113872 1113873 times r4 + lbj1113872 1113873 r3 lt 05

XJ minusTDR times ubj minus lbj1113872 1113873 times r4 + lbj1113872 1113873 r3 ge 05

⎧⎪⎨

⎪⎩r2 ltWEP

xj

i r2 geWEP

⎧⎪⎪⎪⎪⎨

⎪⎪⎪⎪⎩

(3)

where Xj is the jth parameter of best universe formed so farTDR (travelling distance rate) and WEP (wormhole exis-tence probability) are coefficients lbj and ubj are the lowerbound and upper bound of jth variable respectively xij isthe jth parameter of ith universe and r2 r3 and r4 are randomnumbers between 0 and 1 WEP and TDR are treated asadaptive formula as follows

WEP Wmin + lWmax minusWmin

L1113874 1113875

TDR 1minusl1p

L1p

(4)

where Wmin is the minimum (in this paper it is set to 02)Wmax is the maximum (in this paper it is set to 1) l is thecurrent iteration L is the maximum iterations and p is theexploitation accuracy over the iterations (in this paper it isset to 6) Higher the value of p the sooner andmore accurateexploitationlocal search is performed [31] It is worth tohighlight that the MVO algorithm depends on number ofiterations number of universes roulette wheel mechanismand universe sorting mechanisme quick sort algorithm isused to sort universe at each iteration and roulette wheelselection is run for each variable in every universe in alliterations Detailed description of MVO can be seen in [31]

3 Our Proposed Initialization Strategy

According to the trend in stochastic techniques randominitialization in each generation is the frequently usedmethod to initialize algorithms without knowing any prioryinformation about the problem in hand e idea of randominitialization is often pushing the algorithm to explore thegiven domain very well while the exploitation around bestsolutions is not carried out by this type of initialization Wehave used an initialization strategy in which IMVO is bal-anced in terms of exploration and exploitation We havedesigned a two-stage initialization strategy in the first stagethe algorithm is initialized randomly for a certain number ofscattered solutions in the whole search domain In stage twoafter the algorithm completes a certain number of iterationsand collects best points in the search domain we initializethe IMVO with population of these best solutions to con-centrate the algorithm on exploitation around the best so-lutions in the space Hence in current studies we haveassigned the function evaluations fixed to solve a problem

in two parts e first part initializes with random pop-ulations and collects the best solutions of each iteration byusing the following equation

Ui Lbi + Ubi minus Lbi( 1113857lowast rand(0 1) (5)

In the second phase the algorithm is directed to searchin the neighborhood of the best solutions obtained in thefirst part and exploits the search space around the pop-ulation of these best solutions

4 Modeling of Electricity Production Cost as aSingle Objective LinearProgramming Problem

In this paper we have presented an optimal mixture ofenergy production system as a linear programming (LP)model consisting of different decision variables representingdifferent electricity production sources of Pakistan seeNomenclature [21] Each variable is bounded and generateselectricity through different fuel types like hydro thermalnuclear wind and solar energies e suggested LP modelincludes different production sources as xi i 1 2 95and ui i 1 2 3 95 represent different costs per kWhfor each source e objective function represents the totalcost (C) incurred to meet the demand of energy in differentsituations Mathematically

minimize cost 111394495

i1uixi (6)

where ui represents the cost per MWh and xi are the dif-ferent sources given in nomenclature e objective of thisstudy is to produce a data set of solutions so that we canselect the required optimal solution fulfilling the givendemand with lowest cost per kWh as compared to othersolutions in the data set For more details about the data setgenerated the reader may refer to [35] e problem is tosearch for best solutions among several candidate solutionsand to meet the required power demand and satisfy con-straints on each variable ese constraints are given inEquation (7) and Table 1 as follows

Total demand constraint

111394495

t1xt ge d (7)

5 Experimental Settings Resultsand Discussion

We have implemented IMVO which is coded in MatlabR2016 [31]emain features of our computer included 8GBRAM with Intelreg Coretrade i7-7500U CPU 27GHz 29GHzwith a 64-bit operating system Windows 10 For a faircomparison the population size was taken as 100 and thenumber of iterations was 100 We have repeated our simu-lations 10 times To elaborate the efficiency of IMVO we haveconsidered three special cases e experimental outcome iscompared with state-of-the-art algorithms firefly algorithm

4 Computational Intelligence and Neuroscience

bat algorithm and grasshopper optimization algorithm as inTables 2 3 and 4 Also we have picked 5 solutions fromoverall 100000 solutions and presented these solutions asdifferent case studies with their respective costs per MWh(Table 5) which are based on the power demand in summersas provided in [20 36ndash38] e power demands and decisionvariables which represent the 95 production sources inPakistan and cost incurred along with the total power pro-duced are given in Table 5 e individual variations of 20best variables required to produce a particular solution in allcase studies are furnished in Table 6 and a weighted com-parison of the 95 energy sources is given in Figure 2 Lookingat these graphs the reader can deduce the importance of eachproduction source of electricity in national grid of thecountry One can deduce which solution to choose if aparticular source is down due to some fault or which sourcesare very impotent and acting as a backbone in generating therequired electricity We have depicted five case studies

graphically as shown in Figure 3 ese graphs are collectiverepresentation of 95 production sources acting to produce acertain demand It is interesting to note that the production ofelectricity from available sources is manageable if propertechniques like IMVO algorithm are implemented to solvethe problem It is worth to note that we have pointed out thetop 20 production sources of electricity in Pakistan accordingto the five case studies listed as in Table 5 ese sources playvital part in the energy production as shown in Table 6 It isobvious that certain sources like x1 are producing higherdemand which are overburdened and could be relaxed byinstalling or expanding alternate sources In Table 7 pricesdepending on different fuel types are listed for a megawatt ofelectricity e convergence plots for these three case studiesare depicted in Figures 4ndash6 It is interesting to note that in allcases with demands of 15000 19000 and 23000megawattsIMVO produced better solutions with lowest costs in millions(Table 2ndash4)

Table 2 Case Study A demand for 15000megawatt where S1 minus S8 represent the collection of sources operating on 8 fuel types

Firefly BAT GOA IMVOPrice in PKR 390831986 252289853 2013324084 1115048004Variable (MW) 150174015 150064398 1500226667 1506746055S1 403519978 289304991 3513562502 4785656S2 140773428 187328453 1072160605 1338551S3 981013264 158209497 624800805 4319034S4 113747918 567079361 3954767659 1476913S5 568488097 850204227 8812308041 5366239S6 921438836 523099019 6841945259 118003S7 393294457 218122192 4421898083 1507902S8 456360696 467863004 198943367 3373776

Table 3 Case Study B demand for 19000megawatt where S1 minus S8 represent collection of sources operating on 8 fuel types

Firefly BAT GOA IMVOPrice in PKR 327227212 236951036 2333069629 1556167319Variable (MW) 190763946 19017236 1902302749 1904411301S1 676141122 492840531 5283899334 3905454S2 239521169 200662552 1695397916 1655S3 146931172 204258471 1671485397 1674898S4 170102742 11029362 1720041194 2433113S5 558369119 101167438 9981020494 816088S6 517009725 15365083 2865642935 4802648S7 489383474 933714342 1374132769 3947306S8 159348169 411244455 9450307236 3397717

Table 4 Case Study C demand for 23000megawatt where S1 minus S8 represent collection of sources operating on 8 fuel types

Firefly BAT GOA IMVOPrice in PKR 350831986 263667565 2766948704 187660591Variable (MW) 230610476 230227254 2304431656 230641461S1 733180841 6292 7333779792 506958882S2 249378785 2618 1725823048 1670682S3 187100046 219 560182213 251706661S4 1756 1756 533408886 246749605S5 768567332 11612 1155322811 978275386S6 110462969 002326828 1089543135 6963726S7 436442721 525 4625011979 448716537S8 381705102 070208538 2900141633 411469586

Computational Intelligence and Neuroscience 5

Table 5 Electricity production of all 95 sources for five case studies

Case Study 1 Case Study 2 Case Study 3 Case Study 4 Case Study 5Price in PKR 112E+ 08 151E+ 08 184E + 08 197E + 08 216E + 08Variables (megawatts) 1500316 19003 2300008 250003 2720836TD (x1) 2379137 156635 2938164 3478 347616MD (x2) 818677 1000 9057829 7634957 98348GBHPP (x3) 5165337 1450 1023352 1347306 1421054WD (x4) 1307975 2104076 1777411 1064834 1815488CB (x5) 3874718 184 7542442 1744151 1638171DKD (x6) 4256789 1163349 1160204 6036495 1274962AKHPP (x7) 2502909 0415286 1190034 3387101 4799439KKHP (x8) 604886 1592544 4172064 72 1927703JagHP (x9) 1417929 30 1285605 8998066 2138508JabHP (x10) 8375935 1057083 1806 9438497 0704657RG (x11) 6866051 3330527 0380166 4987555 9745063DHP (x12) 1428187 1353056 1265834 20 2044366GHD (x13) 605225 0280779 2219217 940119 155921NHP (x14) 6647023 1140453 7595507 6010873 1386329SHP (x15) 1155404 112018 8391618 1116708 13093KHP (x16) 1869716 1137132 1534735 2692804 1023365RKHP (x17) 0905093 1 1 0651626 0854247CHPP (x18) 0864139 0815802 0815802 0965926 0830172GTPP (x19) 1305331 1655 1655 1655 164554MTPP (x20) 6400394 54627 1350 1350 1350JTPP (x21) 1495429 850 850 850 8490554FGTPP (x22) 1489675 1812005 1880609 1031949 217891MGTPP (x23) 4385999 748375 1554596 1458149 1681718MGTPP (x24) 127056 6527735 16615 341201 1109528KGTPP (x25) 1128329 116059 3098832 0567566 1495035LTPP (x26) 4037149 0883692 243518 1205104 1174427FSPP (x27) 3919613 5427258 59 5663659 5509061SGTPP (x28) 0914076 2186785 1466417 2223108 3108445PGTPP (x29) 2730059 1445997 0589928 8484009 2307876PTPP (x30) 1270353 17 6695689 1685053 1195603KGTPS (x31) 9179519 2282708 247 1276751 2468065KPC (x32) 9112861 100 0076503 1621392 1324039GTPS (x33) 2139859 3086809 0608317 4191513 1135833TPS (x34) 1019436 8525889 9217966 1132252 1260CCPP 1 (x35) 3638285 3759421 4858476 5381132 5524153CCPP 2 (x36) 6716314 3599164 5511955 7985884 8991415AES LL (x37) 1248976 362 3301038 3414665 3464409AES PG (x38) 8779272 2897815 365 2441401 3649033AEL (x39) 3047575 29 29 1208485 195939AP (x40) 1465024 1947207 2149626 225 225AGL (x41) 1539627 1074664 1527011 1143378 1135217CHMC PL (x42) 7513341 265198 2733111 2556046 3227874DHA C L (x43) 6873455 0476099 6545028 6296757 7030826EPC (x44) 2340477 98656 3710004 1413346 1520636EPQL (x45) 1307633 2140389 2223562 2265 2262002FKPCL (x46) 952459 157 1512643 278556 1556898FTSM (x47) 5616674 1044668 1008249 7657812 1070448FPCDL (x48) 101152 1643581 1272432 106039 1777063GHLLP (x49) 101702 5626072 1098266 1402346 1576599GEPtvL (x50) 1623922 188 1444615 1795249 1319891GEL (x51) 8193736 8919682 2015 8489962 2015GAEL (x52) 1005592 9235572 5718626 1104825 8202294HCPC (x53) 1113358 5826757 1109772 4347083 1115484HPGC (x54) 1697313 0807693 1923602 1250309 215355HUBCO NPP (x55) 1478875 225 212279 2095134 2235541HUBCOHPP (x56) 1480634 1292 1167515 1292 1292Iptvl (x57) 2153738 1586019 1416202 1642585 1649125JPG (x58) 8413137 120 120 6522738 119424

6 Computational Intelligence and Neuroscience

Table 5 Continued

Case Study 1 Case Study 2 Case Study 3 Case Study 4 Case Study 5KEL (x59) 4350688 4752342 1038332 3058684 1308207KAPCL (x60) 8114451 1223218 118571 1638 1638LPL (x61) 1530046 052402 9467205 1964468 1822104LPTL (x62) 1241896 681917 5095543 1388238 1986912LEPCL (x63) 2556012 5897144 5785459 660 6586634NCP (x64) 1582538 200 9585135 200 1513611NPL (x65) 3248763 200 1684331 1688323 1991059OPCL (x66) 2052865 089022 1327586 6589102 2200356REPGCL (x67) 3020849 1002075 5299079 164 1634477RP (x68) 3271605 2760325 3021523 412 4118322SPC (x69) 7208175 7502883 9121424 1091339 1126283SPPQ (x70) 1010073 225 1240716 21105 221962SESL (x71) 2081023 265598 6600281 2155041 2003566SSEL (x72) 2205401 141361 3211493 3106587 3432993SNPCL (x73) 393573 4414536 0398791 2011775 5189066SE (x74) 7728166 1107506 6637944 2384816 1650386SEPC (x75) 1201473 7111238 401338 4743561 8328035SPGL (x76) 71382 3585756 1086969 8837954 113884TEL (x77) 1102271 2538428 1135676 265028 9401525UchPL (x78) 7352781 2816507 990 990 9897866KANUPP (x79) 504151 9210906 137 1057683 1347101CHASNUPP-1 (x80) 2829386 863647 2758089 325 2687866CHASNUPP-2 (x81) 2002746 2432484 1494219 325 3208773CHASNUPP-3 (x82) 1918579 340 319874 3016324 2140955NPP (x83) 1816426 173693 3748168 3362965 4207756QezSP (x84) 4971705 1069033 7003342 1473463 1267687YEL (x85) 1558682 2334511 4623074 2448091 1286986MWPCL (x86) 4101434 2135616 2794642 3645242 4521504TGL (x87) 9466357 2520002 49 4779046 4790783GAWPL (x88) 1535919 1891722 4514516 1524926 2794244MWEL (x89) 1496827 2199775 52 4787871 4600231FFCEL (x90) 3026861 4268928 50 50 1558795ZEP (x91) 2088768 1437346 4467045 3045881 4017728TWEL (x92) 1528468 121674 30 2952479 2865781HCDPL (x93) 9876255 2000362 4725205 319031 4152962FWEL 1 (x94) 4369201 2980095 4598028 2968556 2261687FWEPL 2 (x95) 6404915 50 6872093 2165334 4028912

0

2000

4000

6000

8000

10000

12000

14000

16000

1 4 7 10 13 16 19 22 25 28 31 34 37 40 43 46 49 52 55 58 61 64 67 70 73 76 79 82 85 88 91 94

Ener

gy p

rodu

ctio

n in

meg

awat

ts

95 energy sources

Series 1Series 2Series 3

Series 4Series 5

Figure 2 A weighted comparison of the 95 energy sources used in five case studies Series 1ndash5 represent case studies 1ndash5 respectively

Computational Intelligence and Neuroscience 7

0

500

1000

1500

2000

2500

1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 33 35 37 39 41 43 45 47 49 51 53 55 57 59 61 63 65 67 69 71 73 75 77 79 81 83 85 87 89 91 93 95

Elec

tric

ity p

rodu

ctio

nin

meg

awat

ts

Power production sources

(a)

0

400200

600

1000800

1200

16001400

1800

1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 33 35 37 39 41 43 45 47 49 51 53 55 57 59 61 63 65 67 69 71 73 75 77 79 81 83 85 87 89 91 93 95

Elec

tric

ity p

rodu

ctio

nin

meg

awat

ts

Power production sources

(b)

0

500

1000

1500

2000

2500

3000

1 4 7 10 13 16 19 22 25 28 31 34 37 40 43 46 49 52 55 58 61 64 67 70 73 76 79 82 85 88 91 94

Elec

tric

ity p

rodu

ctio

nin

meg

awat

ts

Power production sources

(c)

0500

100015002000250030003500

1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 33 35 37 39 41 43 45 47 49 51 53 55 57 59 61 63 65 67 69 71 73 75 77 79 81 83 85 87 89 91 93 95

Elec

tric

ity p

rodu

ctio

nin

meg

awat

ts

Power production sources

(d)

0500

100015002000250030003500

1 4 7 10 13 16 19 22 25 28 31 34 37 40 43 46 49 52 55 58 61 64 67 70 73 76 79 82 85 88 91 94

Elec

tric

ity p

rodu

ctio

nin

meg

awat

ts

All power production sources

(e)

Figure 3 Comprehensive plots of five case studies discussed in Table 4 All production sources are plotted against the electricity productionin megawatts (a) Case Study 1 demand of 15003MW (b) Case Study 2 demand of 19003MW (c) Case Study 3 demand of 23000MW(d) Case Study 4 demand of 250003MW (e) Case Study 5 demand of 272083MW

8 Computational Intelligence and Neuroscience

6 Conclusions

In this paper an improved multiverse optimization al-gorithm is implemented for solving a linear programmingmodel for proper management of electricity productionsources in Pakistan To address the proper management ofpower production sources several bound constraintssuch as constraint for total demand and bounds on allvariables are considered e objective function is linearwith 95 decision variables and different coefficients eIMVO algorithm is easy to implement with few param-eters We have found solutions for five different casestudies and analyzed all solutions graphically A link to thedata set of 100000 different solutions is provided in this

paper In our results we have obtained better solutions tomeet the power demand in summer It is recommendedthat current resources can produce the required powerdemand but some of the resources are required to beexpanded in capacity along with installation of newsources In future we intend to include other factors likepower loss in our model

Nomenclature

TD Tarbela Dam (x1)MD Mangla Dam (x2)GBHPP Ghazi Barota Hydropower Project (x3)WD Warsak Dam (x4)CB Chashma Barrage (x5)DKD Duber Khwar Dam (x6)AKPH Allai Khwar Hydropower Plant (x7)KKPL Khan Khwar Hydropower Plant (x8)JHP Jagran Hydropower Plant (x9)

Table 6 Top 20 electricity production sources according to the five case studies

No1

No2

No3

No4

No5

No6

No7

No8

No9

No10

No11

No12

No13

No14

No15

No16

No17

No18

No19

No20

x1 x19 x60 x3 x20 x56 x34 x78 x21 x2 x36 x63 x35 x68 x83 x37 x38 x72 x74 x81

15

145

14

135

13

125

12

115

11

105

Cos

t

0 10 20 30 40 50 60 70 80 90 100Iterations

times108

Figure 4 IMVO convergence graph demand for 15000megawatt

15

155

145

14

135

17

175

16

165

Cos

t

0 10 20 30 40 50 60 70 80 90 100Iterations

times108

Figure 5 IMVO convergence graph demand for 19000megawatt

194

192

19

188

186

184

182

18

178

174

172C

ost

0 10 20 30 40 50 60 70 80 90 100Iterations

times108

Figure 6 IMVO convergence graph demand for 23000megawatt

Table 7 Per megawatt cost of electricity for different fuel types

Fuel type Price in PKR per megawattHydel 2500LNG 9070Furnace oil 11050High-speed diesel 17960Coal 12080Solar 16950Wind 16630Nuclear 6860Regasified liquefied natural gas 11270

Computational Intelligence and Neuroscience 9

JabHP Jabban Hydropower Plant (x10)RB Rasal Barrage (x11)DHP Dargai Power Plant (x12)GZD Gomal Zam Dam (x13)NHP Nandipur Hydropower Plant (x14)SHP Shadiwal Hydropower Plant (x15)KHP Khuram Hydropower Plant (x16)RKHP Renela Khuard Hydropower Plant (x17)CHPP Chatral Hydropower Plant (x18)GTPP Guduu ermal Power Plant (x19)MTPP Muzaffargarh ermal Power Plant (x20)JTPP Jamshoro ermal Power Plant (x21)FGTPP Faisalabad Gas Turbine Power Plant (x22)MGTPP Multan Gas Turbine Power Plant (x23)KGTPP Kotri Gas Turbine Power Plant (x24)LTPP Larkana ermal Power Plant (x25)FSPP Faisalabad Steam Power Plant (x26)SGTPP Shahdra Gas Turbine Power Plant (x27)PGTPP Panjgur Gas Turbine Power Plant (x28)QTPP Quetta ermal Power Plant (x29)PTPP Pasni ermal Power Plant (x30)KPC Korangi Power Complex (x31)KGTPS Korang Gas Turbine Power Plant Station

(x32)GTPS Gas Turbine Power Station (x33)KPS ermal Power Plant (x34)CCPP1 Combined Cycle Power Plant 1 (x35)CCPP2 Combined Cycle Power Plant 2 (x36)AESLL AES Lalpir Limited (x37)AESPG AES Pak Gen (x38)AEL Altern Energy Limited (x39)AP Altes Power (x40)AGL Attock Gen Limited (x41)CMECP CMEC Power Pvt (x42)DHACL DHA Cogen Limited (x43)EPC Eastern Power Company (x44)EPQL Engro Powergen Qaidpur Limited (x45)FKPP Fauji Kabirwala Power Plant (x46)FTSM First-Star Modaraba (x47)FPCDL Foundation power company Daharki

Limited (x48)GHLLP Grang Holding Limited Power Plant (x49)GEPtvl Green Electric Pvt Limited (x50)GEL Gujranwala Energy Limited (x51)DAEL Gul Ahmad Energy Limited (x52)HCPC Habibullah Coastal Power Company (x53)HPGC Halmore Power Generation Company (x54)HUBCONPP HUBCO Narowal Power Plant (x55)HUBCOHPP HUBCO Hub Power Plant (x56)IPtvL Intergen PTV Limited (x57)JPG Japan Power Plant (x58)KEL Kohinor Energy Limited (x59)KAPCL Kot Addu Power Company Limited (x60)LPL Liberty Power Limited (x61)LPTL Liberty Power Tech Limited (x62)LEPCL Lucky Electric Power Company Limited

(x63)NCP Nishat Chunian Power (x64)

NPL Nishat Power Limited (x65)OPCPrvL Orient Power Company (Pvt) Limited (x66)REPGC Radian Energy Power Generation Company

(x67)RPK Rousch Power Khanewal (x68)SPC Saba Power Company (x69)SPPQ Saif Power Plant Qadirabad (x70)SECL Sapphire Electric Company Limited (x71)SSEL Siddiqsons Energy Limited (x72)SNPCL Sindh Nooriabad Power Company (Pvt)

Limited (x73)SE Sitara Energy (x74)SEPC Southern Electric Power Company Limited

(x75)SPGL Star Power Generation Limited (x76)TEL Tapal Energy Limited (x77)UchPL Uch (Uch-I and Uch-II) Power Limited (x78)KANUPP KANUPP (x79)CHASNUPP-1 CHASNUPP-1 (x80)CHASNUPP-2 CHASNUPP-2 (x81)CHASNUPP-3 CHASNUPP-3 (x82)NPP Nandipur Power Project (x83)QeaSP Quaid-e-Azam Solar Park (x84)YEL Yunus Energy Limited (x85)MWPCL Metro Wind Power Co Limited (x86)TGL Tenaga Generai Limited (x87)GAWPL Gul Ahmed Wind Power Limited (x88)MWEL Master Wind Energy Limited (x89)FFCEL FFC Energy Limited Jhimpir (x90)ZEPJ Zorlu Enerji Pakistan Jhimpir (x91)TWEL Tapal Wind Energy Limited (x92)HCDPL HydroChina Dawood Power Limited (x93)FEW-1L Foundation Wind Energy-I Limited (x94)FEW-2PT Foundation Wind Energy-II Private Limited

(x95)

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

Authorsrsquo Contributions

All authors contributed equally to the writing of this paperAnd all authors read and approved the final manuscript

Acknowledgments

is paper was supported by the Department of Mathe-matics and the Office of Research Innovation andCommercialization of Abdul Wali Khan UniversityMardan Pakistan

10 Computational Intelligence and Neuroscience

References

[1] A Kumar and G Shankar ldquoQuasi-oppositional harmonysearch algorithm based optimal dynamic load frequencycontrol of a hybrid tidal-diesel power generation systemrdquo IETGeneration Transmission amp Distribution vol 12 no 5pp 1099ndash1108 2018

[2] M Mehdinejad B Mohammadi-Ivatloo and R Dadashzadeh-Bonab ldquoEnergy production cost minimization in a combinedheat and power generation systems using cuckoo optimizationalgorithmrdquo Energy Efficiency vol 10 no 1 pp 81ndash96 2017

[3] K Y Lee C Y Chung B J Huang et al ldquoA novel algorithmfor single-axis maximum power generation sun trackersrdquoEnergy Conversion and Management vol 149 pp 543ndash5522017

[4] L S M Guedes P de Mendonca Maia A C LisboaD A G Vieira and R R Saldanha ldquoA unit commitmentalgorithm and a compact MILP model for short-term hydro-power generation schedulingrdquo IEEE Transactions on PowerSystems vol 32 no 5 pp 3381ndash3390 2017

[5] F Zaman S M Elsayed T Ray and R A Sarker ldquoEvo-lutionary algorithms for power generation planning withuncertain renewable energyrdquo Energy vol 112 pp 408ndash4192016

[6] M E Nazari and M M Ardehali ldquoOptimal coordination ofrenewable wind and pumped storage with thermal powergeneration for maximizing economic profit with consider-ations for environmental emission based on newly developedheuristic optimization algorithmrdquo Journal of Renewable andSustainable Energy vol 8 no 6 article 065905 2016

[7] S Hemalatha and S Chandramohan ldquoCost optimization ofpower generation systems using bat algorithm for remotehealth facilitiesrdquo Journal of Medical Imaging and Health In-formatics vol 6 no 7 pp 1646ndash1651 2016

[8] E Assareh and M Biglari ldquoA novel approach to capture themaximum power generation from wind turbines using hybridMLP neural network and bees algorithm (HNNBA)rdquo IETEJournal of Research vol 62 no 3 pp 368ndash378 2016

[9] N Nikmehr and S Najafi-Ravadanegh ldquoOptimal operation ofdistributed generations in micro-grids under uncertainties inload and renewable power generation using heuristic algo-rithmrdquo IET Renewable Power Generation vol 9 no 8pp 982ndash990 2015

[10] W Sun J Wang and H Chang ldquoForecasting annual powergeneration using a harmony search algorithm-based jointparameters optimization combination modelrdquo Energiesvol 5 no 10 pp 3948ndash3971 2012

[11] J Jasper ldquoCost optimization of power generation using adifferential evolution algorithm enhanced with neighbour-hood search operationrdquo International Review of ElectricalEngineering (IREE) vol 7 no 5 pp 5854ndash5865 2012

[12] G Ali ldquoFactors affecting public investment in manufacturingsector of Pakistanrdquo European Journal of Economic Studiesvol 13 no 3 pp 122ndash130 2015

[13] D H Husaini and H H Lean ldquoDoes electricity drive thedevelopment of manufacturing sector in Malaysiardquo Frontiersin Energy Research vol 3 p 18 2015

[14] M M Rafique and S Rehman ldquoNational energy scenario ofPakistan-current status future alternatives and institutionalinfrastructure an overviewrdquo Renewable and SustainableEnergy Reviews vol 69 pp 156ndash167 2017

[15] NEPRA State of Industry Report 2016 httpwwwnepraorgpkpublicationsstateofindustryreportsstateofindustryreport2016pdf

[16] Electricity demand surges to 22000 MWwith rise in mercuryin Dawn 2017 httpswwwdawncomnews1339210

[17] J L C Meza M B Yildirim and A S M Masud ldquoAmultiobjective evolutionary programming algorithm andits applications to power generation expansion planningrdquoIEEE Transactions on Systems Man and Cybernetics-PartA Systems and Humans vol 39 no 5 pp 1086ndash10962009

[18] M Asif ldquoSustainable energy options for Pakistanrdquo Renewableand Sustainable Energy Reviews vol 13 no 4 pp 903ndash9092009

[19] S Wasti Economic Survey of Pakistan 2014-15 Governmentof Pakistan Islamabad Pakistan 2015

[20] M Kugelman Pakistanrsquos Energy Crisis National Bureau ofAsian Research Washington DC USA 2013

[21] H Zameer and Y Wang ldquoEnergy production system opti-mization evidence from Pakistanrdquo Renewable and Sustain-able Energy Reviews vol 82 pp 886ndash893 2018

[22] B Zafar ldquoFuel Price Adjustmentrdquo httpstribunecompkstory957503fuel-price-adjustment-regulator-cuts-power-tariff-for-june-and-july

[23] X S Yang ldquoA new metaheuristic bat-inspired algorithmrdquo inNature Inspired Cooperative Strategies for Optimization(NICSO 2010) pp 65ndash74 Springer Berlin Germany 2010

[24] B Zhu W Zhu Z Liu Q Duan and L Cao ldquoA novelquantum-behaved bat algorithm with mean best positiondirected for numerical optimizationrdquo Computational in-telligence and neuroscience vol 2016 Article ID 609748417 pages 2016

[25] S Saremi S Mirjalili and A Lewis ldquoGrasshopper optimi-sation algorithm theory and applicationrdquo Advances in En-gineering Software vol 105 pp 30ndash47 2017

[26] X S Yang ldquoFirefly algorithm stochastic test functions anddesign optimisationrdquo 2010 httparxivorgabs10031409

[27] C F Chao and M H Horng ldquoe construction of supportvector machine classifier using the firefly algorithmrdquo Com-putational Intelligence and Neuroscience vol 2015 Article ID212719 8 pages 2015

[28] F Ozkaynak ldquoA novel method to improve the performance ofchaos based evolutionary algorithmsrdquo Optik vol 126 no 24pp 5434ndash5438 2015

[29] M Sulaiman A Ahmad A Khan and S MuhammadldquoHybridized symbiotic organism search algorithm for theoptimal operation of directional overcurrent relaysrdquo Com-plexity vol 2018 Article ID 4605769 11 pages 2018

[30] M Sulaiman S Muhammad and A Khan ldquoImproved solu-tions for the optimal coordination of docrs using firefly al-gorithmrdquo Complexity vol 2018 Article ID 7039790 15 pages2018

[31] S Mirjalili Waseem S MMirjalili and A Hatamlou ldquoMulti-verse optimizer a nature-inspired algorithm for global op-timizationrdquo Neural Computing and Applications vol 27no 2 pp 495ndash513 2016

[32] H Faris I Aljarah and S Mirjalili ldquoTraining feedforwardneural networks using multi-verse optimizer for binaryclassification problemsrdquo Applied Intelligence vol 45 no 2pp 322ndash332 2016

[33] C Hu Z Li T Zhou A Zhu and C Xu ldquoA multi-verseoptimizer with levy flights for numerical optimization and itsapplication in test scheduling for network-on-chiprdquo PLoSOne vol 11 no 12 Article ID e0167341 2016

[34] G I Sayed A Darwish and A E Hassanien ldquoQuantummultiverse optimization algorithm for optimization

Computational Intelligence and Neuroscience 11

bat algorithm and grasshopper optimization algorithm as inTables 2 3 and 4 Also we have picked 5 solutions fromoverall 100000 solutions and presented these solutions asdifferent case studies with their respective costs per MWh(Table 5) which are based on the power demand in summersas provided in [20 36ndash38] e power demands and decisionvariables which represent the 95 production sources inPakistan and cost incurred along with the total power pro-duced are given in Table 5 e individual variations of 20best variables required to produce a particular solution in allcase studies are furnished in Table 6 and a weighted com-parison of the 95 energy sources is given in Figure 2 Lookingat these graphs the reader can deduce the importance of eachproduction source of electricity in national grid of thecountry One can deduce which solution to choose if aparticular source is down due to some fault or which sourcesare very impotent and acting as a backbone in generating therequired electricity We have depicted five case studies

graphically as shown in Figure 3 ese graphs are collectiverepresentation of 95 production sources acting to produce acertain demand It is interesting to note that the production ofelectricity from available sources is manageable if propertechniques like IMVO algorithm are implemented to solvethe problem It is worth to note that we have pointed out thetop 20 production sources of electricity in Pakistan accordingto the five case studies listed as in Table 5 ese sources playvital part in the energy production as shown in Table 6 It isobvious that certain sources like x1 are producing higherdemand which are overburdened and could be relaxed byinstalling or expanding alternate sources In Table 7 pricesdepending on different fuel types are listed for a megawatt ofelectricity e convergence plots for these three case studiesare depicted in Figures 4ndash6 It is interesting to note that in allcases with demands of 15000 19000 and 23000megawattsIMVO produced better solutions with lowest costs in millions(Table 2ndash4)

Table 2 Case Study A demand for 15000megawatt where S1 minus S8 represent the collection of sources operating on 8 fuel types

Firefly BAT GOA IMVOPrice in PKR 390831986 252289853 2013324084 1115048004Variable (MW) 150174015 150064398 1500226667 1506746055S1 403519978 289304991 3513562502 4785656S2 140773428 187328453 1072160605 1338551S3 981013264 158209497 624800805 4319034S4 113747918 567079361 3954767659 1476913S5 568488097 850204227 8812308041 5366239S6 921438836 523099019 6841945259 118003S7 393294457 218122192 4421898083 1507902S8 456360696 467863004 198943367 3373776

Table 3 Case Study B demand for 19000megawatt where S1 minus S8 represent collection of sources operating on 8 fuel types

Firefly BAT GOA IMVOPrice in PKR 327227212 236951036 2333069629 1556167319Variable (MW) 190763946 19017236 1902302749 1904411301S1 676141122 492840531 5283899334 3905454S2 239521169 200662552 1695397916 1655S3 146931172 204258471 1671485397 1674898S4 170102742 11029362 1720041194 2433113S5 558369119 101167438 9981020494 816088S6 517009725 15365083 2865642935 4802648S7 489383474 933714342 1374132769 3947306S8 159348169 411244455 9450307236 3397717

Table 4 Case Study C demand for 23000megawatt where S1 minus S8 represent collection of sources operating on 8 fuel types

Firefly BAT GOA IMVOPrice in PKR 350831986 263667565 2766948704 187660591Variable (MW) 230610476 230227254 2304431656 230641461S1 733180841 6292 7333779792 506958882S2 249378785 2618 1725823048 1670682S3 187100046 219 560182213 251706661S4 1756 1756 533408886 246749605S5 768567332 11612 1155322811 978275386S6 110462969 002326828 1089543135 6963726S7 436442721 525 4625011979 448716537S8 381705102 070208538 2900141633 411469586

Computational Intelligence and Neuroscience 5

Table 5 Electricity production of all 95 sources for five case studies

Case Study 1 Case Study 2 Case Study 3 Case Study 4 Case Study 5Price in PKR 112E+ 08 151E+ 08 184E + 08 197E + 08 216E + 08Variables (megawatts) 1500316 19003 2300008 250003 2720836TD (x1) 2379137 156635 2938164 3478 347616MD (x2) 818677 1000 9057829 7634957 98348GBHPP (x3) 5165337 1450 1023352 1347306 1421054WD (x4) 1307975 2104076 1777411 1064834 1815488CB (x5) 3874718 184 7542442 1744151 1638171DKD (x6) 4256789 1163349 1160204 6036495 1274962AKHPP (x7) 2502909 0415286 1190034 3387101 4799439KKHP (x8) 604886 1592544 4172064 72 1927703JagHP (x9) 1417929 30 1285605 8998066 2138508JabHP (x10) 8375935 1057083 1806 9438497 0704657RG (x11) 6866051 3330527 0380166 4987555 9745063DHP (x12) 1428187 1353056 1265834 20 2044366GHD (x13) 605225 0280779 2219217 940119 155921NHP (x14) 6647023 1140453 7595507 6010873 1386329SHP (x15) 1155404 112018 8391618 1116708 13093KHP (x16) 1869716 1137132 1534735 2692804 1023365RKHP (x17) 0905093 1 1 0651626 0854247CHPP (x18) 0864139 0815802 0815802 0965926 0830172GTPP (x19) 1305331 1655 1655 1655 164554MTPP (x20) 6400394 54627 1350 1350 1350JTPP (x21) 1495429 850 850 850 8490554FGTPP (x22) 1489675 1812005 1880609 1031949 217891MGTPP (x23) 4385999 748375 1554596 1458149 1681718MGTPP (x24) 127056 6527735 16615 341201 1109528KGTPP (x25) 1128329 116059 3098832 0567566 1495035LTPP (x26) 4037149 0883692 243518 1205104 1174427FSPP (x27) 3919613 5427258 59 5663659 5509061SGTPP (x28) 0914076 2186785 1466417 2223108 3108445PGTPP (x29) 2730059 1445997 0589928 8484009 2307876PTPP (x30) 1270353 17 6695689 1685053 1195603KGTPS (x31) 9179519 2282708 247 1276751 2468065KPC (x32) 9112861 100 0076503 1621392 1324039GTPS (x33) 2139859 3086809 0608317 4191513 1135833TPS (x34) 1019436 8525889 9217966 1132252 1260CCPP 1 (x35) 3638285 3759421 4858476 5381132 5524153CCPP 2 (x36) 6716314 3599164 5511955 7985884 8991415AES LL (x37) 1248976 362 3301038 3414665 3464409AES PG (x38) 8779272 2897815 365 2441401 3649033AEL (x39) 3047575 29 29 1208485 195939AP (x40) 1465024 1947207 2149626 225 225AGL (x41) 1539627 1074664 1527011 1143378 1135217CHMC PL (x42) 7513341 265198 2733111 2556046 3227874DHA C L (x43) 6873455 0476099 6545028 6296757 7030826EPC (x44) 2340477 98656 3710004 1413346 1520636EPQL (x45) 1307633 2140389 2223562 2265 2262002FKPCL (x46) 952459 157 1512643 278556 1556898FTSM (x47) 5616674 1044668 1008249 7657812 1070448FPCDL (x48) 101152 1643581 1272432 106039 1777063GHLLP (x49) 101702 5626072 1098266 1402346 1576599GEPtvL (x50) 1623922 188 1444615 1795249 1319891GEL (x51) 8193736 8919682 2015 8489962 2015GAEL (x52) 1005592 9235572 5718626 1104825 8202294HCPC (x53) 1113358 5826757 1109772 4347083 1115484HPGC (x54) 1697313 0807693 1923602 1250309 215355HUBCO NPP (x55) 1478875 225 212279 2095134 2235541HUBCOHPP (x56) 1480634 1292 1167515 1292 1292Iptvl (x57) 2153738 1586019 1416202 1642585 1649125JPG (x58) 8413137 120 120 6522738 119424

6 Computational Intelligence and Neuroscience

Table 5 Continued

Case Study 1 Case Study 2 Case Study 3 Case Study 4 Case Study 5KEL (x59) 4350688 4752342 1038332 3058684 1308207KAPCL (x60) 8114451 1223218 118571 1638 1638LPL (x61) 1530046 052402 9467205 1964468 1822104LPTL (x62) 1241896 681917 5095543 1388238 1986912LEPCL (x63) 2556012 5897144 5785459 660 6586634NCP (x64) 1582538 200 9585135 200 1513611NPL (x65) 3248763 200 1684331 1688323 1991059OPCL (x66) 2052865 089022 1327586 6589102 2200356REPGCL (x67) 3020849 1002075 5299079 164 1634477RP (x68) 3271605 2760325 3021523 412 4118322SPC (x69) 7208175 7502883 9121424 1091339 1126283SPPQ (x70) 1010073 225 1240716 21105 221962SESL (x71) 2081023 265598 6600281 2155041 2003566SSEL (x72) 2205401 141361 3211493 3106587 3432993SNPCL (x73) 393573 4414536 0398791 2011775 5189066SE (x74) 7728166 1107506 6637944 2384816 1650386SEPC (x75) 1201473 7111238 401338 4743561 8328035SPGL (x76) 71382 3585756 1086969 8837954 113884TEL (x77) 1102271 2538428 1135676 265028 9401525UchPL (x78) 7352781 2816507 990 990 9897866KANUPP (x79) 504151 9210906 137 1057683 1347101CHASNUPP-1 (x80) 2829386 863647 2758089 325 2687866CHASNUPP-2 (x81) 2002746 2432484 1494219 325 3208773CHASNUPP-3 (x82) 1918579 340 319874 3016324 2140955NPP (x83) 1816426 173693 3748168 3362965 4207756QezSP (x84) 4971705 1069033 7003342 1473463 1267687YEL (x85) 1558682 2334511 4623074 2448091 1286986MWPCL (x86) 4101434 2135616 2794642 3645242 4521504TGL (x87) 9466357 2520002 49 4779046 4790783GAWPL (x88) 1535919 1891722 4514516 1524926 2794244MWEL (x89) 1496827 2199775 52 4787871 4600231FFCEL (x90) 3026861 4268928 50 50 1558795ZEP (x91) 2088768 1437346 4467045 3045881 4017728TWEL (x92) 1528468 121674 30 2952479 2865781HCDPL (x93) 9876255 2000362 4725205 319031 4152962FWEL 1 (x94) 4369201 2980095 4598028 2968556 2261687FWEPL 2 (x95) 6404915 50 6872093 2165334 4028912

0

2000

4000

6000

8000

10000

12000

14000

16000

1 4 7 10 13 16 19 22 25 28 31 34 37 40 43 46 49 52 55 58 61 64 67 70 73 76 79 82 85 88 91 94

Ener

gy p

rodu

ctio

n in

meg

awat

ts

95 energy sources

Series 1Series 2Series 3

Series 4Series 5

Figure 2 A weighted comparison of the 95 energy sources used in five case studies Series 1ndash5 represent case studies 1ndash5 respectively

Computational Intelligence and Neuroscience 7

0

500

1000

1500

2000

2500

1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 33 35 37 39 41 43 45 47 49 51 53 55 57 59 61 63 65 67 69 71 73 75 77 79 81 83 85 87 89 91 93 95

Elec

tric

ity p

rodu

ctio

nin

meg

awat

ts

Power production sources

(a)

0

400200

600

1000800

1200

16001400

1800

1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 33 35 37 39 41 43 45 47 49 51 53 55 57 59 61 63 65 67 69 71 73 75 77 79 81 83 85 87 89 91 93 95

Elec

tric

ity p

rodu

ctio

nin

meg

awat

ts

Power production sources

(b)

0

500

1000

1500

2000

2500

3000

1 4 7 10 13 16 19 22 25 28 31 34 37 40 43 46 49 52 55 58 61 64 67 70 73 76 79 82 85 88 91 94

Elec

tric

ity p

rodu

ctio

nin

meg

awat

ts

Power production sources

(c)

0500

100015002000250030003500

1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 33 35 37 39 41 43 45 47 49 51 53 55 57 59 61 63 65 67 69 71 73 75 77 79 81 83 85 87 89 91 93 95

Elec

tric

ity p

rodu

ctio

nin

meg

awat

ts

Power production sources

(d)

0500

100015002000250030003500

1 4 7 10 13 16 19 22 25 28 31 34 37 40 43 46 49 52 55 58 61 64 67 70 73 76 79 82 85 88 91 94

Elec

tric

ity p

rodu

ctio

nin

meg

awat

ts

All power production sources

(e)

Figure 3 Comprehensive plots of five case studies discussed in Table 4 All production sources are plotted against the electricity productionin megawatts (a) Case Study 1 demand of 15003MW (b) Case Study 2 demand of 19003MW (c) Case Study 3 demand of 23000MW(d) Case Study 4 demand of 250003MW (e) Case Study 5 demand of 272083MW

8 Computational Intelligence and Neuroscience

6 Conclusions

In this paper an improved multiverse optimization al-gorithm is implemented for solving a linear programmingmodel for proper management of electricity productionsources in Pakistan To address the proper management ofpower production sources several bound constraintssuch as constraint for total demand and bounds on allvariables are considered e objective function is linearwith 95 decision variables and different coefficients eIMVO algorithm is easy to implement with few param-eters We have found solutions for five different casestudies and analyzed all solutions graphically A link to thedata set of 100000 different solutions is provided in this

paper In our results we have obtained better solutions tomeet the power demand in summer It is recommendedthat current resources can produce the required powerdemand but some of the resources are required to beexpanded in capacity along with installation of newsources In future we intend to include other factors likepower loss in our model

Nomenclature

TD Tarbela Dam (x1)MD Mangla Dam (x2)GBHPP Ghazi Barota Hydropower Project (x3)WD Warsak Dam (x4)CB Chashma Barrage (x5)DKD Duber Khwar Dam (x6)AKPH Allai Khwar Hydropower Plant (x7)KKPL Khan Khwar Hydropower Plant (x8)JHP Jagran Hydropower Plant (x9)

Table 6 Top 20 electricity production sources according to the five case studies

No1

No2

No3

No4

No5

No6

No7

No8

No9

No10

No11

No12

No13

No14

No15

No16

No17

No18

No19

No20

x1 x19 x60 x3 x20 x56 x34 x78 x21 x2 x36 x63 x35 x68 x83 x37 x38 x72 x74 x81

15

145

14

135

13

125

12

115

11

105

Cos

t

0 10 20 30 40 50 60 70 80 90 100Iterations

times108

Figure 4 IMVO convergence graph demand for 15000megawatt

15

155

145

14

135

17

175

16

165

Cos

t

0 10 20 30 40 50 60 70 80 90 100Iterations

times108

Figure 5 IMVO convergence graph demand for 19000megawatt

194

192

19

188

186

184

182

18

178

174

172C

ost

0 10 20 30 40 50 60 70 80 90 100Iterations

times108

Figure 6 IMVO convergence graph demand for 23000megawatt

Table 7 Per megawatt cost of electricity for different fuel types

Fuel type Price in PKR per megawattHydel 2500LNG 9070Furnace oil 11050High-speed diesel 17960Coal 12080Solar 16950Wind 16630Nuclear 6860Regasified liquefied natural gas 11270

Computational Intelligence and Neuroscience 9

JabHP Jabban Hydropower Plant (x10)RB Rasal Barrage (x11)DHP Dargai Power Plant (x12)GZD Gomal Zam Dam (x13)NHP Nandipur Hydropower Plant (x14)SHP Shadiwal Hydropower Plant (x15)KHP Khuram Hydropower Plant (x16)RKHP Renela Khuard Hydropower Plant (x17)CHPP Chatral Hydropower Plant (x18)GTPP Guduu ermal Power Plant (x19)MTPP Muzaffargarh ermal Power Plant (x20)JTPP Jamshoro ermal Power Plant (x21)FGTPP Faisalabad Gas Turbine Power Plant (x22)MGTPP Multan Gas Turbine Power Plant (x23)KGTPP Kotri Gas Turbine Power Plant (x24)LTPP Larkana ermal Power Plant (x25)FSPP Faisalabad Steam Power Plant (x26)SGTPP Shahdra Gas Turbine Power Plant (x27)PGTPP Panjgur Gas Turbine Power Plant (x28)QTPP Quetta ermal Power Plant (x29)PTPP Pasni ermal Power Plant (x30)KPC Korangi Power Complex (x31)KGTPS Korang Gas Turbine Power Plant Station

(x32)GTPS Gas Turbine Power Station (x33)KPS ermal Power Plant (x34)CCPP1 Combined Cycle Power Plant 1 (x35)CCPP2 Combined Cycle Power Plant 2 (x36)AESLL AES Lalpir Limited (x37)AESPG AES Pak Gen (x38)AEL Altern Energy Limited (x39)AP Altes Power (x40)AGL Attock Gen Limited (x41)CMECP CMEC Power Pvt (x42)DHACL DHA Cogen Limited (x43)EPC Eastern Power Company (x44)EPQL Engro Powergen Qaidpur Limited (x45)FKPP Fauji Kabirwala Power Plant (x46)FTSM First-Star Modaraba (x47)FPCDL Foundation power company Daharki

Limited (x48)GHLLP Grang Holding Limited Power Plant (x49)GEPtvl Green Electric Pvt Limited (x50)GEL Gujranwala Energy Limited (x51)DAEL Gul Ahmad Energy Limited (x52)HCPC Habibullah Coastal Power Company (x53)HPGC Halmore Power Generation Company (x54)HUBCONPP HUBCO Narowal Power Plant (x55)HUBCOHPP HUBCO Hub Power Plant (x56)IPtvL Intergen PTV Limited (x57)JPG Japan Power Plant (x58)KEL Kohinor Energy Limited (x59)KAPCL Kot Addu Power Company Limited (x60)LPL Liberty Power Limited (x61)LPTL Liberty Power Tech Limited (x62)LEPCL Lucky Electric Power Company Limited

(x63)NCP Nishat Chunian Power (x64)

NPL Nishat Power Limited (x65)OPCPrvL Orient Power Company (Pvt) Limited (x66)REPGC Radian Energy Power Generation Company

(x67)RPK Rousch Power Khanewal (x68)SPC Saba Power Company (x69)SPPQ Saif Power Plant Qadirabad (x70)SECL Sapphire Electric Company Limited (x71)SSEL Siddiqsons Energy Limited (x72)SNPCL Sindh Nooriabad Power Company (Pvt)

Limited (x73)SE Sitara Energy (x74)SEPC Southern Electric Power Company Limited

(x75)SPGL Star Power Generation Limited (x76)TEL Tapal Energy Limited (x77)UchPL Uch (Uch-I and Uch-II) Power Limited (x78)KANUPP KANUPP (x79)CHASNUPP-1 CHASNUPP-1 (x80)CHASNUPP-2 CHASNUPP-2 (x81)CHASNUPP-3 CHASNUPP-3 (x82)NPP Nandipur Power Project (x83)QeaSP Quaid-e-Azam Solar Park (x84)YEL Yunus Energy Limited (x85)MWPCL Metro Wind Power Co Limited (x86)TGL Tenaga Generai Limited (x87)GAWPL Gul Ahmed Wind Power Limited (x88)MWEL Master Wind Energy Limited (x89)FFCEL FFC Energy Limited Jhimpir (x90)ZEPJ Zorlu Enerji Pakistan Jhimpir (x91)TWEL Tapal Wind Energy Limited (x92)HCDPL HydroChina Dawood Power Limited (x93)FEW-1L Foundation Wind Energy-I Limited (x94)FEW-2PT Foundation Wind Energy-II Private Limited

(x95)

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

Authorsrsquo Contributions

All authors contributed equally to the writing of this paperAnd all authors read and approved the final manuscript

Acknowledgments

is paper was supported by the Department of Mathe-matics and the Office of Research Innovation andCommercialization of Abdul Wali Khan UniversityMardan Pakistan

10 Computational Intelligence and Neuroscience

References

[1] A Kumar and G Shankar ldquoQuasi-oppositional harmonysearch algorithm based optimal dynamic load frequencycontrol of a hybrid tidal-diesel power generation systemrdquo IETGeneration Transmission amp Distribution vol 12 no 5pp 1099ndash1108 2018

[2] M Mehdinejad B Mohammadi-Ivatloo and R Dadashzadeh-Bonab ldquoEnergy production cost minimization in a combinedheat and power generation systems using cuckoo optimizationalgorithmrdquo Energy Efficiency vol 10 no 1 pp 81ndash96 2017

[3] K Y Lee C Y Chung B J Huang et al ldquoA novel algorithmfor single-axis maximum power generation sun trackersrdquoEnergy Conversion and Management vol 149 pp 543ndash5522017

[4] L S M Guedes P de Mendonca Maia A C LisboaD A G Vieira and R R Saldanha ldquoA unit commitmentalgorithm and a compact MILP model for short-term hydro-power generation schedulingrdquo IEEE Transactions on PowerSystems vol 32 no 5 pp 3381ndash3390 2017

[5] F Zaman S M Elsayed T Ray and R A Sarker ldquoEvo-lutionary algorithms for power generation planning withuncertain renewable energyrdquo Energy vol 112 pp 408ndash4192016

[6] M E Nazari and M M Ardehali ldquoOptimal coordination ofrenewable wind and pumped storage with thermal powergeneration for maximizing economic profit with consider-ations for environmental emission based on newly developedheuristic optimization algorithmrdquo Journal of Renewable andSustainable Energy vol 8 no 6 article 065905 2016

[7] S Hemalatha and S Chandramohan ldquoCost optimization ofpower generation systems using bat algorithm for remotehealth facilitiesrdquo Journal of Medical Imaging and Health In-formatics vol 6 no 7 pp 1646ndash1651 2016

[8] E Assareh and M Biglari ldquoA novel approach to capture themaximum power generation from wind turbines using hybridMLP neural network and bees algorithm (HNNBA)rdquo IETEJournal of Research vol 62 no 3 pp 368ndash378 2016

[9] N Nikmehr and S Najafi-Ravadanegh ldquoOptimal operation ofdistributed generations in micro-grids under uncertainties inload and renewable power generation using heuristic algo-rithmrdquo IET Renewable Power Generation vol 9 no 8pp 982ndash990 2015

[10] W Sun J Wang and H Chang ldquoForecasting annual powergeneration using a harmony search algorithm-based jointparameters optimization combination modelrdquo Energiesvol 5 no 10 pp 3948ndash3971 2012

[11] J Jasper ldquoCost optimization of power generation using adifferential evolution algorithm enhanced with neighbour-hood search operationrdquo International Review of ElectricalEngineering (IREE) vol 7 no 5 pp 5854ndash5865 2012

[12] G Ali ldquoFactors affecting public investment in manufacturingsector of Pakistanrdquo European Journal of Economic Studiesvol 13 no 3 pp 122ndash130 2015

[13] D H Husaini and H H Lean ldquoDoes electricity drive thedevelopment of manufacturing sector in Malaysiardquo Frontiersin Energy Research vol 3 p 18 2015

[14] M M Rafique and S Rehman ldquoNational energy scenario ofPakistan-current status future alternatives and institutionalinfrastructure an overviewrdquo Renewable and SustainableEnergy Reviews vol 69 pp 156ndash167 2017

[15] NEPRA State of Industry Report 2016 httpwwwnepraorgpkpublicationsstateofindustryreportsstateofindustryreport2016pdf

[16] Electricity demand surges to 22000 MWwith rise in mercuryin Dawn 2017 httpswwwdawncomnews1339210

[17] J L C Meza M B Yildirim and A S M Masud ldquoAmultiobjective evolutionary programming algorithm andits applications to power generation expansion planningrdquoIEEE Transactions on Systems Man and Cybernetics-PartA Systems and Humans vol 39 no 5 pp 1086ndash10962009

[18] M Asif ldquoSustainable energy options for Pakistanrdquo Renewableand Sustainable Energy Reviews vol 13 no 4 pp 903ndash9092009

[19] S Wasti Economic Survey of Pakistan 2014-15 Governmentof Pakistan Islamabad Pakistan 2015

[20] M Kugelman Pakistanrsquos Energy Crisis National Bureau ofAsian Research Washington DC USA 2013

[21] H Zameer and Y Wang ldquoEnergy production system opti-mization evidence from Pakistanrdquo Renewable and Sustain-able Energy Reviews vol 82 pp 886ndash893 2018

[22] B Zafar ldquoFuel Price Adjustmentrdquo httpstribunecompkstory957503fuel-price-adjustment-regulator-cuts-power-tariff-for-june-and-july

[23] X S Yang ldquoA new metaheuristic bat-inspired algorithmrdquo inNature Inspired Cooperative Strategies for Optimization(NICSO 2010) pp 65ndash74 Springer Berlin Germany 2010

[24] B Zhu W Zhu Z Liu Q Duan and L Cao ldquoA novelquantum-behaved bat algorithm with mean best positiondirected for numerical optimizationrdquo Computational in-telligence and neuroscience vol 2016 Article ID 609748417 pages 2016

[25] S Saremi S Mirjalili and A Lewis ldquoGrasshopper optimi-sation algorithm theory and applicationrdquo Advances in En-gineering Software vol 105 pp 30ndash47 2017

[26] X S Yang ldquoFirefly algorithm stochastic test functions anddesign optimisationrdquo 2010 httparxivorgabs10031409

[27] C F Chao and M H Horng ldquoe construction of supportvector machine classifier using the firefly algorithmrdquo Com-putational Intelligence and Neuroscience vol 2015 Article ID212719 8 pages 2015

[28] F Ozkaynak ldquoA novel method to improve the performance ofchaos based evolutionary algorithmsrdquo Optik vol 126 no 24pp 5434ndash5438 2015

[29] M Sulaiman A Ahmad A Khan and S MuhammadldquoHybridized symbiotic organism search algorithm for theoptimal operation of directional overcurrent relaysrdquo Com-plexity vol 2018 Article ID 4605769 11 pages 2018

[30] M Sulaiman S Muhammad and A Khan ldquoImproved solu-tions for the optimal coordination of docrs using firefly al-gorithmrdquo Complexity vol 2018 Article ID 7039790 15 pages2018

[31] S Mirjalili Waseem S MMirjalili and A Hatamlou ldquoMulti-verse optimizer a nature-inspired algorithm for global op-timizationrdquo Neural Computing and Applications vol 27no 2 pp 495ndash513 2016

[32] H Faris I Aljarah and S Mirjalili ldquoTraining feedforwardneural networks using multi-verse optimizer for binaryclassification problemsrdquo Applied Intelligence vol 45 no 2pp 322ndash332 2016

[33] C Hu Z Li T Zhou A Zhu and C Xu ldquoA multi-verseoptimizer with levy flights for numerical optimization and itsapplication in test scheduling for network-on-chiprdquo PLoSOne vol 11 no 12 Article ID e0167341 2016

[34] G I Sayed A Darwish and A E Hassanien ldquoQuantummultiverse optimization algorithm for optimization

Computational Intelligence and Neuroscience 11

Table 5 Electricity production of all 95 sources for five case studies

Case Study 1 Case Study 2 Case Study 3 Case Study 4 Case Study 5Price in PKR 112E+ 08 151E+ 08 184E + 08 197E + 08 216E + 08Variables (megawatts) 1500316 19003 2300008 250003 2720836TD (x1) 2379137 156635 2938164 3478 347616MD (x2) 818677 1000 9057829 7634957 98348GBHPP (x3) 5165337 1450 1023352 1347306 1421054WD (x4) 1307975 2104076 1777411 1064834 1815488CB (x5) 3874718 184 7542442 1744151 1638171DKD (x6) 4256789 1163349 1160204 6036495 1274962AKHPP (x7) 2502909 0415286 1190034 3387101 4799439KKHP (x8) 604886 1592544 4172064 72 1927703JagHP (x9) 1417929 30 1285605 8998066 2138508JabHP (x10) 8375935 1057083 1806 9438497 0704657RG (x11) 6866051 3330527 0380166 4987555 9745063DHP (x12) 1428187 1353056 1265834 20 2044366GHD (x13) 605225 0280779 2219217 940119 155921NHP (x14) 6647023 1140453 7595507 6010873 1386329SHP (x15) 1155404 112018 8391618 1116708 13093KHP (x16) 1869716 1137132 1534735 2692804 1023365RKHP (x17) 0905093 1 1 0651626 0854247CHPP (x18) 0864139 0815802 0815802 0965926 0830172GTPP (x19) 1305331 1655 1655 1655 164554MTPP (x20) 6400394 54627 1350 1350 1350JTPP (x21) 1495429 850 850 850 8490554FGTPP (x22) 1489675 1812005 1880609 1031949 217891MGTPP (x23) 4385999 748375 1554596 1458149 1681718MGTPP (x24) 127056 6527735 16615 341201 1109528KGTPP (x25) 1128329 116059 3098832 0567566 1495035LTPP (x26) 4037149 0883692 243518 1205104 1174427FSPP (x27) 3919613 5427258 59 5663659 5509061SGTPP (x28) 0914076 2186785 1466417 2223108 3108445PGTPP (x29) 2730059 1445997 0589928 8484009 2307876PTPP (x30) 1270353 17 6695689 1685053 1195603KGTPS (x31) 9179519 2282708 247 1276751 2468065KPC (x32) 9112861 100 0076503 1621392 1324039GTPS (x33) 2139859 3086809 0608317 4191513 1135833TPS (x34) 1019436 8525889 9217966 1132252 1260CCPP 1 (x35) 3638285 3759421 4858476 5381132 5524153CCPP 2 (x36) 6716314 3599164 5511955 7985884 8991415AES LL (x37) 1248976 362 3301038 3414665 3464409AES PG (x38) 8779272 2897815 365 2441401 3649033AEL (x39) 3047575 29 29 1208485 195939AP (x40) 1465024 1947207 2149626 225 225AGL (x41) 1539627 1074664 1527011 1143378 1135217CHMC PL (x42) 7513341 265198 2733111 2556046 3227874DHA C L (x43) 6873455 0476099 6545028 6296757 7030826EPC (x44) 2340477 98656 3710004 1413346 1520636EPQL (x45) 1307633 2140389 2223562 2265 2262002FKPCL (x46) 952459 157 1512643 278556 1556898FTSM (x47) 5616674 1044668 1008249 7657812 1070448FPCDL (x48) 101152 1643581 1272432 106039 1777063GHLLP (x49) 101702 5626072 1098266 1402346 1576599GEPtvL (x50) 1623922 188 1444615 1795249 1319891GEL (x51) 8193736 8919682 2015 8489962 2015GAEL (x52) 1005592 9235572 5718626 1104825 8202294HCPC (x53) 1113358 5826757 1109772 4347083 1115484HPGC (x54) 1697313 0807693 1923602 1250309 215355HUBCO NPP (x55) 1478875 225 212279 2095134 2235541HUBCOHPP (x56) 1480634 1292 1167515 1292 1292Iptvl (x57) 2153738 1586019 1416202 1642585 1649125JPG (x58) 8413137 120 120 6522738 119424

6 Computational Intelligence and Neuroscience

Table 5 Continued

Case Study 1 Case Study 2 Case Study 3 Case Study 4 Case Study 5KEL (x59) 4350688 4752342 1038332 3058684 1308207KAPCL (x60) 8114451 1223218 118571 1638 1638LPL (x61) 1530046 052402 9467205 1964468 1822104LPTL (x62) 1241896 681917 5095543 1388238 1986912LEPCL (x63) 2556012 5897144 5785459 660 6586634NCP (x64) 1582538 200 9585135 200 1513611NPL (x65) 3248763 200 1684331 1688323 1991059OPCL (x66) 2052865 089022 1327586 6589102 2200356REPGCL (x67) 3020849 1002075 5299079 164 1634477RP (x68) 3271605 2760325 3021523 412 4118322SPC (x69) 7208175 7502883 9121424 1091339 1126283SPPQ (x70) 1010073 225 1240716 21105 221962SESL (x71) 2081023 265598 6600281 2155041 2003566SSEL (x72) 2205401 141361 3211493 3106587 3432993SNPCL (x73) 393573 4414536 0398791 2011775 5189066SE (x74) 7728166 1107506 6637944 2384816 1650386SEPC (x75) 1201473 7111238 401338 4743561 8328035SPGL (x76) 71382 3585756 1086969 8837954 113884TEL (x77) 1102271 2538428 1135676 265028 9401525UchPL (x78) 7352781 2816507 990 990 9897866KANUPP (x79) 504151 9210906 137 1057683 1347101CHASNUPP-1 (x80) 2829386 863647 2758089 325 2687866CHASNUPP-2 (x81) 2002746 2432484 1494219 325 3208773CHASNUPP-3 (x82) 1918579 340 319874 3016324 2140955NPP (x83) 1816426 173693 3748168 3362965 4207756QezSP (x84) 4971705 1069033 7003342 1473463 1267687YEL (x85) 1558682 2334511 4623074 2448091 1286986MWPCL (x86) 4101434 2135616 2794642 3645242 4521504TGL (x87) 9466357 2520002 49 4779046 4790783GAWPL (x88) 1535919 1891722 4514516 1524926 2794244MWEL (x89) 1496827 2199775 52 4787871 4600231FFCEL (x90) 3026861 4268928 50 50 1558795ZEP (x91) 2088768 1437346 4467045 3045881 4017728TWEL (x92) 1528468 121674 30 2952479 2865781HCDPL (x93) 9876255 2000362 4725205 319031 4152962FWEL 1 (x94) 4369201 2980095 4598028 2968556 2261687FWEPL 2 (x95) 6404915 50 6872093 2165334 4028912

0

2000

4000

6000

8000

10000

12000

14000

16000

1 4 7 10 13 16 19 22 25 28 31 34 37 40 43 46 49 52 55 58 61 64 67 70 73 76 79 82 85 88 91 94

Ener

gy p

rodu

ctio

n in

meg

awat

ts

95 energy sources

Series 1Series 2Series 3

Series 4Series 5

Figure 2 A weighted comparison of the 95 energy sources used in five case studies Series 1ndash5 represent case studies 1ndash5 respectively

Computational Intelligence and Neuroscience 7

0

500

1000

1500

2000

2500

1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 33 35 37 39 41 43 45 47 49 51 53 55 57 59 61 63 65 67 69 71 73 75 77 79 81 83 85 87 89 91 93 95

Elec

tric

ity p

rodu

ctio

nin

meg

awat

ts

Power production sources

(a)

0

400200

600

1000800

1200

16001400

1800

1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 33 35 37 39 41 43 45 47 49 51 53 55 57 59 61 63 65 67 69 71 73 75 77 79 81 83 85 87 89 91 93 95

Elec

tric

ity p

rodu

ctio

nin

meg

awat

ts

Power production sources

(b)

0

500

1000

1500

2000

2500

3000

1 4 7 10 13 16 19 22 25 28 31 34 37 40 43 46 49 52 55 58 61 64 67 70 73 76 79 82 85 88 91 94

Elec

tric

ity p

rodu

ctio

nin

meg

awat

ts

Power production sources

(c)

0500

100015002000250030003500

1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 33 35 37 39 41 43 45 47 49 51 53 55 57 59 61 63 65 67 69 71 73 75 77 79 81 83 85 87 89 91 93 95

Elec

tric

ity p

rodu

ctio

nin

meg

awat

ts

Power production sources

(d)

0500

100015002000250030003500

1 4 7 10 13 16 19 22 25 28 31 34 37 40 43 46 49 52 55 58 61 64 67 70 73 76 79 82 85 88 91 94

Elec

tric

ity p

rodu

ctio

nin

meg

awat

ts

All power production sources

(e)

Figure 3 Comprehensive plots of five case studies discussed in Table 4 All production sources are plotted against the electricity productionin megawatts (a) Case Study 1 demand of 15003MW (b) Case Study 2 demand of 19003MW (c) Case Study 3 demand of 23000MW(d) Case Study 4 demand of 250003MW (e) Case Study 5 demand of 272083MW

8 Computational Intelligence and Neuroscience

6 Conclusions

In this paper an improved multiverse optimization al-gorithm is implemented for solving a linear programmingmodel for proper management of electricity productionsources in Pakistan To address the proper management ofpower production sources several bound constraintssuch as constraint for total demand and bounds on allvariables are considered e objective function is linearwith 95 decision variables and different coefficients eIMVO algorithm is easy to implement with few param-eters We have found solutions for five different casestudies and analyzed all solutions graphically A link to thedata set of 100000 different solutions is provided in this

paper In our results we have obtained better solutions tomeet the power demand in summer It is recommendedthat current resources can produce the required powerdemand but some of the resources are required to beexpanded in capacity along with installation of newsources In future we intend to include other factors likepower loss in our model

Nomenclature

TD Tarbela Dam (x1)MD Mangla Dam (x2)GBHPP Ghazi Barota Hydropower Project (x3)WD Warsak Dam (x4)CB Chashma Barrage (x5)DKD Duber Khwar Dam (x6)AKPH Allai Khwar Hydropower Plant (x7)KKPL Khan Khwar Hydropower Plant (x8)JHP Jagran Hydropower Plant (x9)

Table 6 Top 20 electricity production sources according to the five case studies

No1

No2

No3

No4

No5

No6

No7

No8

No9

No10

No11

No12

No13

No14

No15

No16

No17

No18

No19

No20

x1 x19 x60 x3 x20 x56 x34 x78 x21 x2 x36 x63 x35 x68 x83 x37 x38 x72 x74 x81

15

145

14

135

13

125

12

115

11

105

Cos

t

0 10 20 30 40 50 60 70 80 90 100Iterations

times108

Figure 4 IMVO convergence graph demand for 15000megawatt

15

155

145

14

135

17

175

16

165

Cos

t

0 10 20 30 40 50 60 70 80 90 100Iterations

times108

Figure 5 IMVO convergence graph demand for 19000megawatt

194

192

19

188

186

184

182

18

178

174

172C

ost

0 10 20 30 40 50 60 70 80 90 100Iterations

times108

Figure 6 IMVO convergence graph demand for 23000megawatt

Table 7 Per megawatt cost of electricity for different fuel types

Fuel type Price in PKR per megawattHydel 2500LNG 9070Furnace oil 11050High-speed diesel 17960Coal 12080Solar 16950Wind 16630Nuclear 6860Regasified liquefied natural gas 11270

Computational Intelligence and Neuroscience 9

JabHP Jabban Hydropower Plant (x10)RB Rasal Barrage (x11)DHP Dargai Power Plant (x12)GZD Gomal Zam Dam (x13)NHP Nandipur Hydropower Plant (x14)SHP Shadiwal Hydropower Plant (x15)KHP Khuram Hydropower Plant (x16)RKHP Renela Khuard Hydropower Plant (x17)CHPP Chatral Hydropower Plant (x18)GTPP Guduu ermal Power Plant (x19)MTPP Muzaffargarh ermal Power Plant (x20)JTPP Jamshoro ermal Power Plant (x21)FGTPP Faisalabad Gas Turbine Power Plant (x22)MGTPP Multan Gas Turbine Power Plant (x23)KGTPP Kotri Gas Turbine Power Plant (x24)LTPP Larkana ermal Power Plant (x25)FSPP Faisalabad Steam Power Plant (x26)SGTPP Shahdra Gas Turbine Power Plant (x27)PGTPP Panjgur Gas Turbine Power Plant (x28)QTPP Quetta ermal Power Plant (x29)PTPP Pasni ermal Power Plant (x30)KPC Korangi Power Complex (x31)KGTPS Korang Gas Turbine Power Plant Station

(x32)GTPS Gas Turbine Power Station (x33)KPS ermal Power Plant (x34)CCPP1 Combined Cycle Power Plant 1 (x35)CCPP2 Combined Cycle Power Plant 2 (x36)AESLL AES Lalpir Limited (x37)AESPG AES Pak Gen (x38)AEL Altern Energy Limited (x39)AP Altes Power (x40)AGL Attock Gen Limited (x41)CMECP CMEC Power Pvt (x42)DHACL DHA Cogen Limited (x43)EPC Eastern Power Company (x44)EPQL Engro Powergen Qaidpur Limited (x45)FKPP Fauji Kabirwala Power Plant (x46)FTSM First-Star Modaraba (x47)FPCDL Foundation power company Daharki

Limited (x48)GHLLP Grang Holding Limited Power Plant (x49)GEPtvl Green Electric Pvt Limited (x50)GEL Gujranwala Energy Limited (x51)DAEL Gul Ahmad Energy Limited (x52)HCPC Habibullah Coastal Power Company (x53)HPGC Halmore Power Generation Company (x54)HUBCONPP HUBCO Narowal Power Plant (x55)HUBCOHPP HUBCO Hub Power Plant (x56)IPtvL Intergen PTV Limited (x57)JPG Japan Power Plant (x58)KEL Kohinor Energy Limited (x59)KAPCL Kot Addu Power Company Limited (x60)LPL Liberty Power Limited (x61)LPTL Liberty Power Tech Limited (x62)LEPCL Lucky Electric Power Company Limited

(x63)NCP Nishat Chunian Power (x64)

NPL Nishat Power Limited (x65)OPCPrvL Orient Power Company (Pvt) Limited (x66)REPGC Radian Energy Power Generation Company

(x67)RPK Rousch Power Khanewal (x68)SPC Saba Power Company (x69)SPPQ Saif Power Plant Qadirabad (x70)SECL Sapphire Electric Company Limited (x71)SSEL Siddiqsons Energy Limited (x72)SNPCL Sindh Nooriabad Power Company (Pvt)

Limited (x73)SE Sitara Energy (x74)SEPC Southern Electric Power Company Limited

(x75)SPGL Star Power Generation Limited (x76)TEL Tapal Energy Limited (x77)UchPL Uch (Uch-I and Uch-II) Power Limited (x78)KANUPP KANUPP (x79)CHASNUPP-1 CHASNUPP-1 (x80)CHASNUPP-2 CHASNUPP-2 (x81)CHASNUPP-3 CHASNUPP-3 (x82)NPP Nandipur Power Project (x83)QeaSP Quaid-e-Azam Solar Park (x84)YEL Yunus Energy Limited (x85)MWPCL Metro Wind Power Co Limited (x86)TGL Tenaga Generai Limited (x87)GAWPL Gul Ahmed Wind Power Limited (x88)MWEL Master Wind Energy Limited (x89)FFCEL FFC Energy Limited Jhimpir (x90)ZEPJ Zorlu Enerji Pakistan Jhimpir (x91)TWEL Tapal Wind Energy Limited (x92)HCDPL HydroChina Dawood Power Limited (x93)FEW-1L Foundation Wind Energy-I Limited (x94)FEW-2PT Foundation Wind Energy-II Private Limited

(x95)

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

Authorsrsquo Contributions

All authors contributed equally to the writing of this paperAnd all authors read and approved the final manuscript

Acknowledgments

is paper was supported by the Department of Mathe-matics and the Office of Research Innovation andCommercialization of Abdul Wali Khan UniversityMardan Pakistan

10 Computational Intelligence and Neuroscience

References

[1] A Kumar and G Shankar ldquoQuasi-oppositional harmonysearch algorithm based optimal dynamic load frequencycontrol of a hybrid tidal-diesel power generation systemrdquo IETGeneration Transmission amp Distribution vol 12 no 5pp 1099ndash1108 2018

[2] M Mehdinejad B Mohammadi-Ivatloo and R Dadashzadeh-Bonab ldquoEnergy production cost minimization in a combinedheat and power generation systems using cuckoo optimizationalgorithmrdquo Energy Efficiency vol 10 no 1 pp 81ndash96 2017

[3] K Y Lee C Y Chung B J Huang et al ldquoA novel algorithmfor single-axis maximum power generation sun trackersrdquoEnergy Conversion and Management vol 149 pp 543ndash5522017

[4] L S M Guedes P de Mendonca Maia A C LisboaD A G Vieira and R R Saldanha ldquoA unit commitmentalgorithm and a compact MILP model for short-term hydro-power generation schedulingrdquo IEEE Transactions on PowerSystems vol 32 no 5 pp 3381ndash3390 2017

[5] F Zaman S M Elsayed T Ray and R A Sarker ldquoEvo-lutionary algorithms for power generation planning withuncertain renewable energyrdquo Energy vol 112 pp 408ndash4192016

[6] M E Nazari and M M Ardehali ldquoOptimal coordination ofrenewable wind and pumped storage with thermal powergeneration for maximizing economic profit with consider-ations for environmental emission based on newly developedheuristic optimization algorithmrdquo Journal of Renewable andSustainable Energy vol 8 no 6 article 065905 2016

[7] S Hemalatha and S Chandramohan ldquoCost optimization ofpower generation systems using bat algorithm for remotehealth facilitiesrdquo Journal of Medical Imaging and Health In-formatics vol 6 no 7 pp 1646ndash1651 2016

[8] E Assareh and M Biglari ldquoA novel approach to capture themaximum power generation from wind turbines using hybridMLP neural network and bees algorithm (HNNBA)rdquo IETEJournal of Research vol 62 no 3 pp 368ndash378 2016

[9] N Nikmehr and S Najafi-Ravadanegh ldquoOptimal operation ofdistributed generations in micro-grids under uncertainties inload and renewable power generation using heuristic algo-rithmrdquo IET Renewable Power Generation vol 9 no 8pp 982ndash990 2015

[10] W Sun J Wang and H Chang ldquoForecasting annual powergeneration using a harmony search algorithm-based jointparameters optimization combination modelrdquo Energiesvol 5 no 10 pp 3948ndash3971 2012

[11] J Jasper ldquoCost optimization of power generation using adifferential evolution algorithm enhanced with neighbour-hood search operationrdquo International Review of ElectricalEngineering (IREE) vol 7 no 5 pp 5854ndash5865 2012

[12] G Ali ldquoFactors affecting public investment in manufacturingsector of Pakistanrdquo European Journal of Economic Studiesvol 13 no 3 pp 122ndash130 2015

[13] D H Husaini and H H Lean ldquoDoes electricity drive thedevelopment of manufacturing sector in Malaysiardquo Frontiersin Energy Research vol 3 p 18 2015

[14] M M Rafique and S Rehman ldquoNational energy scenario ofPakistan-current status future alternatives and institutionalinfrastructure an overviewrdquo Renewable and SustainableEnergy Reviews vol 69 pp 156ndash167 2017

[15] NEPRA State of Industry Report 2016 httpwwwnepraorgpkpublicationsstateofindustryreportsstateofindustryreport2016pdf

[16] Electricity demand surges to 22000 MWwith rise in mercuryin Dawn 2017 httpswwwdawncomnews1339210

[17] J L C Meza M B Yildirim and A S M Masud ldquoAmultiobjective evolutionary programming algorithm andits applications to power generation expansion planningrdquoIEEE Transactions on Systems Man and Cybernetics-PartA Systems and Humans vol 39 no 5 pp 1086ndash10962009

[18] M Asif ldquoSustainable energy options for Pakistanrdquo Renewableand Sustainable Energy Reviews vol 13 no 4 pp 903ndash9092009

[19] S Wasti Economic Survey of Pakistan 2014-15 Governmentof Pakistan Islamabad Pakistan 2015

[20] M Kugelman Pakistanrsquos Energy Crisis National Bureau ofAsian Research Washington DC USA 2013

[21] H Zameer and Y Wang ldquoEnergy production system opti-mization evidence from Pakistanrdquo Renewable and Sustain-able Energy Reviews vol 82 pp 886ndash893 2018

[22] B Zafar ldquoFuel Price Adjustmentrdquo httpstribunecompkstory957503fuel-price-adjustment-regulator-cuts-power-tariff-for-june-and-july

[23] X S Yang ldquoA new metaheuristic bat-inspired algorithmrdquo inNature Inspired Cooperative Strategies for Optimization(NICSO 2010) pp 65ndash74 Springer Berlin Germany 2010

[24] B Zhu W Zhu Z Liu Q Duan and L Cao ldquoA novelquantum-behaved bat algorithm with mean best positiondirected for numerical optimizationrdquo Computational in-telligence and neuroscience vol 2016 Article ID 609748417 pages 2016

[25] S Saremi S Mirjalili and A Lewis ldquoGrasshopper optimi-sation algorithm theory and applicationrdquo Advances in En-gineering Software vol 105 pp 30ndash47 2017

[26] X S Yang ldquoFirefly algorithm stochastic test functions anddesign optimisationrdquo 2010 httparxivorgabs10031409

[27] C F Chao and M H Horng ldquoe construction of supportvector machine classifier using the firefly algorithmrdquo Com-putational Intelligence and Neuroscience vol 2015 Article ID212719 8 pages 2015

[28] F Ozkaynak ldquoA novel method to improve the performance ofchaos based evolutionary algorithmsrdquo Optik vol 126 no 24pp 5434ndash5438 2015

[29] M Sulaiman A Ahmad A Khan and S MuhammadldquoHybridized symbiotic organism search algorithm for theoptimal operation of directional overcurrent relaysrdquo Com-plexity vol 2018 Article ID 4605769 11 pages 2018

[30] M Sulaiman S Muhammad and A Khan ldquoImproved solu-tions for the optimal coordination of docrs using firefly al-gorithmrdquo Complexity vol 2018 Article ID 7039790 15 pages2018

[31] S Mirjalili Waseem S MMirjalili and A Hatamlou ldquoMulti-verse optimizer a nature-inspired algorithm for global op-timizationrdquo Neural Computing and Applications vol 27no 2 pp 495ndash513 2016

[32] H Faris I Aljarah and S Mirjalili ldquoTraining feedforwardneural networks using multi-verse optimizer for binaryclassification problemsrdquo Applied Intelligence vol 45 no 2pp 322ndash332 2016

[33] C Hu Z Li T Zhou A Zhu and C Xu ldquoA multi-verseoptimizer with levy flights for numerical optimization and itsapplication in test scheduling for network-on-chiprdquo PLoSOne vol 11 no 12 Article ID e0167341 2016

[34] G I Sayed A Darwish and A E Hassanien ldquoQuantummultiverse optimization algorithm for optimization

Computational Intelligence and Neuroscience 11

Table 5 Continued

Case Study 1 Case Study 2 Case Study 3 Case Study 4 Case Study 5KEL (x59) 4350688 4752342 1038332 3058684 1308207KAPCL (x60) 8114451 1223218 118571 1638 1638LPL (x61) 1530046 052402 9467205 1964468 1822104LPTL (x62) 1241896 681917 5095543 1388238 1986912LEPCL (x63) 2556012 5897144 5785459 660 6586634NCP (x64) 1582538 200 9585135 200 1513611NPL (x65) 3248763 200 1684331 1688323 1991059OPCL (x66) 2052865 089022 1327586 6589102 2200356REPGCL (x67) 3020849 1002075 5299079 164 1634477RP (x68) 3271605 2760325 3021523 412 4118322SPC (x69) 7208175 7502883 9121424 1091339 1126283SPPQ (x70) 1010073 225 1240716 21105 221962SESL (x71) 2081023 265598 6600281 2155041 2003566SSEL (x72) 2205401 141361 3211493 3106587 3432993SNPCL (x73) 393573 4414536 0398791 2011775 5189066SE (x74) 7728166 1107506 6637944 2384816 1650386SEPC (x75) 1201473 7111238 401338 4743561 8328035SPGL (x76) 71382 3585756 1086969 8837954 113884TEL (x77) 1102271 2538428 1135676 265028 9401525UchPL (x78) 7352781 2816507 990 990 9897866KANUPP (x79) 504151 9210906 137 1057683 1347101CHASNUPP-1 (x80) 2829386 863647 2758089 325 2687866CHASNUPP-2 (x81) 2002746 2432484 1494219 325 3208773CHASNUPP-3 (x82) 1918579 340 319874 3016324 2140955NPP (x83) 1816426 173693 3748168 3362965 4207756QezSP (x84) 4971705 1069033 7003342 1473463 1267687YEL (x85) 1558682 2334511 4623074 2448091 1286986MWPCL (x86) 4101434 2135616 2794642 3645242 4521504TGL (x87) 9466357 2520002 49 4779046 4790783GAWPL (x88) 1535919 1891722 4514516 1524926 2794244MWEL (x89) 1496827 2199775 52 4787871 4600231FFCEL (x90) 3026861 4268928 50 50 1558795ZEP (x91) 2088768 1437346 4467045 3045881 4017728TWEL (x92) 1528468 121674 30 2952479 2865781HCDPL (x93) 9876255 2000362 4725205 319031 4152962FWEL 1 (x94) 4369201 2980095 4598028 2968556 2261687FWEPL 2 (x95) 6404915 50 6872093 2165334 4028912

0

2000

4000

6000

8000

10000

12000

14000

16000

1 4 7 10 13 16 19 22 25 28 31 34 37 40 43 46 49 52 55 58 61 64 67 70 73 76 79 82 85 88 91 94

Ener

gy p

rodu

ctio

n in

meg

awat

ts

95 energy sources

Series 1Series 2Series 3

Series 4Series 5

Figure 2 A weighted comparison of the 95 energy sources used in five case studies Series 1ndash5 represent case studies 1ndash5 respectively

Computational Intelligence and Neuroscience 7

0

500

1000

1500

2000

2500

1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 33 35 37 39 41 43 45 47 49 51 53 55 57 59 61 63 65 67 69 71 73 75 77 79 81 83 85 87 89 91 93 95

Elec

tric

ity p

rodu

ctio

nin

meg

awat

ts

Power production sources

(a)

0

400200

600

1000800

1200

16001400

1800

1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 33 35 37 39 41 43 45 47 49 51 53 55 57 59 61 63 65 67 69 71 73 75 77 79 81 83 85 87 89 91 93 95

Elec

tric

ity p

rodu

ctio

nin

meg

awat

ts

Power production sources

(b)

0

500

1000

1500

2000

2500

3000

1 4 7 10 13 16 19 22 25 28 31 34 37 40 43 46 49 52 55 58 61 64 67 70 73 76 79 82 85 88 91 94

Elec

tric

ity p

rodu

ctio

nin

meg

awat

ts

Power production sources

(c)

0500

100015002000250030003500

1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 33 35 37 39 41 43 45 47 49 51 53 55 57 59 61 63 65 67 69 71 73 75 77 79 81 83 85 87 89 91 93 95

Elec

tric

ity p

rodu

ctio

nin

meg

awat

ts

Power production sources

(d)

0500

100015002000250030003500

1 4 7 10 13 16 19 22 25 28 31 34 37 40 43 46 49 52 55 58 61 64 67 70 73 76 79 82 85 88 91 94

Elec

tric

ity p

rodu

ctio

nin

meg

awat

ts

All power production sources

(e)

Figure 3 Comprehensive plots of five case studies discussed in Table 4 All production sources are plotted against the electricity productionin megawatts (a) Case Study 1 demand of 15003MW (b) Case Study 2 demand of 19003MW (c) Case Study 3 demand of 23000MW(d) Case Study 4 demand of 250003MW (e) Case Study 5 demand of 272083MW

8 Computational Intelligence and Neuroscience

6 Conclusions

In this paper an improved multiverse optimization al-gorithm is implemented for solving a linear programmingmodel for proper management of electricity productionsources in Pakistan To address the proper management ofpower production sources several bound constraintssuch as constraint for total demand and bounds on allvariables are considered e objective function is linearwith 95 decision variables and different coefficients eIMVO algorithm is easy to implement with few param-eters We have found solutions for five different casestudies and analyzed all solutions graphically A link to thedata set of 100000 different solutions is provided in this

paper In our results we have obtained better solutions tomeet the power demand in summer It is recommendedthat current resources can produce the required powerdemand but some of the resources are required to beexpanded in capacity along with installation of newsources In future we intend to include other factors likepower loss in our model

Nomenclature

TD Tarbela Dam (x1)MD Mangla Dam (x2)GBHPP Ghazi Barota Hydropower Project (x3)WD Warsak Dam (x4)CB Chashma Barrage (x5)DKD Duber Khwar Dam (x6)AKPH Allai Khwar Hydropower Plant (x7)KKPL Khan Khwar Hydropower Plant (x8)JHP Jagran Hydropower Plant (x9)

Table 6 Top 20 electricity production sources according to the five case studies

No1

No2

No3

No4

No5

No6

No7

No8

No9

No10

No11

No12

No13

No14

No15

No16

No17

No18

No19

No20

x1 x19 x60 x3 x20 x56 x34 x78 x21 x2 x36 x63 x35 x68 x83 x37 x38 x72 x74 x81

15

145

14

135

13

125

12

115

11

105

Cos

t

0 10 20 30 40 50 60 70 80 90 100Iterations

times108

Figure 4 IMVO convergence graph demand for 15000megawatt

15

155

145

14

135

17

175

16

165

Cos

t

0 10 20 30 40 50 60 70 80 90 100Iterations

times108

Figure 5 IMVO convergence graph demand for 19000megawatt

194

192

19

188

186

184

182

18

178

174

172C

ost

0 10 20 30 40 50 60 70 80 90 100Iterations

times108

Figure 6 IMVO convergence graph demand for 23000megawatt

Table 7 Per megawatt cost of electricity for different fuel types

Fuel type Price in PKR per megawattHydel 2500LNG 9070Furnace oil 11050High-speed diesel 17960Coal 12080Solar 16950Wind 16630Nuclear 6860Regasified liquefied natural gas 11270

Computational Intelligence and Neuroscience 9

JabHP Jabban Hydropower Plant (x10)RB Rasal Barrage (x11)DHP Dargai Power Plant (x12)GZD Gomal Zam Dam (x13)NHP Nandipur Hydropower Plant (x14)SHP Shadiwal Hydropower Plant (x15)KHP Khuram Hydropower Plant (x16)RKHP Renela Khuard Hydropower Plant (x17)CHPP Chatral Hydropower Plant (x18)GTPP Guduu ermal Power Plant (x19)MTPP Muzaffargarh ermal Power Plant (x20)JTPP Jamshoro ermal Power Plant (x21)FGTPP Faisalabad Gas Turbine Power Plant (x22)MGTPP Multan Gas Turbine Power Plant (x23)KGTPP Kotri Gas Turbine Power Plant (x24)LTPP Larkana ermal Power Plant (x25)FSPP Faisalabad Steam Power Plant (x26)SGTPP Shahdra Gas Turbine Power Plant (x27)PGTPP Panjgur Gas Turbine Power Plant (x28)QTPP Quetta ermal Power Plant (x29)PTPP Pasni ermal Power Plant (x30)KPC Korangi Power Complex (x31)KGTPS Korang Gas Turbine Power Plant Station

(x32)GTPS Gas Turbine Power Station (x33)KPS ermal Power Plant (x34)CCPP1 Combined Cycle Power Plant 1 (x35)CCPP2 Combined Cycle Power Plant 2 (x36)AESLL AES Lalpir Limited (x37)AESPG AES Pak Gen (x38)AEL Altern Energy Limited (x39)AP Altes Power (x40)AGL Attock Gen Limited (x41)CMECP CMEC Power Pvt (x42)DHACL DHA Cogen Limited (x43)EPC Eastern Power Company (x44)EPQL Engro Powergen Qaidpur Limited (x45)FKPP Fauji Kabirwala Power Plant (x46)FTSM First-Star Modaraba (x47)FPCDL Foundation power company Daharki

Limited (x48)GHLLP Grang Holding Limited Power Plant (x49)GEPtvl Green Electric Pvt Limited (x50)GEL Gujranwala Energy Limited (x51)DAEL Gul Ahmad Energy Limited (x52)HCPC Habibullah Coastal Power Company (x53)HPGC Halmore Power Generation Company (x54)HUBCONPP HUBCO Narowal Power Plant (x55)HUBCOHPP HUBCO Hub Power Plant (x56)IPtvL Intergen PTV Limited (x57)JPG Japan Power Plant (x58)KEL Kohinor Energy Limited (x59)KAPCL Kot Addu Power Company Limited (x60)LPL Liberty Power Limited (x61)LPTL Liberty Power Tech Limited (x62)LEPCL Lucky Electric Power Company Limited

(x63)NCP Nishat Chunian Power (x64)

NPL Nishat Power Limited (x65)OPCPrvL Orient Power Company (Pvt) Limited (x66)REPGC Radian Energy Power Generation Company

(x67)RPK Rousch Power Khanewal (x68)SPC Saba Power Company (x69)SPPQ Saif Power Plant Qadirabad (x70)SECL Sapphire Electric Company Limited (x71)SSEL Siddiqsons Energy Limited (x72)SNPCL Sindh Nooriabad Power Company (Pvt)

Limited (x73)SE Sitara Energy (x74)SEPC Southern Electric Power Company Limited

(x75)SPGL Star Power Generation Limited (x76)TEL Tapal Energy Limited (x77)UchPL Uch (Uch-I and Uch-II) Power Limited (x78)KANUPP KANUPP (x79)CHASNUPP-1 CHASNUPP-1 (x80)CHASNUPP-2 CHASNUPP-2 (x81)CHASNUPP-3 CHASNUPP-3 (x82)NPP Nandipur Power Project (x83)QeaSP Quaid-e-Azam Solar Park (x84)YEL Yunus Energy Limited (x85)MWPCL Metro Wind Power Co Limited (x86)TGL Tenaga Generai Limited (x87)GAWPL Gul Ahmed Wind Power Limited (x88)MWEL Master Wind Energy Limited (x89)FFCEL FFC Energy Limited Jhimpir (x90)ZEPJ Zorlu Enerji Pakistan Jhimpir (x91)TWEL Tapal Wind Energy Limited (x92)HCDPL HydroChina Dawood Power Limited (x93)FEW-1L Foundation Wind Energy-I Limited (x94)FEW-2PT Foundation Wind Energy-II Private Limited

(x95)

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

Authorsrsquo Contributions

All authors contributed equally to the writing of this paperAnd all authors read and approved the final manuscript

Acknowledgments

is paper was supported by the Department of Mathe-matics and the Office of Research Innovation andCommercialization of Abdul Wali Khan UniversityMardan Pakistan

10 Computational Intelligence and Neuroscience

References

[1] A Kumar and G Shankar ldquoQuasi-oppositional harmonysearch algorithm based optimal dynamic load frequencycontrol of a hybrid tidal-diesel power generation systemrdquo IETGeneration Transmission amp Distribution vol 12 no 5pp 1099ndash1108 2018

[2] M Mehdinejad B Mohammadi-Ivatloo and R Dadashzadeh-Bonab ldquoEnergy production cost minimization in a combinedheat and power generation systems using cuckoo optimizationalgorithmrdquo Energy Efficiency vol 10 no 1 pp 81ndash96 2017

[3] K Y Lee C Y Chung B J Huang et al ldquoA novel algorithmfor single-axis maximum power generation sun trackersrdquoEnergy Conversion and Management vol 149 pp 543ndash5522017

[4] L S M Guedes P de Mendonca Maia A C LisboaD A G Vieira and R R Saldanha ldquoA unit commitmentalgorithm and a compact MILP model for short-term hydro-power generation schedulingrdquo IEEE Transactions on PowerSystems vol 32 no 5 pp 3381ndash3390 2017

[5] F Zaman S M Elsayed T Ray and R A Sarker ldquoEvo-lutionary algorithms for power generation planning withuncertain renewable energyrdquo Energy vol 112 pp 408ndash4192016

[6] M E Nazari and M M Ardehali ldquoOptimal coordination ofrenewable wind and pumped storage with thermal powergeneration for maximizing economic profit with consider-ations for environmental emission based on newly developedheuristic optimization algorithmrdquo Journal of Renewable andSustainable Energy vol 8 no 6 article 065905 2016

[7] S Hemalatha and S Chandramohan ldquoCost optimization ofpower generation systems using bat algorithm for remotehealth facilitiesrdquo Journal of Medical Imaging and Health In-formatics vol 6 no 7 pp 1646ndash1651 2016

[8] E Assareh and M Biglari ldquoA novel approach to capture themaximum power generation from wind turbines using hybridMLP neural network and bees algorithm (HNNBA)rdquo IETEJournal of Research vol 62 no 3 pp 368ndash378 2016

[9] N Nikmehr and S Najafi-Ravadanegh ldquoOptimal operation ofdistributed generations in micro-grids under uncertainties inload and renewable power generation using heuristic algo-rithmrdquo IET Renewable Power Generation vol 9 no 8pp 982ndash990 2015

[10] W Sun J Wang and H Chang ldquoForecasting annual powergeneration using a harmony search algorithm-based jointparameters optimization combination modelrdquo Energiesvol 5 no 10 pp 3948ndash3971 2012

[11] J Jasper ldquoCost optimization of power generation using adifferential evolution algorithm enhanced with neighbour-hood search operationrdquo International Review of ElectricalEngineering (IREE) vol 7 no 5 pp 5854ndash5865 2012

[12] G Ali ldquoFactors affecting public investment in manufacturingsector of Pakistanrdquo European Journal of Economic Studiesvol 13 no 3 pp 122ndash130 2015

[13] D H Husaini and H H Lean ldquoDoes electricity drive thedevelopment of manufacturing sector in Malaysiardquo Frontiersin Energy Research vol 3 p 18 2015

[14] M M Rafique and S Rehman ldquoNational energy scenario ofPakistan-current status future alternatives and institutionalinfrastructure an overviewrdquo Renewable and SustainableEnergy Reviews vol 69 pp 156ndash167 2017

[15] NEPRA State of Industry Report 2016 httpwwwnepraorgpkpublicationsstateofindustryreportsstateofindustryreport2016pdf

[16] Electricity demand surges to 22000 MWwith rise in mercuryin Dawn 2017 httpswwwdawncomnews1339210

[17] J L C Meza M B Yildirim and A S M Masud ldquoAmultiobjective evolutionary programming algorithm andits applications to power generation expansion planningrdquoIEEE Transactions on Systems Man and Cybernetics-PartA Systems and Humans vol 39 no 5 pp 1086ndash10962009

[18] M Asif ldquoSustainable energy options for Pakistanrdquo Renewableand Sustainable Energy Reviews vol 13 no 4 pp 903ndash9092009

[19] S Wasti Economic Survey of Pakistan 2014-15 Governmentof Pakistan Islamabad Pakistan 2015

[20] M Kugelman Pakistanrsquos Energy Crisis National Bureau ofAsian Research Washington DC USA 2013

[21] H Zameer and Y Wang ldquoEnergy production system opti-mization evidence from Pakistanrdquo Renewable and Sustain-able Energy Reviews vol 82 pp 886ndash893 2018

[22] B Zafar ldquoFuel Price Adjustmentrdquo httpstribunecompkstory957503fuel-price-adjustment-regulator-cuts-power-tariff-for-june-and-july

[23] X S Yang ldquoA new metaheuristic bat-inspired algorithmrdquo inNature Inspired Cooperative Strategies for Optimization(NICSO 2010) pp 65ndash74 Springer Berlin Germany 2010

[24] B Zhu W Zhu Z Liu Q Duan and L Cao ldquoA novelquantum-behaved bat algorithm with mean best positiondirected for numerical optimizationrdquo Computational in-telligence and neuroscience vol 2016 Article ID 609748417 pages 2016

[25] S Saremi S Mirjalili and A Lewis ldquoGrasshopper optimi-sation algorithm theory and applicationrdquo Advances in En-gineering Software vol 105 pp 30ndash47 2017

[26] X S Yang ldquoFirefly algorithm stochastic test functions anddesign optimisationrdquo 2010 httparxivorgabs10031409

[27] C F Chao and M H Horng ldquoe construction of supportvector machine classifier using the firefly algorithmrdquo Com-putational Intelligence and Neuroscience vol 2015 Article ID212719 8 pages 2015

[28] F Ozkaynak ldquoA novel method to improve the performance ofchaos based evolutionary algorithmsrdquo Optik vol 126 no 24pp 5434ndash5438 2015

[29] M Sulaiman A Ahmad A Khan and S MuhammadldquoHybridized symbiotic organism search algorithm for theoptimal operation of directional overcurrent relaysrdquo Com-plexity vol 2018 Article ID 4605769 11 pages 2018

[30] M Sulaiman S Muhammad and A Khan ldquoImproved solu-tions for the optimal coordination of docrs using firefly al-gorithmrdquo Complexity vol 2018 Article ID 7039790 15 pages2018

[31] S Mirjalili Waseem S MMirjalili and A Hatamlou ldquoMulti-verse optimizer a nature-inspired algorithm for global op-timizationrdquo Neural Computing and Applications vol 27no 2 pp 495ndash513 2016

[32] H Faris I Aljarah and S Mirjalili ldquoTraining feedforwardneural networks using multi-verse optimizer for binaryclassification problemsrdquo Applied Intelligence vol 45 no 2pp 322ndash332 2016

[33] C Hu Z Li T Zhou A Zhu and C Xu ldquoA multi-verseoptimizer with levy flights for numerical optimization and itsapplication in test scheduling for network-on-chiprdquo PLoSOne vol 11 no 12 Article ID e0167341 2016

[34] G I Sayed A Darwish and A E Hassanien ldquoQuantummultiverse optimization algorithm for optimization

Computational Intelligence and Neuroscience 11

0

500

1000

1500

2000

2500

1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 33 35 37 39 41 43 45 47 49 51 53 55 57 59 61 63 65 67 69 71 73 75 77 79 81 83 85 87 89 91 93 95

Elec

tric

ity p

rodu

ctio

nin

meg

awat

ts

Power production sources

(a)

0

400200

600

1000800

1200

16001400

1800

1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 33 35 37 39 41 43 45 47 49 51 53 55 57 59 61 63 65 67 69 71 73 75 77 79 81 83 85 87 89 91 93 95

Elec

tric

ity p

rodu

ctio

nin

meg

awat

ts

Power production sources

(b)

0

500

1000

1500

2000

2500

3000

1 4 7 10 13 16 19 22 25 28 31 34 37 40 43 46 49 52 55 58 61 64 67 70 73 76 79 82 85 88 91 94

Elec

tric

ity p

rodu

ctio

nin

meg

awat

ts

Power production sources

(c)

0500

100015002000250030003500

1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 33 35 37 39 41 43 45 47 49 51 53 55 57 59 61 63 65 67 69 71 73 75 77 79 81 83 85 87 89 91 93 95

Elec

tric

ity p

rodu

ctio

nin

meg

awat

ts

Power production sources

(d)

0500

100015002000250030003500

1 4 7 10 13 16 19 22 25 28 31 34 37 40 43 46 49 52 55 58 61 64 67 70 73 76 79 82 85 88 91 94

Elec

tric

ity p

rodu

ctio

nin

meg

awat

ts

All power production sources

(e)

Figure 3 Comprehensive plots of five case studies discussed in Table 4 All production sources are plotted against the electricity productionin megawatts (a) Case Study 1 demand of 15003MW (b) Case Study 2 demand of 19003MW (c) Case Study 3 demand of 23000MW(d) Case Study 4 demand of 250003MW (e) Case Study 5 demand of 272083MW

8 Computational Intelligence and Neuroscience

6 Conclusions

In this paper an improved multiverse optimization al-gorithm is implemented for solving a linear programmingmodel for proper management of electricity productionsources in Pakistan To address the proper management ofpower production sources several bound constraintssuch as constraint for total demand and bounds on allvariables are considered e objective function is linearwith 95 decision variables and different coefficients eIMVO algorithm is easy to implement with few param-eters We have found solutions for five different casestudies and analyzed all solutions graphically A link to thedata set of 100000 different solutions is provided in this

paper In our results we have obtained better solutions tomeet the power demand in summer It is recommendedthat current resources can produce the required powerdemand but some of the resources are required to beexpanded in capacity along with installation of newsources In future we intend to include other factors likepower loss in our model

Nomenclature

TD Tarbela Dam (x1)MD Mangla Dam (x2)GBHPP Ghazi Barota Hydropower Project (x3)WD Warsak Dam (x4)CB Chashma Barrage (x5)DKD Duber Khwar Dam (x6)AKPH Allai Khwar Hydropower Plant (x7)KKPL Khan Khwar Hydropower Plant (x8)JHP Jagran Hydropower Plant (x9)

Table 6 Top 20 electricity production sources according to the five case studies

No1

No2

No3

No4

No5

No6

No7

No8

No9

No10

No11

No12

No13

No14

No15

No16

No17

No18

No19

No20

x1 x19 x60 x3 x20 x56 x34 x78 x21 x2 x36 x63 x35 x68 x83 x37 x38 x72 x74 x81

15

145

14

135

13

125

12

115

11

105

Cos

t

0 10 20 30 40 50 60 70 80 90 100Iterations

times108

Figure 4 IMVO convergence graph demand for 15000megawatt

15

155

145

14

135

17

175

16

165

Cos

t

0 10 20 30 40 50 60 70 80 90 100Iterations

times108

Figure 5 IMVO convergence graph demand for 19000megawatt

194

192

19

188

186

184

182

18

178

174

172C

ost

0 10 20 30 40 50 60 70 80 90 100Iterations

times108

Figure 6 IMVO convergence graph demand for 23000megawatt

Table 7 Per megawatt cost of electricity for different fuel types

Fuel type Price in PKR per megawattHydel 2500LNG 9070Furnace oil 11050High-speed diesel 17960Coal 12080Solar 16950Wind 16630Nuclear 6860Regasified liquefied natural gas 11270

Computational Intelligence and Neuroscience 9

JabHP Jabban Hydropower Plant (x10)RB Rasal Barrage (x11)DHP Dargai Power Plant (x12)GZD Gomal Zam Dam (x13)NHP Nandipur Hydropower Plant (x14)SHP Shadiwal Hydropower Plant (x15)KHP Khuram Hydropower Plant (x16)RKHP Renela Khuard Hydropower Plant (x17)CHPP Chatral Hydropower Plant (x18)GTPP Guduu ermal Power Plant (x19)MTPP Muzaffargarh ermal Power Plant (x20)JTPP Jamshoro ermal Power Plant (x21)FGTPP Faisalabad Gas Turbine Power Plant (x22)MGTPP Multan Gas Turbine Power Plant (x23)KGTPP Kotri Gas Turbine Power Plant (x24)LTPP Larkana ermal Power Plant (x25)FSPP Faisalabad Steam Power Plant (x26)SGTPP Shahdra Gas Turbine Power Plant (x27)PGTPP Panjgur Gas Turbine Power Plant (x28)QTPP Quetta ermal Power Plant (x29)PTPP Pasni ermal Power Plant (x30)KPC Korangi Power Complex (x31)KGTPS Korang Gas Turbine Power Plant Station

(x32)GTPS Gas Turbine Power Station (x33)KPS ermal Power Plant (x34)CCPP1 Combined Cycle Power Plant 1 (x35)CCPP2 Combined Cycle Power Plant 2 (x36)AESLL AES Lalpir Limited (x37)AESPG AES Pak Gen (x38)AEL Altern Energy Limited (x39)AP Altes Power (x40)AGL Attock Gen Limited (x41)CMECP CMEC Power Pvt (x42)DHACL DHA Cogen Limited (x43)EPC Eastern Power Company (x44)EPQL Engro Powergen Qaidpur Limited (x45)FKPP Fauji Kabirwala Power Plant (x46)FTSM First-Star Modaraba (x47)FPCDL Foundation power company Daharki

Limited (x48)GHLLP Grang Holding Limited Power Plant (x49)GEPtvl Green Electric Pvt Limited (x50)GEL Gujranwala Energy Limited (x51)DAEL Gul Ahmad Energy Limited (x52)HCPC Habibullah Coastal Power Company (x53)HPGC Halmore Power Generation Company (x54)HUBCONPP HUBCO Narowal Power Plant (x55)HUBCOHPP HUBCO Hub Power Plant (x56)IPtvL Intergen PTV Limited (x57)JPG Japan Power Plant (x58)KEL Kohinor Energy Limited (x59)KAPCL Kot Addu Power Company Limited (x60)LPL Liberty Power Limited (x61)LPTL Liberty Power Tech Limited (x62)LEPCL Lucky Electric Power Company Limited

(x63)NCP Nishat Chunian Power (x64)

NPL Nishat Power Limited (x65)OPCPrvL Orient Power Company (Pvt) Limited (x66)REPGC Radian Energy Power Generation Company

(x67)RPK Rousch Power Khanewal (x68)SPC Saba Power Company (x69)SPPQ Saif Power Plant Qadirabad (x70)SECL Sapphire Electric Company Limited (x71)SSEL Siddiqsons Energy Limited (x72)SNPCL Sindh Nooriabad Power Company (Pvt)

Limited (x73)SE Sitara Energy (x74)SEPC Southern Electric Power Company Limited

(x75)SPGL Star Power Generation Limited (x76)TEL Tapal Energy Limited (x77)UchPL Uch (Uch-I and Uch-II) Power Limited (x78)KANUPP KANUPP (x79)CHASNUPP-1 CHASNUPP-1 (x80)CHASNUPP-2 CHASNUPP-2 (x81)CHASNUPP-3 CHASNUPP-3 (x82)NPP Nandipur Power Project (x83)QeaSP Quaid-e-Azam Solar Park (x84)YEL Yunus Energy Limited (x85)MWPCL Metro Wind Power Co Limited (x86)TGL Tenaga Generai Limited (x87)GAWPL Gul Ahmed Wind Power Limited (x88)MWEL Master Wind Energy Limited (x89)FFCEL FFC Energy Limited Jhimpir (x90)ZEPJ Zorlu Enerji Pakistan Jhimpir (x91)TWEL Tapal Wind Energy Limited (x92)HCDPL HydroChina Dawood Power Limited (x93)FEW-1L Foundation Wind Energy-I Limited (x94)FEW-2PT Foundation Wind Energy-II Private Limited

(x95)

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

Authorsrsquo Contributions

All authors contributed equally to the writing of this paperAnd all authors read and approved the final manuscript

Acknowledgments

is paper was supported by the Department of Mathe-matics and the Office of Research Innovation andCommercialization of Abdul Wali Khan UniversityMardan Pakistan

10 Computational Intelligence and Neuroscience

References

[1] A Kumar and G Shankar ldquoQuasi-oppositional harmonysearch algorithm based optimal dynamic load frequencycontrol of a hybrid tidal-diesel power generation systemrdquo IETGeneration Transmission amp Distribution vol 12 no 5pp 1099ndash1108 2018

[2] M Mehdinejad B Mohammadi-Ivatloo and R Dadashzadeh-Bonab ldquoEnergy production cost minimization in a combinedheat and power generation systems using cuckoo optimizationalgorithmrdquo Energy Efficiency vol 10 no 1 pp 81ndash96 2017

[3] K Y Lee C Y Chung B J Huang et al ldquoA novel algorithmfor single-axis maximum power generation sun trackersrdquoEnergy Conversion and Management vol 149 pp 543ndash5522017

[4] L S M Guedes P de Mendonca Maia A C LisboaD A G Vieira and R R Saldanha ldquoA unit commitmentalgorithm and a compact MILP model for short-term hydro-power generation schedulingrdquo IEEE Transactions on PowerSystems vol 32 no 5 pp 3381ndash3390 2017

[5] F Zaman S M Elsayed T Ray and R A Sarker ldquoEvo-lutionary algorithms for power generation planning withuncertain renewable energyrdquo Energy vol 112 pp 408ndash4192016

[6] M E Nazari and M M Ardehali ldquoOptimal coordination ofrenewable wind and pumped storage with thermal powergeneration for maximizing economic profit with consider-ations for environmental emission based on newly developedheuristic optimization algorithmrdquo Journal of Renewable andSustainable Energy vol 8 no 6 article 065905 2016

[7] S Hemalatha and S Chandramohan ldquoCost optimization ofpower generation systems using bat algorithm for remotehealth facilitiesrdquo Journal of Medical Imaging and Health In-formatics vol 6 no 7 pp 1646ndash1651 2016

[8] E Assareh and M Biglari ldquoA novel approach to capture themaximum power generation from wind turbines using hybridMLP neural network and bees algorithm (HNNBA)rdquo IETEJournal of Research vol 62 no 3 pp 368ndash378 2016

[9] N Nikmehr and S Najafi-Ravadanegh ldquoOptimal operation ofdistributed generations in micro-grids under uncertainties inload and renewable power generation using heuristic algo-rithmrdquo IET Renewable Power Generation vol 9 no 8pp 982ndash990 2015

[10] W Sun J Wang and H Chang ldquoForecasting annual powergeneration using a harmony search algorithm-based jointparameters optimization combination modelrdquo Energiesvol 5 no 10 pp 3948ndash3971 2012

[11] J Jasper ldquoCost optimization of power generation using adifferential evolution algorithm enhanced with neighbour-hood search operationrdquo International Review of ElectricalEngineering (IREE) vol 7 no 5 pp 5854ndash5865 2012

[12] G Ali ldquoFactors affecting public investment in manufacturingsector of Pakistanrdquo European Journal of Economic Studiesvol 13 no 3 pp 122ndash130 2015

[13] D H Husaini and H H Lean ldquoDoes electricity drive thedevelopment of manufacturing sector in Malaysiardquo Frontiersin Energy Research vol 3 p 18 2015

[14] M M Rafique and S Rehman ldquoNational energy scenario ofPakistan-current status future alternatives and institutionalinfrastructure an overviewrdquo Renewable and SustainableEnergy Reviews vol 69 pp 156ndash167 2017

[15] NEPRA State of Industry Report 2016 httpwwwnepraorgpkpublicationsstateofindustryreportsstateofindustryreport2016pdf

[16] Electricity demand surges to 22000 MWwith rise in mercuryin Dawn 2017 httpswwwdawncomnews1339210

[17] J L C Meza M B Yildirim and A S M Masud ldquoAmultiobjective evolutionary programming algorithm andits applications to power generation expansion planningrdquoIEEE Transactions on Systems Man and Cybernetics-PartA Systems and Humans vol 39 no 5 pp 1086ndash10962009

[18] M Asif ldquoSustainable energy options for Pakistanrdquo Renewableand Sustainable Energy Reviews vol 13 no 4 pp 903ndash9092009

[19] S Wasti Economic Survey of Pakistan 2014-15 Governmentof Pakistan Islamabad Pakistan 2015

[20] M Kugelman Pakistanrsquos Energy Crisis National Bureau ofAsian Research Washington DC USA 2013

[21] H Zameer and Y Wang ldquoEnergy production system opti-mization evidence from Pakistanrdquo Renewable and Sustain-able Energy Reviews vol 82 pp 886ndash893 2018

[22] B Zafar ldquoFuel Price Adjustmentrdquo httpstribunecompkstory957503fuel-price-adjustment-regulator-cuts-power-tariff-for-june-and-july

[23] X S Yang ldquoA new metaheuristic bat-inspired algorithmrdquo inNature Inspired Cooperative Strategies for Optimization(NICSO 2010) pp 65ndash74 Springer Berlin Germany 2010

[24] B Zhu W Zhu Z Liu Q Duan and L Cao ldquoA novelquantum-behaved bat algorithm with mean best positiondirected for numerical optimizationrdquo Computational in-telligence and neuroscience vol 2016 Article ID 609748417 pages 2016

[25] S Saremi S Mirjalili and A Lewis ldquoGrasshopper optimi-sation algorithm theory and applicationrdquo Advances in En-gineering Software vol 105 pp 30ndash47 2017

[26] X S Yang ldquoFirefly algorithm stochastic test functions anddesign optimisationrdquo 2010 httparxivorgabs10031409

[27] C F Chao and M H Horng ldquoe construction of supportvector machine classifier using the firefly algorithmrdquo Com-putational Intelligence and Neuroscience vol 2015 Article ID212719 8 pages 2015

[28] F Ozkaynak ldquoA novel method to improve the performance ofchaos based evolutionary algorithmsrdquo Optik vol 126 no 24pp 5434ndash5438 2015

[29] M Sulaiman A Ahmad A Khan and S MuhammadldquoHybridized symbiotic organism search algorithm for theoptimal operation of directional overcurrent relaysrdquo Com-plexity vol 2018 Article ID 4605769 11 pages 2018

[30] M Sulaiman S Muhammad and A Khan ldquoImproved solu-tions for the optimal coordination of docrs using firefly al-gorithmrdquo Complexity vol 2018 Article ID 7039790 15 pages2018

[31] S Mirjalili Waseem S MMirjalili and A Hatamlou ldquoMulti-verse optimizer a nature-inspired algorithm for global op-timizationrdquo Neural Computing and Applications vol 27no 2 pp 495ndash513 2016

[32] H Faris I Aljarah and S Mirjalili ldquoTraining feedforwardneural networks using multi-verse optimizer for binaryclassification problemsrdquo Applied Intelligence vol 45 no 2pp 322ndash332 2016

[33] C Hu Z Li T Zhou A Zhu and C Xu ldquoA multi-verseoptimizer with levy flights for numerical optimization and itsapplication in test scheduling for network-on-chiprdquo PLoSOne vol 11 no 12 Article ID e0167341 2016

[34] G I Sayed A Darwish and A E Hassanien ldquoQuantummultiverse optimization algorithm for optimization

Computational Intelligence and Neuroscience 11

6 Conclusions

In this paper an improved multiverse optimization al-gorithm is implemented for solving a linear programmingmodel for proper management of electricity productionsources in Pakistan To address the proper management ofpower production sources several bound constraintssuch as constraint for total demand and bounds on allvariables are considered e objective function is linearwith 95 decision variables and different coefficients eIMVO algorithm is easy to implement with few param-eters We have found solutions for five different casestudies and analyzed all solutions graphically A link to thedata set of 100000 different solutions is provided in this

paper In our results we have obtained better solutions tomeet the power demand in summer It is recommendedthat current resources can produce the required powerdemand but some of the resources are required to beexpanded in capacity along with installation of newsources In future we intend to include other factors likepower loss in our model

Nomenclature

TD Tarbela Dam (x1)MD Mangla Dam (x2)GBHPP Ghazi Barota Hydropower Project (x3)WD Warsak Dam (x4)CB Chashma Barrage (x5)DKD Duber Khwar Dam (x6)AKPH Allai Khwar Hydropower Plant (x7)KKPL Khan Khwar Hydropower Plant (x8)JHP Jagran Hydropower Plant (x9)

Table 6 Top 20 electricity production sources according to the five case studies

No1

No2

No3

No4

No5

No6

No7

No8

No9

No10

No11

No12

No13

No14

No15

No16

No17

No18

No19

No20

x1 x19 x60 x3 x20 x56 x34 x78 x21 x2 x36 x63 x35 x68 x83 x37 x38 x72 x74 x81

15

145

14

135

13

125

12

115

11

105

Cos

t

0 10 20 30 40 50 60 70 80 90 100Iterations

times108

Figure 4 IMVO convergence graph demand for 15000megawatt

15

155

145

14

135

17

175

16

165

Cos

t

0 10 20 30 40 50 60 70 80 90 100Iterations

times108

Figure 5 IMVO convergence graph demand for 19000megawatt

194

192

19

188

186

184

182

18

178

174

172C

ost

0 10 20 30 40 50 60 70 80 90 100Iterations

times108

Figure 6 IMVO convergence graph demand for 23000megawatt

Table 7 Per megawatt cost of electricity for different fuel types

Fuel type Price in PKR per megawattHydel 2500LNG 9070Furnace oil 11050High-speed diesel 17960Coal 12080Solar 16950Wind 16630Nuclear 6860Regasified liquefied natural gas 11270

Computational Intelligence and Neuroscience 9

JabHP Jabban Hydropower Plant (x10)RB Rasal Barrage (x11)DHP Dargai Power Plant (x12)GZD Gomal Zam Dam (x13)NHP Nandipur Hydropower Plant (x14)SHP Shadiwal Hydropower Plant (x15)KHP Khuram Hydropower Plant (x16)RKHP Renela Khuard Hydropower Plant (x17)CHPP Chatral Hydropower Plant (x18)GTPP Guduu ermal Power Plant (x19)MTPP Muzaffargarh ermal Power Plant (x20)JTPP Jamshoro ermal Power Plant (x21)FGTPP Faisalabad Gas Turbine Power Plant (x22)MGTPP Multan Gas Turbine Power Plant (x23)KGTPP Kotri Gas Turbine Power Plant (x24)LTPP Larkana ermal Power Plant (x25)FSPP Faisalabad Steam Power Plant (x26)SGTPP Shahdra Gas Turbine Power Plant (x27)PGTPP Panjgur Gas Turbine Power Plant (x28)QTPP Quetta ermal Power Plant (x29)PTPP Pasni ermal Power Plant (x30)KPC Korangi Power Complex (x31)KGTPS Korang Gas Turbine Power Plant Station

(x32)GTPS Gas Turbine Power Station (x33)KPS ermal Power Plant (x34)CCPP1 Combined Cycle Power Plant 1 (x35)CCPP2 Combined Cycle Power Plant 2 (x36)AESLL AES Lalpir Limited (x37)AESPG AES Pak Gen (x38)AEL Altern Energy Limited (x39)AP Altes Power (x40)AGL Attock Gen Limited (x41)CMECP CMEC Power Pvt (x42)DHACL DHA Cogen Limited (x43)EPC Eastern Power Company (x44)EPQL Engro Powergen Qaidpur Limited (x45)FKPP Fauji Kabirwala Power Plant (x46)FTSM First-Star Modaraba (x47)FPCDL Foundation power company Daharki

Limited (x48)GHLLP Grang Holding Limited Power Plant (x49)GEPtvl Green Electric Pvt Limited (x50)GEL Gujranwala Energy Limited (x51)DAEL Gul Ahmad Energy Limited (x52)HCPC Habibullah Coastal Power Company (x53)HPGC Halmore Power Generation Company (x54)HUBCONPP HUBCO Narowal Power Plant (x55)HUBCOHPP HUBCO Hub Power Plant (x56)IPtvL Intergen PTV Limited (x57)JPG Japan Power Plant (x58)KEL Kohinor Energy Limited (x59)KAPCL Kot Addu Power Company Limited (x60)LPL Liberty Power Limited (x61)LPTL Liberty Power Tech Limited (x62)LEPCL Lucky Electric Power Company Limited

(x63)NCP Nishat Chunian Power (x64)

NPL Nishat Power Limited (x65)OPCPrvL Orient Power Company (Pvt) Limited (x66)REPGC Radian Energy Power Generation Company

(x67)RPK Rousch Power Khanewal (x68)SPC Saba Power Company (x69)SPPQ Saif Power Plant Qadirabad (x70)SECL Sapphire Electric Company Limited (x71)SSEL Siddiqsons Energy Limited (x72)SNPCL Sindh Nooriabad Power Company (Pvt)

Limited (x73)SE Sitara Energy (x74)SEPC Southern Electric Power Company Limited

(x75)SPGL Star Power Generation Limited (x76)TEL Tapal Energy Limited (x77)UchPL Uch (Uch-I and Uch-II) Power Limited (x78)KANUPP KANUPP (x79)CHASNUPP-1 CHASNUPP-1 (x80)CHASNUPP-2 CHASNUPP-2 (x81)CHASNUPP-3 CHASNUPP-3 (x82)NPP Nandipur Power Project (x83)QeaSP Quaid-e-Azam Solar Park (x84)YEL Yunus Energy Limited (x85)MWPCL Metro Wind Power Co Limited (x86)TGL Tenaga Generai Limited (x87)GAWPL Gul Ahmed Wind Power Limited (x88)MWEL Master Wind Energy Limited (x89)FFCEL FFC Energy Limited Jhimpir (x90)ZEPJ Zorlu Enerji Pakistan Jhimpir (x91)TWEL Tapal Wind Energy Limited (x92)HCDPL HydroChina Dawood Power Limited (x93)FEW-1L Foundation Wind Energy-I Limited (x94)FEW-2PT Foundation Wind Energy-II Private Limited

(x95)

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

Authorsrsquo Contributions

All authors contributed equally to the writing of this paperAnd all authors read and approved the final manuscript

Acknowledgments

is paper was supported by the Department of Mathe-matics and the Office of Research Innovation andCommercialization of Abdul Wali Khan UniversityMardan Pakistan

10 Computational Intelligence and Neuroscience

References

[1] A Kumar and G Shankar ldquoQuasi-oppositional harmonysearch algorithm based optimal dynamic load frequencycontrol of a hybrid tidal-diesel power generation systemrdquo IETGeneration Transmission amp Distribution vol 12 no 5pp 1099ndash1108 2018

[2] M Mehdinejad B Mohammadi-Ivatloo and R Dadashzadeh-Bonab ldquoEnergy production cost minimization in a combinedheat and power generation systems using cuckoo optimizationalgorithmrdquo Energy Efficiency vol 10 no 1 pp 81ndash96 2017

[3] K Y Lee C Y Chung B J Huang et al ldquoA novel algorithmfor single-axis maximum power generation sun trackersrdquoEnergy Conversion and Management vol 149 pp 543ndash5522017

[4] L S M Guedes P de Mendonca Maia A C LisboaD A G Vieira and R R Saldanha ldquoA unit commitmentalgorithm and a compact MILP model for short-term hydro-power generation schedulingrdquo IEEE Transactions on PowerSystems vol 32 no 5 pp 3381ndash3390 2017

[5] F Zaman S M Elsayed T Ray and R A Sarker ldquoEvo-lutionary algorithms for power generation planning withuncertain renewable energyrdquo Energy vol 112 pp 408ndash4192016

[6] M E Nazari and M M Ardehali ldquoOptimal coordination ofrenewable wind and pumped storage with thermal powergeneration for maximizing economic profit with consider-ations for environmental emission based on newly developedheuristic optimization algorithmrdquo Journal of Renewable andSustainable Energy vol 8 no 6 article 065905 2016

[7] S Hemalatha and S Chandramohan ldquoCost optimization ofpower generation systems using bat algorithm for remotehealth facilitiesrdquo Journal of Medical Imaging and Health In-formatics vol 6 no 7 pp 1646ndash1651 2016

[8] E Assareh and M Biglari ldquoA novel approach to capture themaximum power generation from wind turbines using hybridMLP neural network and bees algorithm (HNNBA)rdquo IETEJournal of Research vol 62 no 3 pp 368ndash378 2016

[9] N Nikmehr and S Najafi-Ravadanegh ldquoOptimal operation ofdistributed generations in micro-grids under uncertainties inload and renewable power generation using heuristic algo-rithmrdquo IET Renewable Power Generation vol 9 no 8pp 982ndash990 2015

[10] W Sun J Wang and H Chang ldquoForecasting annual powergeneration using a harmony search algorithm-based jointparameters optimization combination modelrdquo Energiesvol 5 no 10 pp 3948ndash3971 2012

[11] J Jasper ldquoCost optimization of power generation using adifferential evolution algorithm enhanced with neighbour-hood search operationrdquo International Review of ElectricalEngineering (IREE) vol 7 no 5 pp 5854ndash5865 2012

[12] G Ali ldquoFactors affecting public investment in manufacturingsector of Pakistanrdquo European Journal of Economic Studiesvol 13 no 3 pp 122ndash130 2015

[13] D H Husaini and H H Lean ldquoDoes electricity drive thedevelopment of manufacturing sector in Malaysiardquo Frontiersin Energy Research vol 3 p 18 2015

[14] M M Rafique and S Rehman ldquoNational energy scenario ofPakistan-current status future alternatives and institutionalinfrastructure an overviewrdquo Renewable and SustainableEnergy Reviews vol 69 pp 156ndash167 2017

[15] NEPRA State of Industry Report 2016 httpwwwnepraorgpkpublicationsstateofindustryreportsstateofindustryreport2016pdf

[16] Electricity demand surges to 22000 MWwith rise in mercuryin Dawn 2017 httpswwwdawncomnews1339210

[17] J L C Meza M B Yildirim and A S M Masud ldquoAmultiobjective evolutionary programming algorithm andits applications to power generation expansion planningrdquoIEEE Transactions on Systems Man and Cybernetics-PartA Systems and Humans vol 39 no 5 pp 1086ndash10962009

[18] M Asif ldquoSustainable energy options for Pakistanrdquo Renewableand Sustainable Energy Reviews vol 13 no 4 pp 903ndash9092009

[19] S Wasti Economic Survey of Pakistan 2014-15 Governmentof Pakistan Islamabad Pakistan 2015

[20] M Kugelman Pakistanrsquos Energy Crisis National Bureau ofAsian Research Washington DC USA 2013

[21] H Zameer and Y Wang ldquoEnergy production system opti-mization evidence from Pakistanrdquo Renewable and Sustain-able Energy Reviews vol 82 pp 886ndash893 2018

[22] B Zafar ldquoFuel Price Adjustmentrdquo httpstribunecompkstory957503fuel-price-adjustment-regulator-cuts-power-tariff-for-june-and-july

[23] X S Yang ldquoA new metaheuristic bat-inspired algorithmrdquo inNature Inspired Cooperative Strategies for Optimization(NICSO 2010) pp 65ndash74 Springer Berlin Germany 2010

[24] B Zhu W Zhu Z Liu Q Duan and L Cao ldquoA novelquantum-behaved bat algorithm with mean best positiondirected for numerical optimizationrdquo Computational in-telligence and neuroscience vol 2016 Article ID 609748417 pages 2016

[25] S Saremi S Mirjalili and A Lewis ldquoGrasshopper optimi-sation algorithm theory and applicationrdquo Advances in En-gineering Software vol 105 pp 30ndash47 2017

[26] X S Yang ldquoFirefly algorithm stochastic test functions anddesign optimisationrdquo 2010 httparxivorgabs10031409

[27] C F Chao and M H Horng ldquoe construction of supportvector machine classifier using the firefly algorithmrdquo Com-putational Intelligence and Neuroscience vol 2015 Article ID212719 8 pages 2015

[28] F Ozkaynak ldquoA novel method to improve the performance ofchaos based evolutionary algorithmsrdquo Optik vol 126 no 24pp 5434ndash5438 2015

[29] M Sulaiman A Ahmad A Khan and S MuhammadldquoHybridized symbiotic organism search algorithm for theoptimal operation of directional overcurrent relaysrdquo Com-plexity vol 2018 Article ID 4605769 11 pages 2018

[30] M Sulaiman S Muhammad and A Khan ldquoImproved solu-tions for the optimal coordination of docrs using firefly al-gorithmrdquo Complexity vol 2018 Article ID 7039790 15 pages2018

[31] S Mirjalili Waseem S MMirjalili and A Hatamlou ldquoMulti-verse optimizer a nature-inspired algorithm for global op-timizationrdquo Neural Computing and Applications vol 27no 2 pp 495ndash513 2016

[32] H Faris I Aljarah and S Mirjalili ldquoTraining feedforwardneural networks using multi-verse optimizer for binaryclassification problemsrdquo Applied Intelligence vol 45 no 2pp 322ndash332 2016

[33] C Hu Z Li T Zhou A Zhu and C Xu ldquoA multi-verseoptimizer with levy flights for numerical optimization and itsapplication in test scheduling for network-on-chiprdquo PLoSOne vol 11 no 12 Article ID e0167341 2016

[34] G I Sayed A Darwish and A E Hassanien ldquoQuantummultiverse optimization algorithm for optimization

Computational Intelligence and Neuroscience 11

JabHP Jabban Hydropower Plant (x10)RB Rasal Barrage (x11)DHP Dargai Power Plant (x12)GZD Gomal Zam Dam (x13)NHP Nandipur Hydropower Plant (x14)SHP Shadiwal Hydropower Plant (x15)KHP Khuram Hydropower Plant (x16)RKHP Renela Khuard Hydropower Plant (x17)CHPP Chatral Hydropower Plant (x18)GTPP Guduu ermal Power Plant (x19)MTPP Muzaffargarh ermal Power Plant (x20)JTPP Jamshoro ermal Power Plant (x21)FGTPP Faisalabad Gas Turbine Power Plant (x22)MGTPP Multan Gas Turbine Power Plant (x23)KGTPP Kotri Gas Turbine Power Plant (x24)LTPP Larkana ermal Power Plant (x25)FSPP Faisalabad Steam Power Plant (x26)SGTPP Shahdra Gas Turbine Power Plant (x27)PGTPP Panjgur Gas Turbine Power Plant (x28)QTPP Quetta ermal Power Plant (x29)PTPP Pasni ermal Power Plant (x30)KPC Korangi Power Complex (x31)KGTPS Korang Gas Turbine Power Plant Station

(x32)GTPS Gas Turbine Power Station (x33)KPS ermal Power Plant (x34)CCPP1 Combined Cycle Power Plant 1 (x35)CCPP2 Combined Cycle Power Plant 2 (x36)AESLL AES Lalpir Limited (x37)AESPG AES Pak Gen (x38)AEL Altern Energy Limited (x39)AP Altes Power (x40)AGL Attock Gen Limited (x41)CMECP CMEC Power Pvt (x42)DHACL DHA Cogen Limited (x43)EPC Eastern Power Company (x44)EPQL Engro Powergen Qaidpur Limited (x45)FKPP Fauji Kabirwala Power Plant (x46)FTSM First-Star Modaraba (x47)FPCDL Foundation power company Daharki

Limited (x48)GHLLP Grang Holding Limited Power Plant (x49)GEPtvl Green Electric Pvt Limited (x50)GEL Gujranwala Energy Limited (x51)DAEL Gul Ahmad Energy Limited (x52)HCPC Habibullah Coastal Power Company (x53)HPGC Halmore Power Generation Company (x54)HUBCONPP HUBCO Narowal Power Plant (x55)HUBCOHPP HUBCO Hub Power Plant (x56)IPtvL Intergen PTV Limited (x57)JPG Japan Power Plant (x58)KEL Kohinor Energy Limited (x59)KAPCL Kot Addu Power Company Limited (x60)LPL Liberty Power Limited (x61)LPTL Liberty Power Tech Limited (x62)LEPCL Lucky Electric Power Company Limited

(x63)NCP Nishat Chunian Power (x64)

NPL Nishat Power Limited (x65)OPCPrvL Orient Power Company (Pvt) Limited (x66)REPGC Radian Energy Power Generation Company

(x67)RPK Rousch Power Khanewal (x68)SPC Saba Power Company (x69)SPPQ Saif Power Plant Qadirabad (x70)SECL Sapphire Electric Company Limited (x71)SSEL Siddiqsons Energy Limited (x72)SNPCL Sindh Nooriabad Power Company (Pvt)

Limited (x73)SE Sitara Energy (x74)SEPC Southern Electric Power Company Limited

(x75)SPGL Star Power Generation Limited (x76)TEL Tapal Energy Limited (x77)UchPL Uch (Uch-I and Uch-II) Power Limited (x78)KANUPP KANUPP (x79)CHASNUPP-1 CHASNUPP-1 (x80)CHASNUPP-2 CHASNUPP-2 (x81)CHASNUPP-3 CHASNUPP-3 (x82)NPP Nandipur Power Project (x83)QeaSP Quaid-e-Azam Solar Park (x84)YEL Yunus Energy Limited (x85)MWPCL Metro Wind Power Co Limited (x86)TGL Tenaga Generai Limited (x87)GAWPL Gul Ahmed Wind Power Limited (x88)MWEL Master Wind Energy Limited (x89)FFCEL FFC Energy Limited Jhimpir (x90)ZEPJ Zorlu Enerji Pakistan Jhimpir (x91)TWEL Tapal Wind Energy Limited (x92)HCDPL HydroChina Dawood Power Limited (x93)FEW-1L Foundation Wind Energy-I Limited (x94)FEW-2PT Foundation Wind Energy-II Private Limited

(x95)

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

Authorsrsquo Contributions

All authors contributed equally to the writing of this paperAnd all authors read and approved the final manuscript

Acknowledgments

is paper was supported by the Department of Mathe-matics and the Office of Research Innovation andCommercialization of Abdul Wali Khan UniversityMardan Pakistan

10 Computational Intelligence and Neuroscience

References

[1] A Kumar and G Shankar ldquoQuasi-oppositional harmonysearch algorithm based optimal dynamic load frequencycontrol of a hybrid tidal-diesel power generation systemrdquo IETGeneration Transmission amp Distribution vol 12 no 5pp 1099ndash1108 2018

[2] M Mehdinejad B Mohammadi-Ivatloo and R Dadashzadeh-Bonab ldquoEnergy production cost minimization in a combinedheat and power generation systems using cuckoo optimizationalgorithmrdquo Energy Efficiency vol 10 no 1 pp 81ndash96 2017

[3] K Y Lee C Y Chung B J Huang et al ldquoA novel algorithmfor single-axis maximum power generation sun trackersrdquoEnergy Conversion and Management vol 149 pp 543ndash5522017

[4] L S M Guedes P de Mendonca Maia A C LisboaD A G Vieira and R R Saldanha ldquoA unit commitmentalgorithm and a compact MILP model for short-term hydro-power generation schedulingrdquo IEEE Transactions on PowerSystems vol 32 no 5 pp 3381ndash3390 2017

[5] F Zaman S M Elsayed T Ray and R A Sarker ldquoEvo-lutionary algorithms for power generation planning withuncertain renewable energyrdquo Energy vol 112 pp 408ndash4192016

[6] M E Nazari and M M Ardehali ldquoOptimal coordination ofrenewable wind and pumped storage with thermal powergeneration for maximizing economic profit with consider-ations for environmental emission based on newly developedheuristic optimization algorithmrdquo Journal of Renewable andSustainable Energy vol 8 no 6 article 065905 2016

[7] S Hemalatha and S Chandramohan ldquoCost optimization ofpower generation systems using bat algorithm for remotehealth facilitiesrdquo Journal of Medical Imaging and Health In-formatics vol 6 no 7 pp 1646ndash1651 2016

[8] E Assareh and M Biglari ldquoA novel approach to capture themaximum power generation from wind turbines using hybridMLP neural network and bees algorithm (HNNBA)rdquo IETEJournal of Research vol 62 no 3 pp 368ndash378 2016

[9] N Nikmehr and S Najafi-Ravadanegh ldquoOptimal operation ofdistributed generations in micro-grids under uncertainties inload and renewable power generation using heuristic algo-rithmrdquo IET Renewable Power Generation vol 9 no 8pp 982ndash990 2015

[10] W Sun J Wang and H Chang ldquoForecasting annual powergeneration using a harmony search algorithm-based jointparameters optimization combination modelrdquo Energiesvol 5 no 10 pp 3948ndash3971 2012

[11] J Jasper ldquoCost optimization of power generation using adifferential evolution algorithm enhanced with neighbour-hood search operationrdquo International Review of ElectricalEngineering (IREE) vol 7 no 5 pp 5854ndash5865 2012

[12] G Ali ldquoFactors affecting public investment in manufacturingsector of Pakistanrdquo European Journal of Economic Studiesvol 13 no 3 pp 122ndash130 2015

[13] D H Husaini and H H Lean ldquoDoes electricity drive thedevelopment of manufacturing sector in Malaysiardquo Frontiersin Energy Research vol 3 p 18 2015

[14] M M Rafique and S Rehman ldquoNational energy scenario ofPakistan-current status future alternatives and institutionalinfrastructure an overviewrdquo Renewable and SustainableEnergy Reviews vol 69 pp 156ndash167 2017

[15] NEPRA State of Industry Report 2016 httpwwwnepraorgpkpublicationsstateofindustryreportsstateofindustryreport2016pdf

[16] Electricity demand surges to 22000 MWwith rise in mercuryin Dawn 2017 httpswwwdawncomnews1339210

[17] J L C Meza M B Yildirim and A S M Masud ldquoAmultiobjective evolutionary programming algorithm andits applications to power generation expansion planningrdquoIEEE Transactions on Systems Man and Cybernetics-PartA Systems and Humans vol 39 no 5 pp 1086ndash10962009

[18] M Asif ldquoSustainable energy options for Pakistanrdquo Renewableand Sustainable Energy Reviews vol 13 no 4 pp 903ndash9092009

[19] S Wasti Economic Survey of Pakistan 2014-15 Governmentof Pakistan Islamabad Pakistan 2015

[20] M Kugelman Pakistanrsquos Energy Crisis National Bureau ofAsian Research Washington DC USA 2013

[21] H Zameer and Y Wang ldquoEnergy production system opti-mization evidence from Pakistanrdquo Renewable and Sustain-able Energy Reviews vol 82 pp 886ndash893 2018

[22] B Zafar ldquoFuel Price Adjustmentrdquo httpstribunecompkstory957503fuel-price-adjustment-regulator-cuts-power-tariff-for-june-and-july

[23] X S Yang ldquoA new metaheuristic bat-inspired algorithmrdquo inNature Inspired Cooperative Strategies for Optimization(NICSO 2010) pp 65ndash74 Springer Berlin Germany 2010

[24] B Zhu W Zhu Z Liu Q Duan and L Cao ldquoA novelquantum-behaved bat algorithm with mean best positiondirected for numerical optimizationrdquo Computational in-telligence and neuroscience vol 2016 Article ID 609748417 pages 2016

[25] S Saremi S Mirjalili and A Lewis ldquoGrasshopper optimi-sation algorithm theory and applicationrdquo Advances in En-gineering Software vol 105 pp 30ndash47 2017

[26] X S Yang ldquoFirefly algorithm stochastic test functions anddesign optimisationrdquo 2010 httparxivorgabs10031409

[27] C F Chao and M H Horng ldquoe construction of supportvector machine classifier using the firefly algorithmrdquo Com-putational Intelligence and Neuroscience vol 2015 Article ID212719 8 pages 2015

[28] F Ozkaynak ldquoA novel method to improve the performance ofchaos based evolutionary algorithmsrdquo Optik vol 126 no 24pp 5434ndash5438 2015

[29] M Sulaiman A Ahmad A Khan and S MuhammadldquoHybridized symbiotic organism search algorithm for theoptimal operation of directional overcurrent relaysrdquo Com-plexity vol 2018 Article ID 4605769 11 pages 2018

[30] M Sulaiman S Muhammad and A Khan ldquoImproved solu-tions for the optimal coordination of docrs using firefly al-gorithmrdquo Complexity vol 2018 Article ID 7039790 15 pages2018

[31] S Mirjalili Waseem S MMirjalili and A Hatamlou ldquoMulti-verse optimizer a nature-inspired algorithm for global op-timizationrdquo Neural Computing and Applications vol 27no 2 pp 495ndash513 2016

[32] H Faris I Aljarah and S Mirjalili ldquoTraining feedforwardneural networks using multi-verse optimizer for binaryclassification problemsrdquo Applied Intelligence vol 45 no 2pp 322ndash332 2016

[33] C Hu Z Li T Zhou A Zhu and C Xu ldquoA multi-verseoptimizer with levy flights for numerical optimization and itsapplication in test scheduling for network-on-chiprdquo PLoSOne vol 11 no 12 Article ID e0167341 2016

[34] G I Sayed A Darwish and A E Hassanien ldquoQuantummultiverse optimization algorithm for optimization

Computational Intelligence and Neuroscience 11

References

[1] A Kumar and G Shankar ldquoQuasi-oppositional harmonysearch algorithm based optimal dynamic load frequencycontrol of a hybrid tidal-diesel power generation systemrdquo IETGeneration Transmission amp Distribution vol 12 no 5pp 1099ndash1108 2018

[2] M Mehdinejad B Mohammadi-Ivatloo and R Dadashzadeh-Bonab ldquoEnergy production cost minimization in a combinedheat and power generation systems using cuckoo optimizationalgorithmrdquo Energy Efficiency vol 10 no 1 pp 81ndash96 2017

[3] K Y Lee C Y Chung B J Huang et al ldquoA novel algorithmfor single-axis maximum power generation sun trackersrdquoEnergy Conversion and Management vol 149 pp 543ndash5522017

[4] L S M Guedes P de Mendonca Maia A C LisboaD A G Vieira and R R Saldanha ldquoA unit commitmentalgorithm and a compact MILP model for short-term hydro-power generation schedulingrdquo IEEE Transactions on PowerSystems vol 32 no 5 pp 3381ndash3390 2017

[5] F Zaman S M Elsayed T Ray and R A Sarker ldquoEvo-lutionary algorithms for power generation planning withuncertain renewable energyrdquo Energy vol 112 pp 408ndash4192016

[6] M E Nazari and M M Ardehali ldquoOptimal coordination ofrenewable wind and pumped storage with thermal powergeneration for maximizing economic profit with consider-ations for environmental emission based on newly developedheuristic optimization algorithmrdquo Journal of Renewable andSustainable Energy vol 8 no 6 article 065905 2016

[7] S Hemalatha and S Chandramohan ldquoCost optimization ofpower generation systems using bat algorithm for remotehealth facilitiesrdquo Journal of Medical Imaging and Health In-formatics vol 6 no 7 pp 1646ndash1651 2016

[8] E Assareh and M Biglari ldquoA novel approach to capture themaximum power generation from wind turbines using hybridMLP neural network and bees algorithm (HNNBA)rdquo IETEJournal of Research vol 62 no 3 pp 368ndash378 2016

[9] N Nikmehr and S Najafi-Ravadanegh ldquoOptimal operation ofdistributed generations in micro-grids under uncertainties inload and renewable power generation using heuristic algo-rithmrdquo IET Renewable Power Generation vol 9 no 8pp 982ndash990 2015

[10] W Sun J Wang and H Chang ldquoForecasting annual powergeneration using a harmony search algorithm-based jointparameters optimization combination modelrdquo Energiesvol 5 no 10 pp 3948ndash3971 2012

[11] J Jasper ldquoCost optimization of power generation using adifferential evolution algorithm enhanced with neighbour-hood search operationrdquo International Review of ElectricalEngineering (IREE) vol 7 no 5 pp 5854ndash5865 2012

[12] G Ali ldquoFactors affecting public investment in manufacturingsector of Pakistanrdquo European Journal of Economic Studiesvol 13 no 3 pp 122ndash130 2015

[13] D H Husaini and H H Lean ldquoDoes electricity drive thedevelopment of manufacturing sector in Malaysiardquo Frontiersin Energy Research vol 3 p 18 2015

[14] M M Rafique and S Rehman ldquoNational energy scenario ofPakistan-current status future alternatives and institutionalinfrastructure an overviewrdquo Renewable and SustainableEnergy Reviews vol 69 pp 156ndash167 2017

[15] NEPRA State of Industry Report 2016 httpwwwnepraorgpkpublicationsstateofindustryreportsstateofindustryreport2016pdf

[16] Electricity demand surges to 22000 MWwith rise in mercuryin Dawn 2017 httpswwwdawncomnews1339210

[17] J L C Meza M B Yildirim and A S M Masud ldquoAmultiobjective evolutionary programming algorithm andits applications to power generation expansion planningrdquoIEEE Transactions on Systems Man and Cybernetics-PartA Systems and Humans vol 39 no 5 pp 1086ndash10962009

[18] M Asif ldquoSustainable energy options for Pakistanrdquo Renewableand Sustainable Energy Reviews vol 13 no 4 pp 903ndash9092009

[19] S Wasti Economic Survey of Pakistan 2014-15 Governmentof Pakistan Islamabad Pakistan 2015

[20] M Kugelman Pakistanrsquos Energy Crisis National Bureau ofAsian Research Washington DC USA 2013

[21] H Zameer and Y Wang ldquoEnergy production system opti-mization evidence from Pakistanrdquo Renewable and Sustain-able Energy Reviews vol 82 pp 886ndash893 2018

[22] B Zafar ldquoFuel Price Adjustmentrdquo httpstribunecompkstory957503fuel-price-adjustment-regulator-cuts-power-tariff-for-june-and-july

[23] X S Yang ldquoA new metaheuristic bat-inspired algorithmrdquo inNature Inspired Cooperative Strategies for Optimization(NICSO 2010) pp 65ndash74 Springer Berlin Germany 2010

[24] B Zhu W Zhu Z Liu Q Duan and L Cao ldquoA novelquantum-behaved bat algorithm with mean best positiondirected for numerical optimizationrdquo Computational in-telligence and neuroscience vol 2016 Article ID 609748417 pages 2016

[25] S Saremi S Mirjalili and A Lewis ldquoGrasshopper optimi-sation algorithm theory and applicationrdquo Advances in En-gineering Software vol 105 pp 30ndash47 2017

[26] X S Yang ldquoFirefly algorithm stochastic test functions anddesign optimisationrdquo 2010 httparxivorgabs10031409

[27] C F Chao and M H Horng ldquoe construction of supportvector machine classifier using the firefly algorithmrdquo Com-putational Intelligence and Neuroscience vol 2015 Article ID212719 8 pages 2015

[28] F Ozkaynak ldquoA novel method to improve the performance ofchaos based evolutionary algorithmsrdquo Optik vol 126 no 24pp 5434ndash5438 2015

[29] M Sulaiman A Ahmad A Khan and S MuhammadldquoHybridized symbiotic organism search algorithm for theoptimal operation of directional overcurrent relaysrdquo Com-plexity vol 2018 Article ID 4605769 11 pages 2018

[30] M Sulaiman S Muhammad and A Khan ldquoImproved solu-tions for the optimal coordination of docrs using firefly al-gorithmrdquo Complexity vol 2018 Article ID 7039790 15 pages2018

[31] S Mirjalili Waseem S MMirjalili and A Hatamlou ldquoMulti-verse optimizer a nature-inspired algorithm for global op-timizationrdquo Neural Computing and Applications vol 27no 2 pp 495ndash513 2016

[32] H Faris I Aljarah and S Mirjalili ldquoTraining feedforwardneural networks using multi-verse optimizer for binaryclassification problemsrdquo Applied Intelligence vol 45 no 2pp 322ndash332 2016

[33] C Hu Z Li T Zhou A Zhu and C Xu ldquoA multi-verseoptimizer with levy flights for numerical optimization and itsapplication in test scheduling for network-on-chiprdquo PLoSOne vol 11 no 12 Article ID e0167341 2016

[34] G I Sayed A Darwish and A E Hassanien ldquoQuantummultiverse optimization algorithm for optimization

Computational Intelligence and Neuroscience 11

problemsrdquo Neural Computing and Applications vol 28pp 1ndash18 2017

[35] M Sulaiman ldquoOptimal operation of the hybrid electricitygeneration system using multi-verse optimization algorithmrdquoMendeley Data vol 1 2019

[36] K Kiani Power cuts return as shortfall touches 7000 MW inDaily Dawn 2017 httpswwwdawncomnews1331738

[37] K Kiani Record power generation of 18900 MW achieved inDaily Dawn 2017 httpwwwdawncomnews1337054

[38] T N S S Reporter Electricity shortfall widens to 6000 MWin Dawn 2017 httpswwwdawncomnews1327624

12 Computational Intelligence and Neuroscience

Computer Games Technology

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