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energies Article HybridizingChaoticandQuantumMechanismsand FruitFlyOptimizationAlgorithmwithLeastSquares SupportVectorRegressionModel inElectric LoadForecasting Ming-WeiLi 1, JingGeng1,Wei-ChiangHong2,* ID andYangZhang1 1 Collegeofshipbuildingengineering,HarbinEngineeringUniversity,Harbin150001,Heilongjiang,China; limingwei@hrbeu.edu.cn(M.-W.L.);gengjing@hrbeu.edu.cn(J.G.); zhangyang@hrbeu.edu.cn(Y.Z.) 2 SchoolofEducationIntelligentTechnology, JiangsuNormalUniversity/No. 101,ShanghaiRd., TongshanDistrict,Xuzhou221116, Jiangsu,China * Correspondence: samuelsonhong@gmail.com;Tel.:+86-516-83500307 Received: 13August2018;Accepted: 22August2018;Published: 24August2018 Abstract:Comparedwitha largepowergrid,amicrogridelectric load(MEL)has thecharacteristics ofstrongnonlinearity,multiple factors,andlargefluctuation,whichleadtoitbeingdifficult toreceive moreaccurate forecastingperformances. Tosolve theabovementionedcharacteristicsofaMELtime series, the least squaressupportvectormachine (LS-SVR)hybridizingwithmeta-heuristicalgorithms is applied to simulate thenonlinear systemofaMELtimeseries. As it isknownthat the fruitfly optimizationalgorithm(FOA)hasseveralembeddeddrawbacks that leadtoproblems, thispaper applies aquantumcomputingmechanism(QCM) toempowereach fruitfly topossessquantum behaviorduring thesearchingprocesses, i.e., aQFOAalgorithm.Eventually, thecat chaoticmapping function is introducedinto theQFOAalgorithm,namelyCQFOA, to implement thechaoticglobal perturbationstrategytohelpfruitfliestoescapefromthelocaloptimawhilethepopulation’sdiversity ispoor. Finally,anewMELforecastingmethod,namely theLS-SVR-CQFOAmodel, isestablished byhybridizing theLS-SVRmodelwithCQFOA.Theexperimental results illustrate that, in three datasets, theproposedLS-SVR-CQFOAmodel is superior toother alternativemodels, including BPNN(back-propagationneuralnetworks),LS-SVR-CQPSO(LS-SVRwithchaoticquantumparticle swarmoptimizationalgorithm),LS-SVR-CQTS(LS-SVRwithchaoticquantumtabusearchalgorithm), LS-SVR-CQGA(LS-SVRwith chaotic quantumgenetic algorithm), LS-SVR-CQBA(LS-SVRwith chaoticquantumbatalgorithm),LS-SVR-FOA,andLS-SVR-QFOAmodels, in termsof forecasting accuracy indexes. Inaddition, itpasses thesignificance testata97.5%confidence level. Keywords: least squares support vector regression (LS-SVR); chaos theory; quantumcomputing mechanism(QCM); fruitflyoptimizationalgorithm(FOA);microgridelectric loadforecasting (MEL) 1. Introduction 1.1.Motivation MELforecasting is thebasisofmicrogridoperationschedulingandenergymanagement. It is an important prerequisite for the intelligentmanagement of distributed energy. The forecasting performancewoulddirectlyaffect themicrogrid system’s energy trading,power supplyplanning, andpower supply quality. However, theMEL forecasting accuracy is not only influencedby the mathematicalmodel,butalsobytheassociatedhistoricaldataset. Inaddition,comparedwiththe large powergrid,microgridelectric load(MEL)hasthecharacteristicsofstrongnonlinearity,multiplefactors, andlargefluctuation,whichleadtoitbeingdifficult toachievemoreaccurateforecastingperformances. Alongwith the development of artificial intelligent technologies, load forecastingmethods have Energies2018,11, 2226;doi:10.3390/en11092226 www.mdpi.com/journal/energies1