Page - 14 - in Short-Term Load Forecasting by Artificial Intelligent Technologies

Energies2018,11, 2226 IfW is smaller than or equal to the critical value, based on theWilcoxondistributionunder ndegrees of freedom, then the null hypothesis (i.e., equal performance from the two compared forecastingmodels) couldnotbeaccepted, i.e., theproposedmodelachievessignificance. 3.3. TheForecastingResults of theLS-SVR-CQFOAModel 3.3.1. ParameterSettingof theCQFOAAlgorithm Theparametersof theproposedCQFOAalgorithmfor thenumericalexamplearesetas follows: thepopulationsize,popsize, is set to200; themaximal iteration,gen-max, is set to1000;andthecontrol coefficientofchaoticdisturbance,NGCP, is set to15. These twoparametersof theLS-SVRmodelareset as,γ∈ [0,1000], andσ∈ [0,500], respectively. The iterative timeofeachalgorithmissetas thesame toensure thereliabilityof the forecastingresults. 3.3.2. ResultsandAnalysis Considering the CQPSO, CQTS, and CQGA algorithms have been used to determine the parameters of an SVR-based load forecastingmodel in [36–39], those existing algorithms are also hybridizedwith an LS-SVRmodel to provide forecasting values to comparewith the proposed modelhere. Thesealternativemodels includeLS-SVR-FOA,LS-SVR-QFOA,LS-SVR-CQPSO(LS-SVR hybridizedwithchaoticquantumparticleswarmoptimizationalgorithm[36]),LS-SVR-CQTS(LS-SVR hybridizedwithchaoticquantumTabusearchalgorithm[37]),LS-SVR-CQGA(LS-SVRhybridized withchaoticquantumgeneticalgorithm[38]), andLS-SVR-CQBA(LS-SVRhybridizedwithchaotic quantumbatalgorithm[39]), inordertocomparetheforecastingperformanceofLS-SVR-basedmodels comprehensively, thisarticlealsoselectsBPNNmethodasacontrastmodel. Theparametersofan LS-SVRmodelareselectedbytheCQPSO,CQTS,CQGA,CQBA,FOA,QFOA,andCQFOAalgorithms, respectively. Thedetailsof thesuitableparametersofallmodels for the IDAS2014, theGEFCom2014 (Jan.) andtheGEFCom2014(July)dataareshowninTables4–6, respectively. Table 4. LS-SVR parameters, MAPE, and computing times of CQFOA and other algorithms for IDAS2014. OptimizationAlgorithms LS-SVRParameters MAPEofValidation(%) ComputingTimes(s) γ σ LS-SVR-CQPSO[36] 685 125 1.17 129 LS-SVR-CQTS[37] 357 118 1.13 113 LS-SVR-CQGA[38] 623 137 1.11 152 LS-SVR-CQBA[39] 469 116 1.07 227 LS-SVR-FOA 581 109 1.29 87 LS-SVR-QFOA 638 124 1.32 202 LS-SVR-CQFOA, 734 104 1.02 136 Table 5. Parameters combination of LS-SVR determined by CQFOA and other algorithms for GEFCom2014(Jan.). OptimizationAlgorithms Parameters MAPEofValidation(%) ComputationTimes(s) γ σ LS-SVR-CQPSO[36] 574 87 0.98 134 LS-SVR-CQTS[37] 426 68 1.02 109 LS-SVR-CQGA[38] 653 98 0.95 155 LS-SVR-CQBA[39] 501 82 0.9 231 LS-SVR-FOA 482 94 1.54 82 LS-SVR-QFOA 387 79 1.13 205 LS-SVR-CQFOA, 688 88 0.86 132 14