Page - 17 - in Short-Term Load Forecasting by Artificial Intelligent Technologies

Energies2018,11, 2226 accuracy indexes than the other sevenmodels: RMSE (38.70), MAPE (1.01%), andMAE (37.48), respectively. Thedetailsof theanalysis resultsareas follows. Table7.Forecasting indexesofLS-SVR-CQFOAandothermodels for IDAS2014. ComparedModels RMSE MAPE(%) MAE BPNN 24.89 3.92 24.55 LS-SVR-CQPSO[36] 14.40 2.27 14.21 LS-SVR-CQTS[37] 14.50 2.26 14.24 LS-SVR-CQGA[38] 14.41 2.24 14.13 LS-SVR-CQBA[39] 14.45 2.25 14.18 LS-SVR-FOA 15.90 2.48 15.62 LS-SVR-QFOA 15.03 2.32 14.69 LS-SVR-CQFOA 14.10 2.21 13.88 Table8.Forecasting indexesofLS-SVR-CQFOAandothermodels forGEFCom2014(Jan.). ComparedModels RMSE MAPE(%) MAE BPNN 92.30 2.34 90.74 LS-SVR-CQPSO[36] 51.46 1.31 50.69 LS-SVR-CQTS[37] 50.85 1.27 49.70 LS-SVR-CQGA[38] 46.36 1.16 45.31 LS-SVR-CQBA[39] 42.76 1.07 41.80 LS-SVR-FOA 75.55 1.89 73.88 LS-SVR-QFOA 59.74 1.47 57.96 LS-SVR-CQFOA 40.62 1.02 39.76 Table9.Forecasting indexesofLS-SVR-CQFOAandothermodels forGEFCom2014(July). ComparedModels RMSE MAPE(%) MAE BPNN 88.24 2.31 85.51 LS-SVR-CQPSO[36] 51.03 1.33 49.35 LS-SVR-CQTS[37] 45.73 1.22 44.68 LS-SVR-CQGA[38] 46.18 1.19 44.46 LS-SVR-CQBA[39] 40.75 1.09 39.85 LS-SVR-FOA 72.00 1.88 69.69 LS-SVR-QFOA 56.33 1.49 54.81 LS-SVR-CQFOA 38.70 1.01 37.48 Finally, to test thesignificance in termsof forecastingaccuracy improvements fromtheproposed LS-SVR-CQFOAmodel, theWilcoxon signed-rank test is conductedunder two significant levels, α=0.025andα=0.05, byone-tail test. The test results for the IDAS2014, theGEFCom2014 (Jan.), and the GEFCom2014 (July) datasets are described in Tables 10–12, respectively. In these three tables, theresultsdemonstrate that theproposedLS-SVR-CQFOAmodelachievedsignificantlybetter forecastingperformance than theotheralternativemodels. Forexample, in the IDAS2014dataset, forLS-SVR-CQFOAvs. LS-SVR-CQPSO, the statistic ofWilcoxon test,W=72, is smaller than the critical statistics,W**=81 (underα=0.025)andW*=91 (underα=0.05), thuswecouldconclude that the proposedLS-SVR-CQFOAmodel is significantly outperform the LS-SVR-CQPSOmodel. Inaddition, thep-value=0.022 isalsosmaller thanthecriticalα=0.025andα=0.05,whichsupport theconclusion. 17