Page - 339 - in Short-Term Load Forecasting by Artificial Intelligent Technologies

Energies2018,11, 1282 Rt+1=R0(i)·(1−e−θt) (6) whereγandθarebothconstants thatγ iswithin [0,1]andθ>0. Thispaperset the twoparameters asγ=θ=0.9.Thebasicstepsof thestandardbatalgorithmcanbesummarizedas thepseudocode seen in the following: Batalgorithm. 1: Initialize the locationofbatpopulationsxi (i=1,2,3, . . . ,n)andvelocityvi 2: Initialize frequencyFi pulseemissionrateRi andloudnessAi 3:While (t< themaximumnumberof iterations) 4: Generatenewsolutionsbyadjustingthe frequency 5: Generatenewvelocityandlocation 6: If (rand>Ri) 7: Selectasolutionamongbest solutions 8: Generatenewlocal solutionaroundtheselectedbest solution 9: Endif 10: Getanewsolutionthroughflyingrandomly 11: If (rand<Ai&f(xi)< f(x*)) 12: Accept thenewsolution 13: IncreaserianddecreaseAi 14: Endif 15: Rankthebatsandfindthecurrentbestx*. 16: End 2.2. ExtremeLearningMachine After setting the inputweights andhidden layer biases randomly, the outputweights of the ELMcanbeanalyticallydeterminedbysolvinga linearsysteminaccordancewith the thinkingof the Moore–Penrose (MP)generalized inverse. Theonly twoparametersneededtobeassignedallowthe extremelearningmachine togenerate the inputweightsmatrixandhiddenlayerbiasesautomatically at fast runningspeed.Consequently, theextremelearningmachineexpresses theadvantagesofa fast learningspeed,small trainingerrorandstronggeneralizationabilitycomparedwiththe traditional neuralnetworks insolvingnon-linearityproblems[27]. Theconcrete frameworkofELMisshownin Figure1andthecomputational stepsof thestandardELMcanbe illustratedas follows: ,QSXW OD\HU +LGGHQ OD\HU 2XWSXW OD\HU 噯 噯 噯 Figure1.Theframeworkof theextremelearningmachine. Theconnectionweightsbothbetweeninput layerandhiddenlayerandbetweenhiddenlayer andoutput layeraswellas thehiddenlayerneuronthresholdareshowninthe following: ω=[ωi1,ωi2, · · · ,ωin]L×n (7) 339