Seite - 358 - in Short-Term Load Forecasting by Artificial Intelligent Technologies

Energies2018,11, 1253 where f(ψm) and f ( ψf ) represent the values of lion and lioness, respectively; f ( ψm_cubk ) and f ( ψ f_cub k ) equals thevaluesofmalecubandfemalecub, respectively;‖ψm_cub‖means thenumberof malecubs; agemat isemployedtodesignate the timerequiredformating. Step4: Territorial takeover In this step, theoptimalsolutionsamongthe lionandlionessare foundtoreplace the inferiorone. Matingwillnotenduntil the terminatingconditionsarereached. Thebest lionψmbest andlionessψ f best aredeterminedaccordingto the followingcriteria: f(ψmbest)< f ( ψmpride ) ,ψmbest =ψmpride,ψmpride= { ψm,ψm_cub } (3) f ( ψ f best ) < f ( ψ f pride ) ,ψfbest =ψ f pride,ψ f pride= { ψf ,ψf_cub } (4) Inthepseudocode,κ representsthenumberofbreedingandκstrenthdescribesthefemale’soptimal breedingability,generallyset to5. κstrenth is setas0at the timeof initialpridegeneration,andshould be incremented. If the female lion is replaced,κhas tobestartedfrom0.Ontheotherhand, if theold lionesscontinuallyexisted,κ shouldbeaccumulated.Whenthepreviousstepsarecompleted,goback toStep2until the terminationcondition issatisfied. Thebest lionresponds to theoptimalsolution. 2.1.2. LAImprovedbyNicheImmune LA is a parallel combination of self-adaption, group search and a heuristic random search, while inbreedingappearsamongthe lionswith largefitnessduringthe iterativeprocess, resulting in prematureconvergenceanddiversityreduction.Niche immunity isexploited in thispaper torestrict overduplicationofsimilar individuals, soas toensure thediversityofpopulation. Thedetailedsteps ofNIalgorithmaredisplayedin[23]. LAoptimizedbyNIcanbeperformedas follow: Step1:Accordingto thevalueofobjective function,M clonedlionscanbeobtained in thecenter of the locationataspecifiediteration interval. Mj=Mmax×(1− ρj N ∑ j=1 ρj ) (5) whereMj is theclonenumberof the j-th lion,Mmax represents themaximumclonenumber that is set to40here. ρj is theobjective functionvalueof the j-th lion. Step2:M lionsaremutatedbysingleparentafterclone. For the lionwith lowobjective function value,mutation iscarriedoutbytheparthenogenetic lions,asgiven inEquations (6)and(7). xi+1= xi+r×randn(1) (6) r= 2×Pmax N (7) where xi represents the lion, xi+1 is the offspring generation after parthenogenesis, Pmax is the maximumvalueof lion location,N equals thenumberof lions. Step3: Make comparisonamong theMmutated lions and select theonewith themaximum objective functionvalueas thenewlion. 2.2. ConvolutionalNeuralNetwork (CNN) AsakindofANNwithdeeplearningability, theCNNachieves local connectionsandshares the weightsofneurons in thesamelayer [24]. Thenetworkconsistsof1~3featureextraction layersand fullyconnected layers. Eachfeatureextraction layer includesaconvolutionaloneandasubsampling one. ThestructureofCNNcontainingafeatureextraction layer is showninFigure2. 358