Page - 326 - in Short-Term Load Forecasting by Artificial Intelligent Technologies

Energies2018,11, 1449 Environment exploration Perceive the smell of prey Autonomous decisions of wolves Movement Perceive the information of the wolf pack The scout wolf The ferocious wolf The leader wolf Prey Perceive the informatio n of partners Figure5.BionicgraphofWPA. TheprincipleandstepsofWPAaresummarizedas follows[36]: (1) Initializewolfpack. Suppose inDdimensionalspace, thereareNwolves,whereinthe location of the i-thwolf is setas: Xi=(xi1,xi2,...,xid), 1≤ i≤N, 1≤ d≤D (17) The initialposition isgeneratedasEquation(18): xid= xmin+rand×(xmax−xmin) (18) where rand represents randomnumberswithin therange[0,1], andxmax andxmin are theupper limit andlower limitof thesearchspace, respectively. (2)Generate theheadwolf. ThewolfatYleadwiththebest target function isselectedas thehead one. Theheadwolf does not update its position in thehuntingprocess or participate inhunting; instead, it isdirectly iterated. IfYlead<Yi,Ylead=Yi,whereYi represents the locationof thesafariwolf i. Otherwise, thesafariwolf i randomlywalks inhdirectionsuntil themaximumvalueH isachieved or the locationcannotbe furtheroptimized; thenthesearch is stopped. yijd is the locationat j-thpoint ind-thdimensionof the i-thwolf. yijd= yid+rand×stepa (19) (3)Keepclose to theprey. Theheadwolfpushes thewolfpack toupdate theirpositions through call toaction. Thenewpositionof the i-thwolf ind-dimension isdescribedasEquation(20): zid= xid+rand×stepb×(xid−xlid) (20) where stepa is the step length of wolves in search, stepb represents the step length of wolves towards the target, xid and xlid are the location of the i-thwolf and the correspondingheadwolf ind-dimension, respectively. (4)Encircle theprey. Theheadwolf sends signals to the surroundingwolfpackafterfinding thepreysothat theencirclementandsuppressionof the targetpreycanbecompleted,asshownin Equations (21)and(22): Xt+1i = { Xti, rm< θ Xi+rand×ra, rm> θ (21) ra(t)= ramin×(xmax−xmin)×e ln(ramin/ramax) maxt (22) where tequalsthenumberofiterations,ra isthesteplengthatthetimeofencirclementandsuppression, Xi is the locationof theheadwolf thatsends thesignal,andXti is the locationof the i-thwolf in the t-th iteration. 326