Page - 29 - in Short-Term Load Forecasting by Artificial Intelligent Technologies

Energies2018,11, 1009 nests. Let i=0,andnormalize theparametersaschaoticvariables, cx(i)k,j,within the interval [0,1]by Equation(12): cx(i)k,j = x(i)k,j−Mink Maxk−Mink (12) whereMink andMaxk are theminimaandthemaximaof the threeparameters, respectively. Step2:ChaoticMappingandTransferring. Apply the tentchaoticmappingfunction,definedasEquation(8), toobtain thenext iterationof chaoticvariables, cx(i+1)k,j , as showninEquation(13): cx(i+1)k,j = { 2cx(i)k,j cx(i)k,j ∈ [0,0.5] 2 ( 1−cx(i)k,j ) cx(i)k,j ∈ (0.5,1] (13) Then, transform cx(i+1)k,j toobtain threeparameters for thenext iteration,x (i+1) k,j , by the following Equation(14): x(i+1)k,j =Mink+cx (i+1) k,j (Maxk−Mink) (14) Step3: FitnessEvaluation. Evaluate thefitnessvaluewithx(i+1)k,j forallnests tofindout thebestnestposition,x (i+1) k,best, in terms of smaller forecastingaccuracy indexvalue. In thispaper, the forecastingerror is calculatedas the fitnessvaluebythemeanabsolutepercentageerror (MAPE),asshowninEquation(15): MAPE= 1 N N ∑ i=1 ∣∣∣∣ai− fiai ∣∣∣∣×100% (15) whereN is the totalnumberofdata; ai is theactualelectric loadvalueatpoint i; fi is the forecasted electric loadvalueatpoint i. Step4:CuckooGlobalSearch. Implementacuckooglobal search, i.e.,Equation(10),byusingthebestnestposition,x(i+1)k,best, and update other nest positions byLévyflightdistribution (Equation (11)) to obtain anewset of nest positions, then, compute thefitnessvalue. Step5:DetermineNewNestPosition. Compare the fitness value of the new nest positionswith the fitness value of the previous iteration, andupdate thenestpositionwithabetterone. Thendetermine thenewnestpositionas x(t)k,j = [ x(t)k,1,x (t) k,2, . . . ,x (t) k,n ]T . Step6:CuckooLocalSearch. If pa is lower than to a randomnumber r, then turn to discover the nests in x (t) k,j with lower probability instead of the higher one. Then, compute the fitting value of the new nests and continueupdatingthenestpositionx(t)k,j withsmallerMAPEvaluebycomparing itwith theprevious fitnessvalue. Step7:DetermineTheBestNestPosition. Compare thefitnessvalueof thenewnestposition,x(t)k,j , inStep6,with thefitnessvalueof the bestnestposition,x(i+1)k,best. If thefitnessvalueofx (t) k,j is lower thantheoneofx (i+1) k,best, then,updatex (t) k,j as thebestnestposition,x(t)k,best. 29