Page - 7 - in Short-Term Load Forecasting by Artificial Intelligent Technologies

Energies2018,11, 2226 It isnoticed that thereare somesignificantdifferencesbetween theFOAandPSOalgorithms. For FOA, the taste concentration (S) is used todetermine the individual position of each fruit fly, andthehighestodorconcentration in thispopulation is retainedalongwith thexandycoordinates; eventually, theDrosophilapopulationusesvisiontoflyto thisposition. Therefore, it isbasedonthe taste concentration tocontrol the searchingdirection tofindout theoptimal solution. For thePSO algorithm, the inertiaweightcontrols the impactof thepreviousvelocityof theparticleon itscurrent onebyusingtwopositiveconstantscalledaccelerationcoefficientsandtwoindependentuniformly distributedrandomvariables. Therefore, it isbasedonthe inertiaweight tocontrol thevelocity tofind out theoptimalsolution. Thus, aiming to deal with the inherent drawback of FOA, i.e., suffering from premature convergenceortrappinginto localoptimaeasily, thispapertries tousetheQCMtoempowereachfruit flytopossessquantumbehavior (namelyQFOA)duringthemodelingprocesses.At thesametime, thecatmappingfunction is introducedintoQFOA(namelyCQFOA)to implement thechaoticglobal perturbationstrategytohelpafruitflyescapefromthe localoptimawhenthepopulation’sdiversity is poor. Eventually, theproposedCQFOAisemployedtodeterminetheappropriateparametersofan LS-SVRmodelandincrease the forecastingaccuracy. 2.2.2.QuantumComputingMechanismforFOA (1) QuantizationofFruitFlies In the quantum computing process, a sequence consisting of quantumbits is replaced by a traditional sequence. Thequantumfruitfly isa linearcombinationofstate |0〉andstate |1〉,whichcan beexpressedas inEquation(17) [34,35]: |ϕ〉= α|0〉+ β|1〉, (17) whereα2 andβ2 are theprobabilityofstates, |0〉and |1〉, respectively, satisfyingα2+β2=1,and(α,β) arequbitscomposedofquantumbits. Aquantumsequence, i.e., a feasible solution, canbeexpressedasanarrangementof lqubits, asshowninEquation(18) [34,35]: qi= { α1 α2 · · · αl β1 β2 · · · βl } , (18) where the initial values of αj and βj are all set as 1/ √ 2 tomeet the equity principle, α2j +β 2 j = 1 (j=1,2, . . . , l),which isupdatedthroughthequantumrevolvingdoorduringthe iteration. Conversionbetweenquantumsequenceandbinarysequence is thekeytoconvertFOAtoQFOA. Randomlygeneratearandomnumberof [0,1], randj, if randj≥α2j , thecorrespondingbinaryquantum bitvalue is1,otherwise,0,asshowninEquation(19): xj= { 1 randj≥α2j 0 else . (19) Usingtheabovemethod, thequantumsequence,q, canbe transformedintoabinarysequence,x; thentheoptimalparameterproblemofanLS-SVRmodelcanbedeterminedusingQFOA. (2) QuantumFruitFlyPositionUpdateStrategy In theQFOAprocess, thepositionofquantumfruitflies representedbyaquantumsequence is updatedtofindmore feasiblesolutionsandthebestparameters. Thispaperusesquantumrotation to update thepositionofquantumfruitflies. Thequantumpositionof individual i (thereare in totalN quantumfruitflies) canbeextendedfromEquation(18)andisexpressedas inEquation(20): 7