Page - 8 - in Short-Term Load Forecasting by Artificial Intelligent Technologies

Energies2018,11, 2226 qi= { αi1 αi2 · · · αil βi1 βi2 · · · βil } , (20) whereα2ij+β 2 ij=1; i=1,2, . . . ,N; j=1,2, . . . , l; and0≤αij≤1,0≤ βij≤1. Quantum rotation is a quantum revolving door determined by the quantum rotation angle, whichupdates thequantumsequenceandconductsarandomsearcharoundthepositionofquantum fruit flies to explore the local optimal solution. The θgij is the jth quantum rotation angle of the population iterated to the ith fruitflyofgeneration,g, andthequantumbitqgij (due to thenonnegative positionconstraintofqgij, theabsolute function,abs() isusedto take theabsolutevalueofeachelement in the calculation result) isupdatedaccording to thequantumrevolvinggateU ( θ g ij ) , as shown in Equations (21)and(22) [34,35]: qg+1ij =abs ( U ( θ g+1 ij ) ×qgij ) (21) U ( θ g ij ) = [ cosθgij −sinθ g ij sinθgij cosθ g ij ] . (22) In special cases, when the quantum rotation angle, θg+1ij , is equal to 0, the quantum bit, q g+1 ij , usesquantumnon-gateN toupdatewithsomesmallprobability,as indicated inEquation(23) [35]: qt+1ij =N×qtij= [ 0 1 1 0 ] ×qtij. (23) 2.2.3.ChaoticQuantumGlobalPerturbation Forabionicevolutionaryalgorithm, it isageneralphenomenonthat thepopulation’sdiversity wouldbepoor,alongwiththeincreasediterations. Thisphenomenonwouldalsoleadtobeingtrapped into local optimaduringmodelingprocesses. Asmentioned, the chaoticmapping functioncanbe employedtomaintain thepopulation’sdiversity toavoidtrappinginto localoptima.Manystudies haveapplied chaotic theory to improve theperformancesof thesebionic evolutionaryalgorithms, such as the artificial bee colony (ABC) algorithm [41], and theparticle swarmoptimization (PSO) algorithm[42]. Theauthorshavealso employed the cat chaoticmapping function to improve the geneticalgorithm(GA)[43], thePSOalgorithm[44],andthebatalgorithm[39], theresultsofwhich demonstrate that the searchingquality ofGA, PSO,ABC, andBAalgorithms could be improved by employing chaoticmapping functions. Hence, the cat chaoticmapping function is once again usedas theglobalchaoticperturbationstrategy(GCPS) in thispaper,andishybridizedwithQFOA, namelyCQFOA,whichhybridizesGCPSwith theQFOAwhilesufferingfromtheproblemofbeing trappedinto localoptimaduringthe iterativemodelingprocesses. The two-dimensionalcatmappingfunction isshownas inEquation(24) [39]:{ yt+1= frac ( yt+zt ) zt+1= frac ( yt+2zt ) , (24) where frac function is used to calculate the fractional parts of a real number, y, by subtracting an approachedinteger. Theglobalchaoticperturbationstrategy(GCPS) is illustratedas follows. (1) Generate2popsize chaoticdisturbance fruitflies. For eachFruit flyi (I=1, 2, . . . , 2popsize), Equation(24) isappliedtogenerated randomnumbers,zj, j=1,2, . . . ,d. Then, thequbit (with quantumstate, |0〉) amplitude, cosθij, ofFruit flyi is showninEquation(25): cosθij= yj=2zj−1. (25) 8