Page - 24 - in Short-Term Load Forecasting by Artificial Intelligent Technologies

Energies2018,11, 1009 Lotsofelectric loadforecastingmodelshavebeenproposedtocontinue improvingforecasting performances. These forecastingmodelscanbeof twotypes, thefirstone isbasedonthestatistical methodology,andtheotheroneinvolvesapplicationsofartificial intelligencetechnology.Thestatistical models, which include theARIMAmodels [6,7], regressionmodels [8,9], exponential smoothing models [10], Kalman filteringmodels [11,12], Bayesian estimationmodels [13,14], and so on use historicaldatatofindoutthelinearrelationshipsamongtimeperiods.However,duetotheirtheoretical definitions, thesestatisticalmodelscanonlydealwellwith linearrelationshipsamongelectric loads andtheother factorsmentionedabove. Therefore, thesemodelscouldonlyproduceunsatisfactory forecastingperformances [15]. Due to its superiornonlinearprocessing capability, artificial intelligence technologymethods suchasartificialneuralnetworks (ANNs) [16,17], expert systemmodels [18,19], andfuzzy inference systems [20,21] havebeenwidely applied to improve theperformanceof electric load forecasting. To overcome the inherent shortcomings of these artificial intelligent models, hybrid models (hybridizing two artificial intelligentmodelswith each other) and combinedmodels (combining twomodelswitheachother)havebeen the researchhotspots recently. Forexample,hybridizedor combinedwitheachothermodels [22]andwithevolutionaryalgorithms[23].However, theseartificial intelligencemodels (includinghybridorcombinedmodels)alsohaveshortcomings themselves, such asbeing timeconsuming,difficult todeterminestructuralparameters, andtrapping into localminima. Readersmayrefer to [24] formorediscussionsregarding loadforecasting. With outstanding nonlinear processing capability, composed of high dimensional mapping ability and kernel computing technology, the support vector regression (SVR)model [25–27] has alreadyproducedsuperiorabundantapplicationresults inmanyfields. Theapplicationexperience demonstrates that an SVRmodelwithwell-computedparameters by any evolutionary algorithm could provide significant satisfactory forecasting performance, and overcome the shortcomings of evolutionary algorithms to compute appropriate parameters. For applications in electric load forecasting, Hong and his successors [28,29] have used two types of chaoticmapping functions (i.e., logistic functionandcatmappingfunction) tokeepthediversityofpopulationduringthesearch process toavoidtrapping into localoptima, tosignificantly improvethe forecastingaccuracy level. Thecuckoosearch(CS)algorithm[30] isanovelmeta-heuristicoptimizationalgorithminspired by the brood reproductive strategyof cuckoobirds via an interestingbroodparasiticmechanism, i.e.,mimickingthepatternandcolorof thehost’seggs, throwingtheeggsoutornot,orbuildinganew nest, etc. In [31], theauthorsdemonstrate that, byapplyingvarious test functions, it is superior to otheralgorithms, suchasgenetic algorithm(GA),differential evolution (DE), simulatedannealing (SA)algorithm,andparticleswarmoptimization(PSO)algorithminsearchingforaglobaloptimum. Nowadays, theCSalgorithmiswidelyapplied inengineeringapplications, suchasunitmaintenance scheduling [32], data clusteringoptimization [33],medical image recognition [34],manufacturing engineeringoptimization[35],andsoftwarecostestimation[36], etc.However,asmentionedin[37], the original CS algorithmhas some inherent limitations, such as its initialization settings of the host nest location, Lévyflight parameter, and boundary handling problem. In addition, because it is a population-basedoptimization algorithm, the originalCS algorithmalso suffers fromslow convergencerate in the latersearchingperiod,homogeneoussearchingbehaviors (lowdiversityof population),andaprematureconvergence tendency[33,38,39]. Dueto itseasy implementationandability toenrichthecuckoosearchspaceanddiversify the population to avoid trapping into local optima, thispaperwould like to applya chaoticmapping functiontoovercomethecoreshortcomingsof theoriginalCSalgorithm, toproducemoreaccurate electric load forecasting results. Thus, a tent chaoticmapping function, demonstrating a rangeof dynamicalbehaviorrangingfrompredictable tochaos, ishybridizedwithaCSalgorithmtodetermine threeparametersofanSVRmodel.Anewelectric loadforecastingmodel,obtainedbyhybridizing atentchaoticmappingfunctionandCSalgorithmwithanSVRmodel,namely theSVRwithchaotic cuckoo search (SVRCCS)model, is thus proposed. In themeanwhile, asmentioned in existing 24