HindawiPublishingCorporation JournalofAppliedMathematics Volume2013,ArticleID832718, 8pages http://dx.doi.org/10.1155/2013/832718 ResearchArticle Self-Adaptive Step Firefly Algorithm Shuhao Yu,1,2Shanlin Yang,1and Shoubao Su2 1InstituteofComputerNetworkSystems,HefeiUniversityofTechnology,Hefei230009,China 2SchoolofInformationEngineering,WestAnhuiUniversity,Lu’an237012,China CorrespondenceshouldbeaddressedtoShuhaoYu;yush@wxc.edu.cn Received1July2013;Accepted17September2013 AcademicEditor:SabriArik Copyright © 2013 ShuhaoYuetal. This is an open access article distributed under the Creative Commons Attribution License, whichpermitsunrestricteduse,distribution,andreproductio ninanymedium,providedtheoriginalworkisproperlycited. Inthestandardfireflyalgorithm,eachfireflyhasthesamestepsettingsanditsvaluesdecreasefromiterationtoiteration.Therefore, it may fall into the local optimum. Furthermore, the decreasing of step is restrained by the maximum of iteration, which hasan influence on the convergence speed and precision. In order to avoid falling into the local optimum and reduce the impact of the maximum of iteration, a self-adaptive step firefly algorithm is proposed in the paper. Its core idea is setting the step of each firefly varying with the iteration, according to each firefly’s historical information and current situation. Experiments aremade to show the performance of our approach compared with the standard FA, based on sixteen standard testing benchmark functions. The results reveal that our method can prevent the premature convergence and improve the convergence speed and accurateness. 1. Introduction Firefly algorithm (FA) is inspired by biochemical and social aspects of real fireflies [ 1] .I tc o u l dh a n d l em u l - timodal problems of combinational and numerical opti-mization more naturally and efficiently [ 2–5]. Owing to its few parameters to adjust, easy to understand, realize, andcompute, it was applied to various fields, such as code-book of vector quantization [ 6],in-linespring-masssystems [7], mixed variable structural optimization [ 8], nonlinear grayscale image enhancement [ 9], travelling salesman prob- lems[10], continuouslycast steel slabs [ 11],promotingprod- uctsonline[ 12],nonconvexeconomicdispatchproblems[ 13], chiller loading for energy conservation [ 14], stock market price forecasting [ 15], and multiple objectives optimization [16]. Despite these advantages, the FA is also a metaheuristic algorithm; the standard FA can easily get trapped in thelocal optima when solving complex multimodal problems.These weaknesses have restricted wider applications of theFA. Therefore, avoiding the local optima and acceleratingconvergence speed have become the two most importanta n da p p e a l i n gg o a l si nt h eF Ar e s e a r c h .T oo v e r c o m et h e s edisadvantages, many researchers have proposed a variety ofmodificationstotheoriginalFA[ 17–19].Compared with other evolutionary algorithms, such as Genetic Algorithm and Simulated Annealing, standard FAh a st h ef o l l o w i n gp r o b l e m :i ti sn o tr a t i o n a lt h a te a c hfirefly uses the same step or the linear step just dependson maximum iteration not related to experience of fireflies,which may impact on the balance between the global andlocalsearch.Basedontheaboveproblem,aself-adaptivestepfirefly algorithm (SASFA) is proposed in the paper, whichconsiders thehistoricalinformationandcurrentsituationofeachfirefly. The rest of this paper is organized as follows. Section2 s h o w sab r i e fr e v i e wo ft h eu p d a t i n gp r o c e s so ft h es t a n -dard FA and analyzes some problems about the linear stepapproach. In Section3, a novel approach is proposed to set the step of each firefly self-adaptively. In Section4, experimental settings and results compared with the twoalgorithmsarepresented.Finally,wemaketheconclusionsinSection5. 2. Firefly Algorithm Concepts Firefly algorithm is based on the idealized behavior of the flashing feature of