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1、EuropeanJournalofOperationalResearch185(2008)1155–1173www.elsevier.com/locate/ejorAntcolonyoptimizationforcontinuousdomainsKrzysztofSocha*,MarcoDorigo1IRIDIA,Universite´LibredeBruxelles,CP194/6,Ave.FranklinD.Roosevelt50,1050Brussels,BelgiumReceived1August2005;accepted1June2006Availableonline3Novembe
2、r2006AbstractInthispaperwepresentanextensionofantcolonyoptimization(ACO)tocontinuousdomains.WeshowhowACO,whichwasinitiallydevelopedtobeametaheuristicforcombinatorialoptimization,canbeadaptedtocontinuousoptimi-zationwithoutanymajorconceptualchangetoitsstructure.Wepresentthegeneralidea,implementation,
3、andresultsobtained.Wecomparetheresultswiththosereportedintheliteratureforothercontinuousoptimizationmethods:otherant-relatedapproachesandothermetaheuristicsinitiallydevelopedforcombinatorialoptimizationandlateradaptedtohandlethecontinuouscase.WediscusshowourextendedACOcomparestothosealgorithms,andwe
4、presentsomeanalysisofitsefficiencyandrobustness.Ó2006ElsevierB.V.Allrightsreserved.Keywords:Antcolonyoptimization;Continuousoptimization;Metaheuristics1.Introductiontofindapproximatesolutions(i.e.,solutionsthataregood,butnotprovablyoptimal)inareasonableOptimizationalgorithmsinspiredbytheants’amountofti
5、me.foragingbehavior(Dorigo,1992)havebeeninitiallyCombinatorialoptimization—asthenamesug-proposedforsolvingcombinatorialoptimizationgests—dealswithfindingoptimalcombinationsorproblems(COPs).ExamplesofCOPsincludesched-permutationsofavailableproblemcomponents.uling,vehiclerouting,timetabling,andsoon.Man
6、yHence,itisrequiredthattheproblemispartitionedoftheseproblems,especiallythoseofpracticalrele-intoafinitesetofcomponents,andthecombinato-vance,areNP-hard.Inotherwords,itisstronglyrialoptimizationalgorithmattemptstofindtheirbelievedthatitisnotpossibletofindefficient(i.e.,optimalcombinationorpermutation.Man
7、yreal-polynomialtime)algorithmstosolvethemopti-worldoptimizationproblemsmayberepresentedmally.Usuallytheseproblemsaretackledwithheu-asCOPsinastraightforwardway.Thereexistshow-risticmethods(i.e.,notexa
