Ageneticalgorithmapproachforthe time-costtrade-offinPERTnetworks AmirAzaron * ,CahitPerkgoz,MasatoshiSakawa Department of Artificial Complex Systems Engineering, Graduate School of Engineering, Hiroshima University, Kagamiyama 1-4-1, Higashi-Hiroshima, Hiroshima 739-8527, Japan Abstract Wedevelopamulti-objectivemodelforthetime-costtrade-offprobleminPERTnet- workswithgeneralizedErlangdistributionsofactivitydurations,usingageneticalgo- rithm.Themeandurationofeachactivityisassumedtobeanon-increasingfunction andthedirectcostofeachactivityisassumedtobeanon-decreasingfunctionofthe amountofresourceallocatedtoit.Thedecisionvariablesofthemodelaretheallocated resource quantities. The problem is formulated as a multi-objective optimal control problemthatinvolvesfourconflictingobjectivefunctions.Theobjectivefunctionsare the project direct cost (to be minimized), the mean of the project completion time (min),thevarianceoftheprojectcompletiontime(min),andtheprobabilitythatthe projectcompletiontimedoesnotexceedacertainthreshold(max).Itisimpossibleto solvethisproblemoptimally.Therefore,weapplya‘‘GeneticAlgorithmforNumerical Optimizations of Constrained Problems’’ (GENOCOP) to solve this multi-objective problemusingagoalattainmenttechnique.Severalfactorialexperimentsareperformed toidentifyappropriategeneticalgorithmparametersthatproducethebestresultswithin agivenexecutiontimeinthethreetypicalcaseswithdifferentconfigurations.Finally,we comparethegeneticalgorithmresultsagainsttheresultsofadiscrete-timeapproxima- tionmethodforsolvingtheoriginaloptimalcontrolproblem. Ó 2004 Elsevier Inc. All rights reserved. 0096-3003/$-seefrontmatter Ó 2004ElsevierInc.Allrightsreserved. doi:10.1016/j.amc.2004.10.021 * Correspondingauthor. E-mail address: azaron@msl.sys.hiroshima-u.ac.jp (A.Azaron). AppliedMathematicsandComputation168(2005)1317–1339 www.elsevier.com/locate/amc