Constraints, 6, 399–422, 2001 © 2001 Kluwer Academic Publishers. Manufactured in The Netherlands. Keep-Best Reproduction: A Local Family Competition Selection Strategy and the Environment it Flourishes in KAYC.WIESE kay.wiese@techbc.ca Technical University of British Columbia—TechBC, 2400 Surrey Place, 10153 King George Highway, Surrey, B.C., Canada, V3T 2W1 SCOTTD.GOODWIN goodwin@cs.uregina.ca Department of Computer Science, University of Regina, 3737 Wascana Parkway, Regina, Saskatchewan, Canada, S4S 0A2 Abstract. Thispaperpresentsacomparisonoftwogeneticalgorithms(GAs)forconstrainedorderingprob- lems.ThefirstGAusesthestandardselectionstrategyofroulettewheelselectionandgenerationalreplacement (STDS), while the second GA uses an intermediate selection strategy in addition to STDS. This intermediate selectionstrategykeepsonlythesuperioroffspringandreplacestheinferioroffspringwiththesuperiorparent. We call this selection strategy Keep-Best Reproduction (KBR). The effect of recombination alone, mutation alone and both together are studied. We compare the performance of the different selection strategies and discuss the environment that each selection strategy needs to flourish in. Overall, KBR is found to be the selection strategy of choice. We also present empirical evidence that suggests that KBR is more robust than STDS with regard to operator probabilities and works well with smaller population sizes. Keywords: evolutionary computing, genetic algorithms, search, selection strategies, constrained ordering problems 1. Introduction Many problems in artificial intelligence and simulation can be described in a general frameworkasa constraint satisfaction problem (CSP)ora constraint optimization prob- lem (COP).Informally,aCSP(initsfinitedomainformulation)isaproblemcomposed ofafinitesetof variables,eachofwhichhasafinite domain,andasetof constraints that restrict the values that the variables can simultaneously take. Traditional methods for solving CSPs can be divided into three categories: problem reduction, search, and solution synthesis. For many problem domains, however, not all solutions to a CSP are equallygood.Forexample,inthecaseof job shop scheduling differentscheduleswhich all satisfy the resource and capacity constraints can have different makespans (the total time to complete all orders), or different inventory requirements. So, in addition to the standard CSP, a constraint optimization problem has a so-called objective function f which assigns a value to each solution of the underlying CSP. A global solution to a COPisalabellingofallitsvariables,sothatallconstraintsaresatisfied,andtheobjec- tivefunction f isoptimized.Sinceitusuallytakesacompletesearchofthesearchspace to find the optimum f value, for many problems global optimization is not feasible in