A Comparative Study of a Penalty Function, a Repair Heuristic and Stochastic Operators with the Set-Covering Problem

In this paper we compare the effects of using various stochastic operators with the non-unicost set-covering problem. Four different crossover operators are compared to a repair heuristic which consists in transforming infeasible strings into feasible ones. These stochastic operators are incorporated in GENEsYs, the genetic algorithm we apply to problem instances of the set-covering problem we draw from well known test problems. GENEsYs uses a simple fitness function that has a graded penalty term to penalize infeasibly bred strings. The results are compared to a non GA-based algorithm based on the greedy technique. Our computational results are then compared, shedding some light on the effects of using different operators, a penalty function, and a repair heuristic on a highly constrained combinatorial optimization problem.

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