Hybrid genetic algorithms with selective crossover for the capacitated p-median problem

Abstract

The paper suggests two ways of combining a genetic algorithm with integer programming to improve the quality of the problem solution. The motivation is that today’s integer programming solvers are very sophisticated and efficient, and they are worth utilizing in combination with metaheuristics to solve hard combinatorial optimization problems. The capacitated p-median problem is chosen as an example of a problem that is intractable for an exact method and that needs a heuristic or metaheuristic method, e.g. a genetic algorithm, to get a near-optimal solution. A genetic algorithm can be combined with integer programming in such a way that the metaheuristic acts at a higher level and controls the calls to the solver, or the solver can be used as a post-processing technique to improve the best solution. Two variants of the hybrid genetic algorithm are tested using benchmark instances. Moreover, a new crossover operator is proposed, that uses the knowledge of the problem domain to preserve only positive traits of the parents in the offspring. The computational experiments suggest that the operator enables to improve the behaviour of the genetic algorithm.