Evolutionary divide and conquer for the set-covering problem

Abstract

Genetic Algorithms (GAs) attempt to improve on simpler stochastic search methods by using the diversity offered by virtue of using a population of candidate solutions. Depending on the problem at hand, this often promises to provide a better chance (than hillclimbing, for example) of settling on the right peak in the search space, typically at the expense of slower convergence. Nevertheless, real problems tend to present landscapes which require even more sophisticated management of diversity if good solutions are to be discovered in the complex forest of suboptima. This paper describes a ‘divide and conquer’ method, which aims to do this via breaking a problem down into smaller subproblems for each of which a population of solutions is individually evolved. The quality of those ‘sub’-solutions is then assessed depending on how well they combine with other sub-solutions to yield complete solutions to the problem. Via tests on set-covering problems, we find that the method has merit and potential, and we discuss its sensitivity to various parameters.