Bayesian partition crossover for pseudo-Boolean optimization

Abstract

– The recombination of solutions is important for population metaheuristics and other optimization algorithms. Re-cently, an efficient recombination operator that preserve the interaction between the decision variables was proposed for pseudo-Boolean optimization. Partition Crossover (PX) groups decision variables in order to allow the decomposition of the evaluation function. PX allows to find, with computational cost proportional to the cost of evaluating one solution of the problem, the best solution among a number of offspring solutions that grows exponentially with the number of recombining components found by the operator. PX has been so far used only in problems where the information about the linkage between the decision variables is known a priori . This information is stored in a graph, know as variable interaction graph. We propose a new PX for pseudo-Boolean optimization problems that can be used when the variable interaction graph is not known a priori . For this purpose, it is necessary to estimate the linkage between the decision variables by using procedures generally employed in estimation of distribution algorithms. The experimental results show that the new recombination operator generally improves the number of offspring that are better than their parents when compared to traditional recombination operators. However, generating better offspring does not necessarily imply in better performance for the evolutionary algorithm.