Partition Crossover for Pseudo-Boolean Optimization

Abstract

A partition crossover operator is introduced for use with NK landscapes, MAX-kSAT and for all k-bounded pseudo-Boolean functions. By definition, these problems use a bit representation. Under partition crossover, the evaluation of offspring can be directly obtained from partial evaluations of substrings found in the parents. Partition crossover explores the variable interaction graph of the pseudo-Boolean functions in order to partition the variables of the solution vector. Proofs are presented showing that if the differing variable assignments found in the two parents can be partitioned into q non-interacting sets, partition crossover can be used to find the best of 2q possible offspring. Proofs are presented which show that parents that are locally optimal will always generate offspring that are locally optimal with respect to a (more restricted) hyperplane subspace. Empirical experiments show that parents that are locally optimal generate offspring that are locally optimal in the full search space more than 80 percent of the time. Experimental results also show the effectiveness of the proposed crossover when used in combination with a hybrid genetic algorithm.