On the ability of the one-point crossover operator to search the space in genetic algorithms

Abstract

In this paper we study the search abilities of binary one-point crossover (1ptc) operator in a genetic algorithm (GA).We show, that under certain conditions, GA is capable of using only a 1ptc operator to explore the entire search space, fighting premature convergence. Further, we prove that to restore the entire space from any two binary chromosomes, each of length n, at least 2n-1-1 one-point crossover operations is needed. This number can serve as a measure for comparing the search speed of the different algorithms. Moreover, we propose an algorithm spanning the search space in the minimal number of crossovers.