Effects of the use of non-geometric binary crossover on evolutionary multiobjective optimization

In the design of evolutionary multiobjective optimization (EMO) algorithms, it is important to strike a balance between diversity and convergence. Traditional mask-based crossover operators for binary strings (e.g., one-point and uniform) tend to decrease the diversity of solutions in EMO algorithms while they improve the convergence to the Pareto front. This is because such a crossover operator, which is called geometric crossover, always generates an offspring in the segment between its two parents under the Hamming distance in the genotype space. That is, the sum of the distances from the generated offspring to its two parents is always equal to the distance between the parents. In this paper, first we propose a non-geometric binary crossover operator to generate an offspring outside the segment between its parents. Next we examine the effect of the use of non-geometric binary crossover on single-objective genetic algorithms. Experimental results show that non-geometric binary crossover improves their search ability. Then we examine its effect on EMO algorithms. Experimental results show that non-geometric binary crossover drastically increases the diversity of solutions while it slightly degrades their convergence to the Pareto front. As a result, some performance measures such as hypervolume are clearly improved.