Choosing extreme parents for diversity improvement in evolutionary multiobjective optimization algorithms

It has been demonstrated in the literature that a similarity-based mating scheme can increase the diversity of solutions in evolutionary multiobjective optimization (EMO) algorithms. In the similarity-based mating scheme, an extreme solution is chosen from the current population as one parent. A similar solution to the selected parent is chosen from the current population as the other parent (i.e., as a mate of the first parent). In this paper, we first demonstrate that the similarity-based mating scheme works well when it is incorporated into NSGA-II. Next we point out a problematic side effect of choosing extreme solutions as parents using SPEA. That is, the similarity-based mating scheme does not always widen the population along the Pareto front but also lengthen it toward the Pareto front. This is because poor solutions far from the Pareto front have relatively high selection probabilities to be chosen as parents. Then we propose a simple trick to prevent such a poor solution from being selected as the first parent. Finally we demonstrate that the modified similarity-based mating scheme works well in SPEA as well as NSGA-II through computational experiments on multiobjective 0/1 knapsack problems.