A Genetic Algorithm for Superior Solution Set Search Problem

Abstract

The superior solution set search problem contains parameters that provide constraints on evaluation value and distance. However, an optimization method explicitly incorporating these parameters has not yet been proposed. There is a multi-objective optimization problem that is very similar to the superior solution set search problem. Studies on multi-objective optimization problems have been very active recently and solution applications to the superior solution set search problem are to be expected. Therefore, in this paper, we propose an evaluation indicator that is inspired by a method based on a dominance relationships in multi-objective optimization problems and includes the aforementioned parameters. We also propose a search method based on this indicator and perform numerical experiments on unique superior solution set search problems. The proposed method finds more superior solutions than the conventional single-objective optimization method, which confirms its usefulness.