Analysis of Pareto Solutions Based on Non-Correspondence in Spread Between Objective Space and Design Variable Space

Abstract

Recently, many studies have been conducted on Multi-Objective Genetic Algorithm (MOGA), in which Genetic Algorithms are applied to Multi-objective Optimization Problems (MOPs). Among various applications, MOGA is also applied to engineering design problems, which require not only high-performance Pareto solutions to be obtained, but also an analysis of the obtained Pareto solutions and extraction of design knowledge about the problem itself. In order to analyze the Pareto solutions obtained by MOGA, it is necessary to consider the objective space and the design variable space. The aim of this study is to extract and analyze solutions of relevant interest to designers. In this paper, we propose three solutions to analyze and extract design knowledge from MOGA. (1) We define “Non-Correspondence in Spread” between the objective space and the design variable space. (2) We try to extract the Non-Correspondence area in Spread using the index defined in this paper. (3) We apply the defined index to genetic search to obtain Pareto solutions that have different design variables and similar fitness values. This paper applies the above index to the trajectory design optimization problem and extracts Non-Correspondence area in Spread from the obtained Pareto solutions. This paper also shows that robust Pareto solutions can be obtained using genetic search using the defined index.