An Extraction of Non-Correspondence Area between Objective Space and Design Variable Space based on Order Correlation of Distance Relation

Abstract

Recently, a lot of studies on Multi-Objective Genetic Algorithm (MOGA), in which Genetic Algorithm is applied to Multi-objective Optimization Problems (MOPs), have been reported actively. MOGA has been also applied to engineering design fields, then it is important not only to obtain good Pareto Solutions but also to analyze the obtained Pareto Solutions. In order to analyze Pareto solutions obtained by MOGA, it is required to consider both the objective space and the design variable space. In this paper, we define "Non-Correspondence" between the objective space and the design variable space in terms of distance relation between individuals, and extract the non-correspondence area in Pareto Solutions based on Spearman's order correlation coefficient calculated by the distance with each individual between in the objective space and in the design variable space.