A study on Non-Correspondence in Spread between Objective Space and Design Variable Space and Application to Genetic Search

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 high-performance Pareto solutions but also to analyze the obtained Pareto solutions and extract some knowledge in the problem. 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 "NonCorrespondence in Spread" between the objective space and the design variable space. We also try to extract the NonCorrespondence area in Spread with the index defined in this paper. Moreover, we apply the defined index to genetic search to obtain Pareto solutions that have different design variables one another having similar fitness values. This paper applies the above index to the trajectory designing optimization problem and extracts Non-Correspondence area in Spread int the acquired Pareto solutions. This paper also shows that robust Pareto solutions can be acquired by the genetic search with the index.