VISUALIZATION ON PARETO SOLUTIONS IN MULTI-OBJECTIVE OPTIMIZATION

摘要

This paper introduces a method for visualizing the relationshiprnbetween optimized elements and their evaluation valuesrnin multi-objective optimization using the pseudo coloringrnmethod in information visualization techniques. Becausernmulti-objective optimal problem has a lot of optimalrnsolutions (Pareto solution), it is not easy to choose a singlernoptimal solution. There is a tendency that it is confirmedrnnot only the evaluation values but also the optimized elementsrnare necessary when designers specify an optimalrnsolution. Then, we focus on a real-coded genetic algorithmrnthat is one of the multi-objective optimization techniques.rnThe proposed method visualizes the relationship betweenrnthe gene values, which indicate the optimized elements,rnand objective values, which denote the evaluation values,rnof all individuals in a Pareto solution. The gene and objectivernvalues are expressed as color and gray scales, respectively,rnafter normalization. The gene values normalizernusing maximum and minimum values in all genes ofrnPareto solution, and in each gene, respectively. The objectivernfunction values normalize using maximum and minimumrnvalues in each objective function. To show the effectivenessrnof the proposed method, we apply the proposedrnmethod to benchmark problems. We easily found the relationshiprnbetween the gene and objective functions values.