Visualization on Pareto Solutions in Multi-Objective Optimization

Shin-ichi Ito, Yasue Mitsukura, Takafumi Saito, Katsuya Sato, and Shoichiro Fujisawa


Multi-objective optimization, real-coded genetic algorithm, information visualization, pseudo color


This paper introduces a method for visualizing the relationship between optimized elements and their evaluation values in multi-objective optimization using the pseudo coloring method in information visualization techniques. Because multi-objective optimal problem has a lot of optimal solutions (Pareto solution), it is not easy to choose a single optimal solution. There is a tendency that it is confirmed not only the evaluation values but also the optimized elements are necessary when designers specify an optimal solution. Then, we focus on a real-coded genetic algorithm that is one of the multi-objective optimization techniques. The proposed method visualizes the relationship between the gene values, which indicate the optimized elements, and objective values, which denote the evaluation values, of all individuals in a Pareto solution. The gene and objective values are expressed as color and gray scales, respectively, after normalization. The gene values normalize using maximum and minimum values in all genes of Pareto solution, and in each gene, respectively. The objective function values normalize using maximum and minimum values in each objective function. To show the effectiveness of the proposed method, we apply the proposed method to benchmark problems. We easily found the relationship between the gene and objective functions values.

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