Knowledge Extraction from Pareto Solutions in Multi-Objective Engineering Design Problem Based on Geodetic Distance between Objective Space and Design Variable Space

Recently, the application of Multi-Objective Genetic Algorithm to engineering design problem in the real world has been reported because of the advancement of computing capabilities. In this field, it is important not only to acquire Pareto solutions with high performance but also to analyze relationships between objective functions and design variables in Pareto solutions, which gives the designers useful knowledge in the applied problem. This paper proposes a new visualization method which visualizes the Pareto solutions in the design variable space reflecting the proximity of solutions in the objective space. The proposed method uses an idea of Isomap, which visualizes manifold embedded in the high-dimensional space, which was originally proposed in the field of multiple classification analysis. This paper shows that the visualized result gives some knowledge on the features between the design variables and the fitness values in the acquired Pareto solutions.