Analysis of Pareto Solutions Based on Non-Correspondence in Spread Between Objective Space and Design Variable Space
Toru Yoshida and Tomohiro Yoshikawa
Department of Computational Science and Engineering, Nagoya University
Furo-cho, Chikusa-ku, Nagoya, Aichi 464-8603, Japan
Recently, many studies have been conducted on Multi-Objective Genetic Algorithm (MOGA), in which Genetic Algorithms are applied to Multi-objective Optimization Problems (MOPs). Among various applications, MOGA is also applied to engineering design problems, which require not only high-performance Pareto solutions to be obtained, but also an analysis of the obtained Pareto solutions and extraction of design knowledge about the problem itself. In order to analyze the Pareto solutions obtained by MOGA, it is necessary to consider the objective space and the design variable space. The aim of this study is to extract and analyze solutions of relevant interest to designers. In this paper, we propose three solutions to analyze and extract design knowledge from MOGA. (1) We define “Non-Correspondence in Spread” between the objective space and the design variable space. (2) We try to extract the Non-Correspondence area in Spread using the index defined in this paper. (3) We apply the defined index to genetic search to obtain Pareto solutions that have different design variables and similar fitness values. This paper applies the above index to the trajectory design optimization problem and extracts Non-Correspondence area in Spread from the obtained Pareto solutions. This paper also shows that robust Pareto solutions can be obtained using genetic search using the defined index.
-  K. Deb, “Multi-objective optimization using evolutionary algorithms,” Wiley, 2001.
-  A. Oyama, K. Hagiwara, and Y. Kawakatsu, “Application of Multiobjective Design Exploration to Trajectory Design of the Next-Generation Solar Physics Satellite,” Japanese Society for Evolutionary Computation, 2010.
-  K. Deb, “Unveiling innovative design principles by means of multiple conflicting objectives,” Engineering Optimization, Vol.35, No.5, pp. 445-470, 2003.
-  S. Obayashi, “Multiobjective Design Optimization of Aircraft Configuration,” The Japanese Society for Artificial Intelligence, Vol.18, pp. 495-501, 2003 (in Japanese).
-  F. Kudo and T. Yoshikawa, “Knowledge Extraction in Multiobjective Optimization Problem based on Visualization of Pareto Solutions,” WCCI 2012 IEEE World Congress on Computational Intelligence, pp. 860-865, 2012.
-  T. Yoshida and T. Yoshikawa, “An Extraction of Non- Correspondence Area between Objective Space and Design Variable Space based on Order Correlation of Distance Relation,” The Japanese Society for Artificial Intelligence, 2013 (in Japanese).
-  A. L’opez, A. Oyama, and K. Fujii, “Evaluating Two Evolutionary Approaches to Solve a Many-objective Space Trajectory Design Problem,” The Japanese Society for Evolutionary Computation, 2012.
-  K. Deb, “A Fast and Elitist Multiobjective Genetic Algorithm : NSGA-II,” 2002.
-  K. Deb and R. Agrawal, “Simulated binary crossover for continuous search space,” Complex Systems, Vol.1, No.9, pp. 115-148, 1994.
-  K. Deb and M. Goyal, “A combined genetic adaptive search (GeneAS) for engineering design,” Computer Science and Informatics, Vol.26, pp. 30-45, 1996.
-  J. W. Sammon, “A Nonlinear Mapping for Data Structure Analysis,” IEEE Trans. on Computers, Vol.C-18, pp. 401-409, 1969.
-  http://www.ciss.iis.u-tokyo.ac.jp/supercomputer/about/ [Accessed February 1, 2012]