Abstract
Many-objective optimization refers to optimization problems with a number of objectives considerably larger than two or three. In this paper, a study on the performance of the Fast Elitist Non-dominated Sorting Genetic Algorithm (NSGA-II) for handling such many-objective optimization problems is presented. In its basic form, the algorithm is not well suited for the handling of a larger number of objectives. The main reason for this is the decreasing probability of having Pareto-dominated solutions in the initial external population. To overcome this problem, substitute distance assignment schemes are proposed that can replace the crowding distance assignment, which is normally used in NSGA-II. These distances are based on measurement procedures for the highest degree, to which a solution is nearly Pareto-dominated by any other solution: like the number of smaller objectives, the magnitude of all smaller or larger objectives, or a multi-criterion derived from the former ones. For a number of many-objective test problems, all proposed substitute distance assignments resulted into a strongly improved performance of the NSGA-II.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Babbar, M., Lakshmikantha, A., Goldberg, D.E.: A Modified NSGA-II to Solve Noisy Multiobjective Problems. In: Foster, J. (ed.) 2003 Genetic and Evolutionary Computation Conference. Late-Breaking Papers, Chicago, Illinois, USA, July 2003, pp. 21–27. AAAI, Menlo Park (2003)
Das, I.: A preference ordering among various pareto optimal alternatives. Structural and Multidisciplinary Optimization 18(1), 30–35 (1999)
Deb, K., Agrawal, S., Pratab, A., Meyarivan, T.: A Fast Elitist Non-Dominated Sorting Genetic Algorithm for Multi-Objective Optimization: NSGA-II. In: Deb, K., Rudolph, G., Lutton, E., Merelo, J.J., Schoenauer, M., Schwefel, H.-P., Yao, X. (eds.) Parallel Problem Solving from Nature-PPSN VI. LNCS, vol. 1917, pp. 849–858. Springer, Heidelberg (2000)
Deb, K., Jain, S.: Running Performance Metrics for Evolutionary Multi-Objective Optimization. In: Wang, L., Tan, K.C., Furuhashi, T., Kim, J.-H., Yao, X. (eds.) Proceedings of the 4th Asia-Pacific Conference on Simulated Evolution and Learning (SEAL’02), vol. 1, Orchid Country Club, Singapore, November 2002, pp. 13–20. Nanyang Technical University (2002)
Deb, K., Pratap, A., Agarwal, S., Meyarivan, T.: A Fast and Elitist Multiobjective Genetic Algorithm: NSGA–II. IEEE Transactions on Evolutionary Computation 6(2), 182–197 (2002)
Deb, K., Thiele, L., Laumanns, M., Zitzler, E.: Scalable Test Problems for Evolutionary Multi-Objective Optimization. Technical Report 112, Computer Engineering and Networks Laboratory (TIK), Swiss Federal Institute of Technology (ETH), Zurich, Switzerland (2001)
Deb, K., Thiele, L., Laumanns, M., Zitzler, E.: Scalable Multi-Objective Optimization Test Problems. In: Congress on Evolutionary Computation (CEC’2002), vol. 1, Piscataway, New Jersey, May 2002, pp. 825–830. IEEE Computer Society Press, Los Alamitos (2002)
Fleming, P., Purshouse, R.C., Lygoe, R.J.: Many-Objective Optimization: An Engineering Design Perspective. In: Coello Coello, C.A., Hernández Aguirre, A., Zitzler, E. (eds.) EMO 2005. LNCS, vol. 3410, pp. 14–32. Springer, Heidelberg (2005)
Grosan, C.: Multiobjective adaptive representation evolutionary algorithm (MAREA) - a new evolutionary algorithm for multiobjective optimization. In: Abraham, A., De Baets, B., Köppen, M., Nickolay, B. (eds.) Applied Soft Computing Technologies: The Challenge of Complexity. Advances in Soft Computing, pp. 113–121. Springer, Heidelberg (2006)
Khare, V., Yao, X., Deb, K.: Performance Scaling of Multi-objective Evolutionary Algorithms. In: Fonseca, C.M., Fleming, P.J., Zitzler, E., Deb, K., Thiele, L. (eds.) EMO 2003. LNCS, vol. 2632, pp. 376–390. Springer, Heidelberg (2003)
Köppen, M., Vicente Garcia, R.: A fuzzy scheme for the ranking of multivariate data and its application. In: Proceedings of the 2004 Annual Meeting of the NAFIPS (CD-ROM), Banff, Alberta, Canada, pp. 140–145 (2004)
Köppen, M., Vicente-Garcia, R., Nickolay, B.: Fuzzy-Pareto-Dominance and Its Application in Evolutionary Multi-objective Optimization. In: Coello Coello, C.A., Hernández Aguirre, A., Zitzler, E. (eds.) EMO 2005. LNCS, vol. 3410, pp. 399–412. Springer, Heidelberg (2005)
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 2007 Springer Berlin Heidelberg
About this paper
Cite this paper
Köppen, M., Yoshida, K. (2007). Substitute Distance Assignments in NSGA-II for Handling Many-objective Optimization Problems. In: Obayashi, S., Deb, K., Poloni, C., Hiroyasu, T., Murata, T. (eds) Evolutionary Multi-Criterion Optimization. EMO 2007. Lecture Notes in Computer Science, vol 4403. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-70928-2_55
Download citation
DOI: https://doi.org/10.1007/978-3-540-70928-2_55
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-70927-5
Online ISBN: 978-3-540-70928-2
eBook Packages: Computer ScienceComputer Science (R0)