Abstract
In this paper, we use an alternative preference relation that couples an achievement function and the ε-indicator in order to improve the scalability of a Multi-Objective Evolutionary Algorithm (moea) in many-objective optimization problems. The resulting algorithm was assessed using the Deb-Thiele-Laumanns-Zitzler (dtlz) and the Walking- Fish-Group (wfg) test suites. Our experimental results indicate that our proposed approach has a good performance even when using a high number of objectives. Regarding the dtlz test problems, their main difficulty was found to lie on the presence of dominance resistant solutions. In contrast, the hardness of wfg problems was not found to be significantly increased by adding more objectives.
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
Coello Coello, C.A., Lamont, G.B., Van Veldhuizen, D.A.: Evolutionary Algorithms for Solving Multi-Objective Problems, 2nd edn. Springer, New York (2007) ISBN 978-0-387-33254-3
Hughes, E.J.: Evolutionary Many-Objective Optimisation: Many Once or One Many? In: CEC 2005, Edinburgh, Scotland, vol. 1, pp. 222–227 (September 2005)
Wagner, T., Beume, N., Naujoks, B.: Pareto-, Aggregation-, and Indicator-Based Methods in Many-Objective Optimization. In: Obayashi, S., Deb, K., Poloni, C., Hiroyasu, T., Murata, T. (eds.) EMO 2007. LNCS, vol. 4403, pp. 742–756. Springer, Heidelberg (2007)
Purshouse, R.C., Fleming, P.J.: Evolutionary Multi-Objective Optimisation: An Exploratory Analysis. In: CEC 2003, Canberra, Australia, vol. 3, pp. 2066–2073 (December 2003)
Knowles, J., Corne, D.: Quantifying the Effects of Objective Space Dimension in Evolutionary Multiobjective Optimization. In: Obayashi, S., Deb, K., Poloni, C., Hiroyasu, T., Murata, T. (eds.) EMO 2007. LNCS, vol. 4403, pp. 757–771. Springer, Heidelberg (2007)
Ishibuchi, H., Tsukamoto, N., Nojima, Y.: Evolutionary many-objective optimization: A short review. In: CEC 2008, Hong Kong, pp. 2424–2431 (June 2008)
Schütze, O., Lara, A., Coello Coello, C.A.: On the Influence of the Number of Objectives on the Hardness of a Multiobjective Optimization Problem. IEEE Transactions on Evolutionary Computation 15(4), 444–455 (2011)
Sato, H., Aguirre, H.E., Tanaka, K.: Genetic Diversity and Effective Crossover in Evolutionary Many-Objective Optimization. In: Coello, C.A.C. (ed.) LION 5. LNCS, vol. 6683, pp. 91–105. Springer, Heidelberg (2011)
Ikeda, K., Kita, H., Kobayashi, S.: Failure of Pareto-based MOEAs: Does Non-dominated Really Mean Near to Optimal? In: CEC 2001, Piscataway, New Jersey, vol. 2, pp. 957–962 (May 2001)
Deb, K., Thiele, L., Laumanns, M., Zitzler, E.: Scalable Multi-Objective Optimization Test Problems. In: CEC 2002, Piscataway, New Jersey, vol. 1, pp. 825–830 (May 2002)
Huband, S., Barone, L., While, L., Hingston, P.: A Scalable Multi-objective Test Problem Toolkit. In: Coello Coello, C.A., Hernández Aguirre, A., Zitzler, E. (eds.) EMO 2005. LNCS, vol. 3410, pp. 280–295. Springer, Heidelberg (2005)
López Jaimes, A., Arias-Montaño, A., Coello Coello, C.A.: Preference Incorporation to Solve Many-Objective Airfoil Design Problems. In: CEC 2011, New Orleans, USA (June 2011)
Wierzbicki, A.: The use of reference objectives in multiobjective optimisation. In: Fandel, G., Gal, T. (eds.) Multiple Criteria Decision Making Theory and Application. Lecture Notes in Economics and Mathematical Systems, Vol. 177, pp. 468–486. Springer (1980)
Ehrgott, M.: Multicriteria Optimization, 2nd edn. Springer, Berlin (2005)
Bentley, P.J., Wakefield, J.P.: Finding Acceptable Solutions in the Pareto-Optimal Range using Multiobjective Genetic Algorithms. In: Chawdhry, P.K., Roy, R., Pant, R.K. (eds.) Soft Computing in Engineering Design and Manufacturing, pp. 231–240. Springer, London (1997)
Kukkonen, S., Lampinen, J.: Ranking-Dominance and Many-Objective Optimization. In: CEC 2007, Singapore, pp. 3983–3990 (September 2007)
Drechsler, N., Drechsler, R., Becker, B.: Multi-Objected Optimization in Evolutionary Algorithms Using Satisfyability Classes. In: Reusch, B. (ed.) International Conference on Computational Intelligence, Theory and Applications, 6th Fuzzy Days, Dortmund, Germany, pp. 108–117 (1999)
di Pierro, F., Khu, S.T., Savić, D.A.: An Investigation on Preference Order Ranking Scheme for Multiobjective Evolutionary Optimization. IEEE Transactions on Evolutionary Computation 11(1), 17–45 (2007)
Sato, H., Aguirre, H.E., Tanaka, K.: Controlling Dominance Area of Solutions and Its Impact on the Performance of MOEAs. In: Obayashi, S., Deb, K., Poloni, C., Hiroyasu, T., Murata, T. (eds.) EMO 2007. LNCS, vol. 4403, pp. 5–20. Springer, Heidelberg (2007)
Zitzler, E., Thiele, L., Laumanns, M., Fonseca, C.M., da Fonseca, V.G.: Performance Assessment of Multiobjective Optimizers: An Analysis and Review. IEEE Transactions on Evolutionary Computation 7(2), 117–132 (2003)
Zitzler, E., Künzli, S.: Indicator-Based Selection in Multiobjective Search. In: Yao, X., Burke, E.K., Lozano, J.A., Smith, J., Merelo-Guervós, J.J., Bullinaria, J.A., Rowe, J.E., Tiňo, P., Kabán, A., Schwefel, H.-P. (eds.) PPSN VIII. LNCS, vol. 3242, pp. 832–842. Springer, Heidelberg (2004)
Balling, R.: The Maximin Fitness Function; Multi-objective City and Regional Planning. In: Fonseca, C.M., Fleming, P.J., Zitzler, E., Deb, K., Thiele, L. (eds.) EMO 2003. LNCS, vol. 2632, pp. 1–15. Springer, Heidelberg (2003)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2013 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
L’opez, A., Coello, C.A.C., Oyama, A., Fujii, K. (2013). An Alternative Preference Relation to Deal with Many-Objective Optimization Problems. In: Purshouse, R.C., Fleming, P.J., Fonseca, C.M., Greco, S., Shaw, J. (eds) Evolutionary Multi-Criterion Optimization. EMO 2013. Lecture Notes in Computer Science, vol 7811. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-37140-0_24
Download citation
DOI: https://doi.org/10.1007/978-3-642-37140-0_24
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-37139-4
Online ISBN: 978-3-642-37140-0
eBook Packages: Computer ScienceComputer Science (R0)