Abstract
This paper studies the fuzzification of the Pareto dominance relation and its application to the design of Evolutionary Multi-Objective Optimization algorithms. A generic ranking scheme is presented that assigns dominance degrees to any set of vectors in a scale-independent, non-symmetric and set-dependent manner. Based on such a ranking scheme, the vector fitness values of a population can be replaced by the computed ranking values (representing the ”dominating strength” of an individual against all other individuals in the population) and used to perform standard single-objective genetic operators. The corresponding extension of the Standard Genetic Algorithm, so-called Fuzzy-Dominance-Driven GA (FDD-GA), will be presented as well. To verify the usefulness of such an approach, an analytic study of the Pareto-Box problem is provided, showing the characteristical parameters of a random search for the Pareto front in a unit hypercube in arbitrary dimension. The basic problem here is the loss of dominated points with increasing problem dimension, which can be successfully resolved by basing the search procedure on the fuzzy dominance degrees.
This is a preview of subscription content, log in via an institution to check access.
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.: A short tutorial on evolutionary multiobjective optimization. In: Zitzler, E., Deb, K., Thiele, L., Coello Coello, C.A., Corne, D.W. (eds.) EMO 2001, vol. 1993, pp. 21–40. Springer, Heidelberg (2001)
Coello Coello, C.A.: An updated survey of GA-based multiobjective optimization techniques. Technical Report RD-98-08, Laboratorio Nacional de Informática Avanzada (LANIA), Xalapa, Veracruz, México (1998)
Fonseca, C.M., Fleming, P.J.: An overview of evolutionary algorithms in multiobjective optimization. Evolutionary Computation 3(1), 1–16 (1995)
Deb, K., Agrawal, S., Pratap, A., Meyarivan, T.: A fast elitist non-dominated sorting genetic algorithm for multi-objective optimization: NSGA-II. In: Schoenauer, M., Deb, K., Rudolph, G., Yao, X., Lutton, E., Merelo, J.J., Schwefel, H.P. (eds.) PPSN 2000, vol. 1917, pp. 849–858. Springer, Paris (2000)
Zitzler, E., Laumanns, M., Thiele, L.: SPEA2: Improving the strength pareto evolutionary algorithm. Technical Report 103, Computer Engineering and Networks Laboratory (TIK), Swiss Federal Institute of Technology, Zurich, ETH Zentrum, Gloriastr 35, CH-8092 Zurich, Switzerland (2001)
Farina, M., Amato, P.: Fuzzy optimality and evolutionary multiobjective optimization. In: Fonseca, C.M., Fleming, P.J., Zitzler, E., Deb, K., Thiele, L. (eds.) EMO 2003, vol. 2632, pp. 58–72. Springer, Heidelberg (2003)
Köppen, M., Franke, K., Nickolay, B.: Fuzzy-pareto-dominance driven multiobjective genetic algorithm. In: Proceedings of the 10th IFSA World Congress, pp. 450–453 (2003)
Okabe, T., Jin, Y., Sendhoff, B.: A critical survey of performance indices for multi-objective optimization. In: Proceedings of the 2003 Congress on Evolutionary Computation (CEC 2003), Canberra, Australia, pp. 878–885. IEEE Press, Los Alamitos (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. NAFIPS (2004)
Corne, D.W., Knowles, J.D., Oates, M.J.: The pareto envelope-based selection algorithm for multiobjective optimization. In: Deb, K., Rudolph, G., Lutton, E., Merelo, J.J., Schoenauer, M., Schwefel, H.-P., Yao, X. (eds.) PPSN 2000, vol. 1917, pp. 839–848. Springer, Heidelberg (2000)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2005 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Köppen, M., Vicente-Garcia, R., Nickolay, B. (2005). Fuzzy-Pareto-Dominance and its Application in Evolutionary Multi-objective Optimization. In: Coello Coello, C.A., Hernández Aguirre, A., Zitzler, E. (eds) Evolutionary Multi-Criterion Optimization. EMO 2005. Lecture Notes in Computer Science, vol 3410. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-31880-4_28
Download citation
DOI: https://doi.org/10.1007/978-3-540-31880-4_28
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-24983-2
Online ISBN: 978-3-540-31880-4
eBook Packages: Computer ScienceComputer Science (R0)