Abstract
This paper examines the use of fitness sharing in evolutionary multiobjective optimization (EMO) algorithms to form a uniform distribution of niches along the non-dominated frontier. A long-standing, implicit assumption is that fitness sharing within an equivalence class, such as the Pareto optimal set, can form dynamically stable (under selection) subpopulations evenly spaced along the front. We show that this behavior can occur, but that it is highly unlikely. Rather, it is much more likely that a steady-state will be reached in which stable niches are maintained, but at inter-niche distances much less than the specified niche radius, with several times more niches than previously predicted, and with non-uniform sub-population sizes. These results might have implications for EMO population sizing, and perhaps even for EMO algorithm design itself.
Keywords
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsPreview
Unable to display preview. Download preview PDF.
References
Deb, K.: Genetic Algorithms in Multi-Modal Function Optimization. Masters thesis, University of Alabama at Tuscaloosa, AL (1989)
Deb, K.: Multi-Objective Optimization using Evolutionary Algorithms. John Wiley & Sons, Ltd., Chichester (2001)
Fonseca, C. M., & Fleming, P. J.: Genetic algorithms for multiobjective optimization: Formulation, discussion, and generalization. Proceedings of the Fifth International Conference on Genetic Algorithms. Morgan Kaufmann, San Mateo, CA (1993) 416–423
Goldberg, D. E., Richardson, J.: Genetic Algorithms with Sharing for Multimodal Function Optimization. In: Grefenstette, J. (ed.): Proceedings of the 2 nd International Conference on Genetic Algorithms. Lawrence Erlbaum Associates, Hillsdale, New Jersey (1987) 1–8
Horn, J.: The Nature of Niching: Genetic Algorithms and the Evolution of Optimal, Cooperative Populations. Ph.D. thesis, University of Illinois at Urbana-Champaign, (UMI Dissertation Services, No. 9812622) (1997)
Horn, J.: Multicriterion Decision Making. In: Bäck, T., Fogel, D. (eds.): The Handbook of Evolutionary Computation. Oxford University Press, New York (1997) F1.9:1–15
Horn J., Nafpliotis, N., Goldberg, D. E.: A niched Pareto genetic algorithm for multiobjective optimization. Proceedings of 1 st IEEE International Conference on Evolutionary Computation, Volume 1. IEEE Service Center, Piscataway, New Jersey (1994) 82–87
Horn J., & Nafpliotis: Multi-objective optimization using the niched Pareto genetic algorithm. IlliGAL Report Number 93005. Illinois Genetic Algorithms Laboratory, University of Illinois at Urbana-Champaign (1993)
Mahfoud, S. W.: Niching Methods for Genetic Algorithms. Ph.D. thesis, University of Illinois at Urbana-Champaign (1995)
Srinivas, N. & Deb, K.: Multi-objective function optimization using non-dominated sorting genetic algorithms. The Journal of Evolutionary Computation 2(3) (1994) 221–248
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2003 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Horn, J. (2003). Niche Distributions on the Pareto Optimal Front. In: Fonseca, C.M., Fleming, P.J., Zitzler, E., Thiele, L., Deb, K. (eds) Evolutionary Multi-Criterion Optimization. EMO 2003. Lecture Notes in Computer Science, vol 2632. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-36970-8_26
Download citation
DOI: https://doi.org/10.1007/3-540-36970-8_26
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-01869-8
Online ISBN: 978-3-540-36970-7
eBook Packages: Springer Book Archive