Abstract
In this paper, we revisit a general class of multimodal function optimizations using Evolutionary Algorithms (EAs) and, in particular, study a reformulation of multimodal optimization into a multiobjective framework. For both multimodal and multiobjective problems, most implementations need niching/sharing to promote diversity in order to obtain multiple (near-) optimal solutions. Such techniques work best when one has a priori knowledge of the problem – for most real problems, however, this is not the case. In this paper, we solve multimodal optimizations reformulated into multiobjective problems using a steady-state multiobjective genetic algorithm which preserves diversity without niching. We find diverse solutions in objective space for two multimodal functions and compare these with previously published work. The algorithm without any explicit diversity-preserving operator is found to produce diverse sampling of the Pareto-front with significantly lower computational effort.
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
Goldberg, D.E., Richardson, J.: Genetic Algorithms with Sharing for Multimodal Function Optimization. In: Proc. 2nd Int. Conf. Genetic Algorithms, pp. 41–49 (1987)
Deb, K., Goldberg, D.E.: An Investigation of Niche and Species Formation in Genetic Function Optimization. In: Proc. 3rd Int. Conf. Genetic Algorithms, pp. 42–50 (1989)
Mahfoud, S.W.: Crowding and Preselection Revisited. In: Proc. Parallel Problem Solving from Nature, PPSN-2 (1992)
Beasley, D., Bull, D.R., Martin, R.R.: A Sequential Niche Technique for Multimodal Function Optimization. Evolutionary Computation 1, 101–125 (1993)
Yin, X., Germay, N.: A Fast Genetic Algorithm with Sharing Scheme using Cluster Analysis Methods in Multimodal Function Optimization. In: Proc. Int. Conf. Artificial Neural Nets and Genetic Algorithms (1993)
Goldberg, D.E., Wang, L.: Adaptive Niching via Coevolutionary Sharing. Genetic Algorithms and Evolutionary Strategies in Engineering and Computer Science (1998)
Mahfoud, S.W.: Niching Methods for Genetic Algorithms. IlliGAL Tech. Report 95001, Illinois Genetic Algorithm Laboratory, Univ. Illinois, Urbana (1995)
Watson, J. P.: A Performance Assessment of Modern Niching Methods for Parameter Optimization Problems. In: Gecco 1999 (1999)
Hocaoglu, C., Sanderson, A.C.: Multimodal Function Optimization Using Minimal Representation Size Clustering and Its Application to Planning Multipaths. Evolutionary Computation 5, 81–104 (1997)
Deb, K.: Multiobjective Optimization Using Evolutionary Algorithms. Wiley, Chichester (2001)
Coello, C.A.C., Van Veldhuizen, D.A., Lamont, G.B.: Evolutionary Algorithms for Solving Multi-Objective Problems, May 2002. Kluwer, Boston (2002)
Fonseca, C.M., Fleming, P.J.: Multiobjective optimization and multiple constraint handling with evolutionary algorithms-Part I: a unified formulation. IEEE Trans. Systems, Man and Cybernetics-Part A: Systems and Humans 28(1), 26–37 (1998)
Zitzler, E., Laumanns, M., Thiele, L.: SPEA2 – Improving the Strength Pareto Evolutionary Algorithm. EUROGEN (2001)
Laumanns, M., Thiele, L., Deo, K., Zitzler, E.: Combining Convergence and Diversity in Evolutionary Multiobjective Optimization. Evolutionary Computation 10, 182–263 (2002)
Kumar, R., Rockett, P.I.: Assessing the Convergence of Rank-Based Multiobjective Genetic Algorithms. In: Proc. IEE/ IEEE 2nd Int. Conf. Genetic Algorithms in Engineering Systems: Innovations & Applications, pp. 19–23 (1997)
Kumar, R., Rockett, P.I.: Improved Sampling of the Pareto-Front in Multiobjective Genetic Optimizations by Steady-State Evolution: A Pareto Converging Genetic Algorithm. Evolutionary Computation 10(3), 282–314 (2002)
Deb, K.: Multiobjective Genetic Algorithms: Problem Difficulties and Construction of Test Problems. Evolutionary Computation 7, 1–26 (1999)
Purshouse, R.C., Fleming, P.J.: Elitism, Sharing and Ranking Choices in Evolutionary Multi-criterion Optimization. Research Report No. 815, Dept. Automatic Control & Systems Engineering, University of Sheffield (January 2002)
Whitley, L.D.: The GENITOR Algorithm and Selection Pressure: Why Rank Based Allocation of Reproductive Trials is Best. In: Proc. 3rd Int. Conf. Genetic Algorithm, pp. 116–121 (1989)
Davidor, Y.: A Naturally Occurring Niche and Species Phenomenon: the Model and First Results. In: Proc. 4th Int. Conf. Genetic Algorithm, pp. 257–262 (1991)
Eshelman, L.J.: The CHC Adaptive Search Algorithm: How to have Safe Search when Engaging in Nontraditional Genetic Recombination. In: FOGA, pp. 265–283 (1991)
De Jong, K., Sarma, J.: Generation Gap Revisited. Foundations of Genetic Algorithms II, 19–28 (1993)
Mengshoel, O.J., Goldberg, D.E.: Probability Crowding: Deterministic Crowding with Probabilistic Replacement. In: Proc. GECCO, pp. 409–416 (1999)
Li, J.-P., Balazs, M.E., Parks, G.T., Clarkson, P.J.: A Species Conserving Genetic Algorithm for Multimodal Function Optimization. Evolutionary Computation 10(3), 207–234 (2002)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2004 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Kumar, R., Rockett, P. (2004). Effective Evolutionary Multimodal Optimization by Multiobjective Reformulation Without Explicit Niching/Sharing. In: Manandhar, S., Austin, J., Desai, U., Oyanagi, Y., Talukder, A.K. (eds) Applied Computing. AACC 2004. Lecture Notes in Computer Science, vol 3285. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-30176-9_1
Download citation
DOI: https://doi.org/10.1007/978-3-540-30176-9_1
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-23659-7
Online ISBN: 978-3-540-30176-9
eBook Packages: Springer Book Archive