A Bi-criterion Approach to Multimodal Optimization: Self-adaptive Approach
In a multimodal optimization task, the main purpose is to find multiple optimal solutions, so that the user can have a better knowledge about different optimal solutions in the search space and as and when needed, the current solution may be replaced by another optimum solution. Recently, we proposed a novel and successful evolutionary multi-objective approach to multimodal optimization. Our work however made use of three different parameters which had to be set properly for the optimal performance of the proposed algorithm. In this paper, we have eliminated one of the parameters and made the other two self-adaptive. This makes the proposed multimodal optimization procedure devoid of user specified parameters (other than the parameters required for the evolutionary algorithm). We present successful results on a number of different multimodal optimization problems of upto 16 variables to demonstrate the generic applicability of the proposed algorithm.
KeywordsMultimodal optimization Multi-objective optimization Self-adaptive algorithm Hooke-Jeeves search
Unable to display preview. Download preview PDF.
- 1.Deb, K., Saha, A.: Finding Multiple Solutions for Multimodal Optimization Problems Using a Multi-Objective Evolutionary Approach. In: Proceedings of the 12th Annual Conference on Genetic and Evolutionary Computation, GECCO 2010, pp. 447–454. ACM, New York (2010)Google Scholar
- 4.Goldberg, D.E., Wang, L.: Adaptive niching via coevolutionary sharing. In: Genetic Algorithms and Evolution Strategy in Engineering and Computer Science: Recent Advances and Industrial Applications, pp. 21–38. John Wiley & Son Ltd., Chichester (1997)Google Scholar
- 6.Leung, K.S., Liang, Y.: Adaptive elitist-population based genetic algorithm for multimodal function optimization. In: Cantú-Paz, E., Foster, J.A., Deb, K., Davis, L., Roy, R., O’Reilly, U.-M., Beyer, H.-G., Kendall, G., Wilson, S.W., Harman, M., Wegener, J., Dasgupta, D., Potter, M.A., Schultz, A., Dowsland, K.A., Jonoska, N., Miller, J., Standish, R.K. (eds.) GECCO 2003. LNCS, vol. 2724, pp. 1160–1171. Springer, Heidelberg (2003)CrossRefGoogle Scholar
- 8.Goldberg, D.E., Richardson, J.: Genetic algorithms with sharing for multimodal function optimization. In: Proceedings of the Second International Conference on Genetic Algorithms and Their Applications, pp. 41–49. L. Erlbaum Associates Inc., NJ (1987)Google Scholar
- 9.Deb, K., Goldberg, D.E.: An investigation of niche and species formation in genetic function optimization. In: Proceedings of the Third International Conference on Genetic Algorithms, pp. 42–50. Morgan Kaufmann Publishers Inc., USA (1989)Google Scholar