Abstract
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.
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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)
Deb, K., Pratap, A., Agarwal, S., Meyarivan, T.: A fast and elitist multi-objective genetic algorithm: NSGA-II. IEEE Transactions on Evolutionary Computation 6(2), 182–197 (2002)
Li, X.: Niching Without Niching Parameters: Particle Swarm Optimization Using a Ring Topology. IEEE Transactions on Evolutionary Computation 14(1), 150–169 (2010)
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)
Shir, O., Back, T.: Niche radius adaptation in the CMA-ES niching algorithm. In: Proceedings of the Parallel Problem Solving from Nature-PPSN IX, pp. 142–151. Springer, Heidelberg (2006)
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)
Srinivas, M., Patnaik, L.M.: Adaptive probabilities of crossover and mutation in genetic algorithms. IEEE Transactions on Systems, Man and Cybernetics 24(4), 656–667 (1994)
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)
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)
Pétrowski, A.: A clearing procedure as a niching method for genetic algorithms. In: Proceedings of the IEEE 3rd International Conference on Evolutionary Computation (ICEC 1996), pp. 798–803. IEEE Press, Los Alamitos (1996)
Streichert, F., Stein, G., Ulmer, H., Zell, A.: A clustering based niching EA for multimodal search spaces. In: Liardet, P., Collet, P., Fonlupt, C., Lutton, E., Schoenauer, M. (eds.) EA 2003. LNCS, vol. 2936, pp. 293–304. Springer, Heidelberg (2004)
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Saha, A., Deb, K. (2010). A Bi-criterion Approach to Multimodal Optimization: Self-adaptive Approach. In: Deb, K., et al. Simulated Evolution and Learning. SEAL 2010. Lecture Notes in Computer Science, vol 6457. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-17298-4_10
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DOI: https://doi.org/10.1007/978-3-642-17298-4_10
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