Abstract
Genetic Algorithms have been successfully used to solve multi-modal optimization problems, mainly due to their population approach and implicit parallel processing among multiple subpopulations. In order to find and maintain multiple regions, GAs implement a niching principle motivated from nature. The selection procedure of a GA is modified by restricting a comparison among similar solutions to bring about an additional level of diversity in the population. In another recent study, a real-parameter push-operator based on non-uniform coding principle applied to binary-coded GAs was proposed. The push-operator has shown to exhibit better convergence properties on many optimization problems compared to standard GA implementations. In this paper, we extend the push-operator and its implementation with the niching principle to solve multi-modal problems. On a number of constrained and unconstrained multi-modal test problems, we demonstrate its superior convergence to multiple optimal solutions simultaneously. Results are interesting and motivate us to extend the push-operator to multi-objective and other complex optimization tasks.
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Notes
- 1.
For a maximization problem, CV(\(\mathbf {x}\)) will be subtracted.
References
Barrera, J., Coello, C.A.C.: A review of particle swarm optimization methods used for multimodal optimization. In: Lim, C.P., Jain, L.C., Dehuri, S. (eds.) Innovations in Swarm Intelligence, vol. 248, pp. 9–37. Springer, Berlin (2009)
Coello, C.A.C., VanVeldhuizen, D.A., Lamont, G.: Evolutionary Algorithms for Solving Multi-Objective Problems. Kluwer, Boston (2002)
Deb, K.: An efficient constraint handling method for genetic algorithms. Comput. Meth. Appl. Mech. Eng. 186(2), 311–338 (2000)
Deb, K.: Multi-objective Optimization Using Evolutionary Algorithms, vol. 16. Wiley, Hoboken (2001)
Dhebar, Y., Deb, K.: A computationally fast multimodal optimization with push enabled genetic algorithm. In: Proceedings of Genetic and Evolutionary Computation Conference Companion, pp. 191–192. ACM, Chicago (2017)
Deb, K., Dhebar, Y.D., Pavan, N.: Non-uniform mapping in binary-coded genetic algorithms. In: Bansal, J., Singh, P., Deep, K., Pant, M., Nagar, A. (eds.) Proceedings of Seventh International Conference on Bio-Inspired Computing: Theories and Applications (BIC-TA 2012). Advances in Intelligent Systems and Computing, vol. 201, pp. 133–144. Springer, Gwalior (2013)
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 (1989)
Deb, K., Saha, A.: Multimodal optimization using a bi-objective evolutionary algorithm. Evol. Comput. 20(1), 27–62 (2012)
Goldberg, D.E., Richardson, J.: Genetic algorithms with sharing for multimodal function optimization. In: Proceedings of the First International Conference on Genetic Algorithms and Their Applications, pp. 41–49 (1987)
Lee, C., Cho, D., Jung, H.: Niching genetic algorithm with restricted competition selection for multimodal function optimization. IEEE Trans. Magn. 35(3), 1722–1725 (1999)
Li, X.: Efficient differential evolution using speciation for multimodal function optimization. In: Proceedings of the Conference on Genetic and Evolutionary Computation (GECCO-2005), pp. 873–880 (2005)
Li, X., Engelbrecht, A., Epitropakis, M.G.: Benchmark functions for cec2013 special session and competition on niching methods for multimodal function optimization. RMIT University, Evolutionary Computation and Machine Learning Group, Australia, Technical report (2013)
Mengsheol, O., Goldberg, D.E.: Probabilistic crowding: deterministic crowding with probabilistic replacement. In: Proceedings of Genetic and Evolutionary Computation Conference (GECCO-1999), pp. 409–416 (1999)
Petrowski, A.: A clearing procedure as a niching method for genetic algorithms. In: Proceedings of Third IEEE International Conference on Evolutionary Computation (ICEC 1996), pp. 798–803. IEEE Press, Piscataway (1996)
Rönkkönen, J., Lampinen, J.: On determining multiple global optima by differential evolution. In: Proceedings of Evolutionary and Deterministic Methods for Design, Optimization and Control (Eurogen 2007), pp. 146–151 (2007)
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). doi:10.1007/978-3-540-24621-3_24
Yashesh, D., Deb, K., Bandaru, S.: Non-uniform mapping in real-coded genetic algorithms. In: 2014 IEEE Congress on Evolutionary Computation (CEC), pp. 2237–2244. IEEE (2014)
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This material is based in part upon work supported by the National Science Foundation under Cooperative Agreement No. DBI-0939454. Any opinions, findings, and conclusions or recommendations expressed in this material are those of the author(s) and do not necessarily reflect the views of the National Science Foundation.
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Dhebar, Y., Deb, K. (2017). Effect of a Push Operator in Genetic Algorithms for Multimodal Optimization. In: Mandal, J., Dutta, P., Mukhopadhyay, S. (eds) Computational Intelligence, Communications, and Business Analytics. CICBA 2017. Communications in Computer and Information Science, vol 775. Springer, Singapore. https://doi.org/10.1007/978-981-10-6427-2_1
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