Abstract
Multi-modal multi-objective optimization problems are commonly seen in real-world applications. However, most existing researches focus on solving multi-objective optimization problems without multi-modal property or multi-modal optimization problems with single objective. In this paper, we propose a double-niched evolutionary algorithm for multi-modal multi-objective optimization. The proposed algorithm employs a niche sharing method to diversify the solution set in both the objective and decision spaces. We examine the behaviors of the proposed algorithm and its two variants as well as three other existing evolutionary optimizers on three types of polygon-based problems. Our experimental results suggest that the proposed algorithm is able to find multiple Pareto optimal solution sets in the decision space, even if the diversity requirements in the objective and decision spaces are inconsistent or there exist local optimal areas in the decision space.
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References
Deb, K., Pratap, A., Agarwal, S., Meyarivan, T.: A fast and elitist multiobjective genetic algorithm: NSGA-II. IEEE Trans. Evol. Comput. 6(2), 182–197 (2002)
Deb, K., Tiwari, S.: Omni-optimizer: a generic evolutionary algorithm for single and multi-objective optimization. Eur. J. Oper. Res. 185(3), 1062–1087 (2008)
Goldberg, D.E., Richardson, J., et al.: Genetic algorithms with sharing for multimodal function optimization. In: Proceedings of the Second International Conference on Genetic Algorithms Genetic algorithms and their applications, pp. 41–49. Lawrence Erlbaum, Hillsdale (1987)
Horn, J., Nafpliotis, N., Goldberg, D.E.: A Niched Pareto genetic algorithm for multiobjective optimization. In: Proceedings of IEEE World Congress on Computational Intelligence, pp. 82–87. IEEE (1994)
Ishibuchi, H., Akedo, N., Nojima, Y.: A many-objective test problem for visually examining diversity maintenance behavior in a decision space. In: Proceedings of the 13th Annual Conference on Genetic and Evolutionary computation, pp. 649–656. ACM (2011)
Li, J.P., Balazs, M.E., Parks, G.T., Clarkson, P.J.: A species conserving genetic algorithm for multimodal function optimization. Evol. Comput. 10(3), 207–234 (2002)
Liang, J., Yue, C., Qu, B.: Multimodal multi-objective optimization: a preliminary study. In: 2016 IEEE Congress on Evolutionary Computation (CEC), pp. 2454–2461. IEEE (2016)
Liu, Y., Gong, D., Sun, J., Jin, Y.: A many-objective evolutionary algorithm using a one-by-one selection strategy. IEEE Trans. Cybern. 47(9), 2689–2702 (2017)
Liu, Y., Gong, D., Sun, X., Zhang, Y.: Many-objective evolutionary optimization based on reference points. Appl. Soft Comput. 50(1), 344–355 (2017)
Pétrowski, A.: A clearing procedure as a niching method for genetic algorithms. In: Proceedings of IEEE International Conference on Evolutionary Computation, pp. 798–803. IEEE (1996)
Preuss, M., Kausch, C., Bouvy, C., Henrich, F.: Decision space diversity can be essential for solving multiobjective real-world problems. In: Ehrgott, M., Naujoks, B., Stewart, T., Wallenius, J. (eds.) Multiple Criteria Decision Making for Sustainable Energy and Transportation Systems, vol. 634, pp. 367–377. Springer, Heidelberg (2010). https://doi.org/10.1007/978-3-642-04045-0_31
Thomsen, R.: Multimodal optimization using crowding-based differential evolution. In: IEEE Congress on Evolutionary Computation, vol. 2, pp. 1382–1389. IEEE (2004)
Yue, C., Qu, B., Liang, J.: A multi-objective particle swarm optimizer using ring topology for solving multimodal multi-objective problems. IEEE Trans. Evol. Comput. (2017, early access)
Zhang, Q., Li, H.: MOEA/D: a multiobjective evolutionary algorithm based on decomposition. IEEE Trans. Evol. Comput. 11(6), 712–731 (2007)
Zitzler, E., Künzli, S.: Indicator-based selection in multiobjective search. In: Yao, X. (ed.) Parallel Problem Solving from Nature-PPSN VIII, vol. 3242, pp. 832–842. Springer, Heidelberg (2004). https://doi.org/10.1007/978-3-540-30217-9_84
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This work was supported by the Science and Technology Innovation Committee Foundation of Shenzhen (Grant No. ZDSYS201703031748284).
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Liu, Y., Ishibuchi, H., Nojima, Y., Masuyama, N., Shang, K. (2018). A Double-Niched Evolutionary Algorithm and Its Behavior on Polygon-Based Problems. In: Auger, A., Fonseca, C., Lourenço, N., Machado, P., Paquete, L., Whitley, D. (eds) Parallel Problem Solving from Nature – PPSN XV. PPSN 2018. Lecture Notes in Computer Science(), vol 11101. Springer, Cham. https://doi.org/10.1007/978-3-319-99253-2_21
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