Abstract
Penalty parameters play a key role when adopting the penalty function method for solution ranking. In the previous study, a corresponding relationship between the constrained optimization problems and the penalty parameters was constructed. This paper tries to verify whether the relationship is related with the evolutionary algorithms (EAs), i.e., how the EAs influence the relationship. Two differential evolution algorithms are taken as an example. Experimental results confirm the influence and show that an improved EA will enlarge the available value of corresponding penalty parameter, especially for the intermittent relationship. The findings also prove that EA can make up the shortcoming of constraint handling techniques to some extent.
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References
Mezura-Montes, E., Coello, C.A.C.: A simple multimembered evolution strategy to solve constrained optimization problems. IEEE Trans. Evol. Comput. 9(1), 1–17 (2005)
Mezura-Montes, E., Coello, C.A.C.: Constraint-handling in nature-inspired numerical optimization: past, present and future. Swarm Evol. Comput. 1(4), 173–194 (2011)
Li, X., Yao, X.: Cooperatively coevolving particle swarm for large scale optimization. IEEE Tran. Evol. Comput. 16(2), 210–224 (2012)
Zhao, S.Z., Suganthan, P.N., Zhang, Q.: Decomposition based multiobjetive evolutionary algorithm with an ensemble of neighborhood sizes. IEEE Trans. Evol. Comput. 16(3), 442–446 (2012)
Mallipeddi, R., Suganthan, P.N.: Ensemble of constraint handling techniques. IEEE Tran. Evol. Comput. 14(4), 561–579 (2010)
Wang, Y., Cai, Z., Zhou, Y., Zeng, W.: An adaptive tradeoff model for constrained evolutionary optimization. IEEE Trans. Evol. Comput. 12(1), 80–92 (2008)
Michalewicz, Z.: Quo Vadis, evolutionary computation? on a growing gap between theory and practice. In: Liu, J., Alippi, C., Bouchon-Meunier, B., Greenwood, Garrison W., Abbass, Hussein A. (eds.) WCCI 2012. LNCS, vol. 7311, pp. 98–121. Springer, Heidelberg (2012). doi:10.1007/978-3-642-30687-7_6
Tsang, E., Kwan, A.: Mapping constraint satisfaction problems to algorithms and heuristics. Technical report, CSM-198 (1993)
Mezura-Montes, E., Miranda-Varela, M.E., Gómez-Ramón, R.C.: Differential evolution in constrained numerical optimization: an empirical study. Inform. Sci. 180(22), 4223–4262 (2010)
Gibbs, M., Maier, H., Dandy, G.: Relationship between problem characteristics and the optimal number of genetic algorithm generations. Eng. Optim. 43(4), 349–376 (2011)
Si, C., Wang, L., Wu, Q.: Mapping constrained optimization problems to algorithms and constraint handling techniques. In: Proceedings of the CEC, pp. 3308–3315 (2012)
Si, C., Hu, J., Lan, T., Wang, L., Wu, Q.: A combined constraint handling framework: an empirical study. Memet. Comput. 9(1), 69–88 (2017)
Si, C., Shen, J., Zou, X., Wang, L., Wu, Q.: Mapping constrained optimization problems to penalty parameters: an empirical study. In: Proceedings of the CEC, pp. 3073–3079 (2014)
Storn, R., Price, K.: Differential evolution: a simple and efficient adaptive scheme for global optimization over continuous spaces. Technical report, TR-95-012 (1995)
Das, S., Suganthan, P.N.: Differential evolution: a survey of the state-of-the-art. IEEE Trans. Evol. Comput. 15(1), 4–31 (2011)
Menchaca-Mendez, K., Coello Coello, C.A.: Solving multiobjective optimization problems using differential evolution and a maximin selection criterion. In: Proceedings of the CEC, pp. 3143–3150 (2012)
Wang, Y., Cai, Z., Zhang, Q.: Differential evolution with composite trial vector generation strategies and control parameters. IEEE Trans. Evol. Comput. 15(1), 55–66 (2011)
Si, C., Lan, T., Hu, J., Wang, L., Wu, Q.: On the penalty parameter of the penalty function method. Control Decis. 9, 1707–1710 (2014)
Liang, J.J., Runarsson, T.P., Mezura-Montes, E., Clerc, M., Suganthan, P.N., Coello Coello, C.A., Deb, K.: Problem definitions and evaluation criteria for the CEC 2006. Technical report, Special Session on Constrained Real-Parameter Optimization (2006)
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This work was supported in part by the National Natural Science Foundation of China under Grants 71371142, Shanghai Young Teachers’ Training Program under Grants ZZslg15087.
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Si, C., Shen, J., Zou, X., Wang, L. (2017). Comparison of Differential Evolution Algorithms on the Mapping Between Problems and Penalty Parameters. In: Tan, Y., Takagi, H., Shi, Y. (eds) Advances in Swarm Intelligence. ICSI 2017. Lecture Notes in Computer Science(), vol 10385. Springer, Cham. https://doi.org/10.1007/978-3-319-61824-1_46
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DOI: https://doi.org/10.1007/978-3-319-61824-1_46
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