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A memetic differential evolution algorithm based on dynamic preference for constrained optimization problems. (English) Zbl 1442.90179

Summary: The constrained optimization problem (COP) is converted into a biobjective optimization problem first, and then a new memetic differential evolution algorithm with dynamic preference is proposed for solving the converted problem. In the memetic algorithm, the global search, which uses differential evolution (DE) as the search scheme, is guided by a novel fitness function based on achievement scalarizing function (ASF). The novel fitness function constructed by a reference point and a weighting vector adjusts preference dynamically towards different objectives during evolution, in which the reference point and weighting vector are determined adapting to the current population. In the local search procedure, simplex crossover (SPX) is used as the search engine, which concentrates on the neighborhood embraced by both the best feasible and infeasible individuals and guides the search approaching the optimal solution from both sides of the boundary of the feasible region. As a result, the search can efficiently explore and exploit the search space. Numerical experiments on 22 well-known benchmark functions are executed, and comparisons with five state-of-the-art algorithms are made. The results illustrate that the proposed algorithm is competitive with and in some cases superior to the compared ones in terms of the quality, efficiency, and the robustness of the obtained results.

MSC:

90C30 Nonlinear programming
68T05 Learning and adaptive systems in artificial intelligence
90C59 Approximation methods and heuristics in mathematical programming
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[1] Mohamed, A. W.; Sabry, H. Z., Constrained optimization based on modified differential evolution algorithm, Information Sciences, 194, 171-208 (2012)
[2] Runarsson, T. P.; Yao, X., Stochastic ranking for constrained evolutionary optimization, IEEE Transactions on Evolutionary Computation, 4, 3, 284-294 (2000)
[3] Deb, K., An efficient constraint handling method for genetic algorithms, Computer Methods in Applied Mechanics and Engineering, 186, 2-4, 311-338 (2000) · Zbl 1028.90533
[4] Farmani, R.; Wright, J. A., Self-adaptive fitness formulation for constrained optimization, IEEE Transactions on Evolutionary Computation, 7, 5, 445-455 (2003)
[5] Tessema, B.; Yen, G. G., An adaptive penalty formulation for constrained evolutionary optimization, IEEE Transactions on Systems, Man, and Cybernetics Part A: Systems and Humans, 39, 3, 565-578 (2009)
[6] Powell, D.; Skolnick, M. M., Using genetic algorithms in engineering design optimization with nonlinear constraints, Proceedings of the 5th International Conference on Genetic Algorithms (ICGA ’93)
[7] Zhou, Y.-R.; Li, Y.-X.; Wang, Y.; Kang, L.-S., Pareto strength evolutionary algorithm for constrained optimization, Journal of Software, 14, 7, 1243-1249 (2003) · Zbl 1092.68659
[8] Cai, Z.; Wang, Y., A multiobjective optimization-based evolutionary algorithm for constrained optimization, IEEE Transactions on Evolutionary Computation, 10, 6, 658-675 (2006)
[9] Wang, Y.; Cai, Z.; Zhou, Y.; Zeng, W., An adaptive tradeoff model for constrained evolutionary optimization, IEEE Transactions on Evolutionary Computation, 12, 1, 80-92 (2008)
[10] Takahama, T.; Sakai, S., Constrained optimization by the ε constrained differential evolution with gradient-based mutation and feasible elites, Proceedings of the IEEE Congress on Evolutionary Computation (CEC ’06)
[11] Runarsson, T. P.; Yao, X., Search biases in constrained evolutionary optimization, IEEE Transactions on Systems, Man and Cybernetics Part C: Applications and Reviews, 35, 2, 233-243 (2005)
[12] Mezura-Montes, E.; Coello Coello, C. A., A simple multimembered evolution strategy to solve constrained optimization problems, IEEE Transactions on Evolutionary Computation, 9, 1, 1-17 (2005)
[13] Sun, C.-L.; Zeng, J.-C.; Pan, J.-S., An improved vector particle swarm optimization for constrained optimization problems, Information Sciences, 181, 6, 1153-1163 (2011)
[14] Ghosh, A.; Das, S.; Chowdhury, A.; Giri, R., An improved differential evolution algorithm with fitness-based adaptation of the control parameters, Information Sciences, 181, 18, 3749-3765 (2011)
[15] Gong, W.; Fialho, Á.; Cai, Z.; Li, H., Adaptive strategy selection in differential evolution for numerical optimization: An Empirical Study, Information Sciences, 181, 24, 5364-5386 (2011)
[16] Weber, M.; Neri, F.; Tirronen, V., A study on scale factor in distributed differential evolution, Information Sciences, 181, 12, 2488-2511 (2011)
[17] Lampinen, J., A constraint handling approach for the differential evolution algorithm, Proceedings of the Congress on Evolutionary Computation (CEC ’2002), IEEE Press
[18] Zhang, C.; Li, X.; Gao, L.; Wu, Q., An improved electromagnetism-like mechanism algorithm for constrained optimization, Expert Systems with Applications, 40, 14, 5621-5634 (2013)
[19] Wang, Y.; Cai, Z., Combining multiobjective optimization with differential evolution to solve constrained optimization problems, IEEE Transactions on Evolutionary Computation, 16, 1, 117-134 (2012)
[20] Zhang, M.; Luo, W.; Wang, X., Differential evolution with dynamic stochastic selection for constrained optimization, Information Sciences, 178, 15, 3043-3074 (2008)
[21] Mezura-Montes, E.; Velázquez-Reyes, J.; Coello, C. A. C., Promising infeasibility and multiple offspring incorporated to differential evolution for constrained optimization, Proceedings of the Genetic and Evolutionary Computation Conference (GECCO ’05)
[22] Jia, G.; Wang, Y.; Cai, Z.; Jin, Y., An improved (μ+λ)-constrained differential evolution for constrained optimization, Information Sciences, 222, 302-322 (2013) · Zbl 1293.68228
[23] Huang, V. L.; Qin, A. K.; Suganthan, P. N., Self-adaptive differential evolution algorithm for constrained real-parameter optimization, Proceedings of the IEEE Congress on Evolutionary Computation (CEC ’06)
[24] Elsayed, S. M.; Sarker, R. A.; Essam, D. L., On an evolutionary approach for constrained optimization problem solving, Applied Soft Computing Journal, 12, 10, 3208-3227 (2012)
[25] Boussaïd, I.; Chatterjee, A.; Siarry, P.; Ahmed-Nacer, M., Biogeography-based optimization for constrained optimization problems, Computers & Operations Research, 39, 12, 3293-3304 (2012) · Zbl 1349.90847
[26] Storn, R.; Price, K., Differential evolution-a simple and efficient adaptative scheme for global optimization over continuous spaces, TR-95-12 (1995), Berkeley, Calif, USA: International Computer Science, Berkeley, Calif, USA
[27] Tsutsui, S.; Yamamura, M.; Higuchi, T., Multi-parent recombination with simplex crossover in real-coded genetic algorithms, Proceedings of the Genetic and Evolutionary Computing Conference, Morgan Kaufmann
[28] Miettinen, K., Nonlinear Multiobjective Optimization. Nonlinear Multiobjective Optimization, International Series in Operations Research & Management Science, 12, xxii+298 (1999), Boston, Mass, USA: Kluwer Academic Publishers, Boston, Mass, USA
[29] Ben Hamida, S.; Schoenauer, M., ASCHEA: new results using adaptive segregational constraint handling, Proceedings of the Congress on Evolutionary Computation (CEC ’2002), IEEE Press
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