Abstract
Among the multi-objective optimization methods proposed so far, Genetic Algorithms (GA) have been shown to be more effective in recent decades. Most of such methods were developed to solve primarily unconstrained problems. However, many real-world problems are constrained, which necessitates appropriate handling of constraints. Despite much effort devoted to the studies of constraint-handling methods, it has been reported that each of them has certain limitations. Hence, further studies for designing more effective constraint-handling methods are needed.
For this reason, we investigated the guidelines for a method to effectively handle constraints. Based on these guidelines, we designed a new constraint-handling method, Pareto Descent Repair operator (PDR), in which ideas derived from multi-objective local search and gradient projection method are incorporated. An experiment comparing GA that use PDR and some of the existing constraint-handling methods confirmed the effectiveness of PDR.
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References
Deb, K.: Multi-Objective Optimization Using Evolutionary Algorithms. John Wiley & Sons, Chichester (2001)
Coello, C.A.C.: Theoretical and numerical constraint handling techniques used with evolutionary algorithms: A survey of the state of the art. Computer Methods in Applied Mechanics and Engineering 191(11-12), 1245–1287 (2002)
Knowles, J.D., Corne, D.W.: Memetic algorithms for multiobjective optimization: issues, methods and prospects. In: Krasnogor, N., Smith, J.E., Hart, W.E. (eds.) Recent Advances in Memetic Algorithms, pp. 313–352. Springer, Heidelberg (2004)
Coello, C.A.C.: Treating constraints as objectives for single-objective evolutionary optimization. Engineering Optimization 32(3), 275–308 (2000)
Deb, K.: An efficient constraint handling method for genetic algorithms. Computer Methods in Applied Mechanics and Engineering 186, 311–338 (2000)
Oyama, A., Shimoyama, K., Fujii, K.: New constraint-handling method for multi-objective multi-constraint evolutionary optimization and its application to space plane design. In: Schilling, R., Haase, W., Periaux, J., Baier, H., Bugeda, G. (eds.) Evolutionary and Deterministic Methods for Design, Optimization and Control with Applications to Industrial and Societal Problems (EUROGEN 2005), pp. 416–428 (2005)
Michalewicz, Z., Nazhiyath, G.: Genocop III: A co-evolutionary algorithm for numerical optimization problems with nonlinear constraints. In: Proceedings of the 2nd IEEE International Conference on Evolutionary Computation, vol. 2, pp. 647–651. IEEE Computer Society Press, Los Alamitos (1995)
Harada, K., Sakuma, J., Ikeda, K., Ono, I., Kobayashi, S.: Local search for multiobjective function optimization: Pareto descent method ((in Japanese)). Transactions of the Japanese Society for Artificial Intelligence 21(4), 340–350 (2006)
Harada, K., Sakuma, J., Ikeda, K., Ono, I., Kobayashi, S.: Local search for multiobjective function optimization: Pareto descent method. In: Proceedings of the Genetic and Evolutionary Computation Conference (GECCO-2006), pp. 659–666. ACM Press, New York (2006)
Luenberger, D.G.: Linear and Nonlinear Programming. Addison-Wesley, Reading (1984)
Gellert, W., Gottwald, S., Hellwich, M., Kästner, H., Künstner, H.: VNR Concise Encyclopedia of Mathematics. Van Nostrand Reinhold, New York (1989)
Cormen, T.H., Leiserson, C.E., Rivest, R.L., Stein, C.: Introduction to Algorithms, 2nd edn. MIT Press, Cambridge (2001)
Ono, I., Kobayashi, S.: A real-coded genetic algorithm for function optimization using unimodal normal distribution crossover. In: 7th International Conference on Genetic Algorithms (ICGA7), pp. 246–253 (1997)
Knowles, J.D., Corne, D.W.: On metrics for comparing non-dominated sets. In: Proceedings of the 2002 Congress on Evolutionary Computation Conference (CEC02), pp. 711–716. IEEE Computer Society Press, Los Alamitos (2002)
Harada, K., Sakuma, J., Kobayashi, S., Ikeda, K., Ono, I.: Hybridization of genetic algorithm and local search in multiobjective function optimization: Recommendation of GA then LS. In: Proceedings of the Genetic and Evolutionary Computation Conference (GECCO-2006), pp. 667–674. ACM Press, New York (2006)
Harada, K., Ikeda, K., Sakuma, J., Ono, I., Kobayashi, S.: Hybridization of genetic algorithm with local search in multiobjective function optimization: Recommendation of GA then LS ((in Japanese)). Transactions of the Japanese Society for Artificial Intelligence 21(6), 482–492 (2006)
Zitzler, E., Laumanns, M., Thiele, L.: SPEA2: Improving the strength pareto evolutionary algorithm for multiobjective optimization. In: Giannakoglou, K., et al. (eds.) EUROGEN 2001, Evolutionary Methods for Design, Optimization and Control with Applications to Industrial Problems, pp. 12–21 (2001)
Deb, K., Thiele, L., Laumanns, M., Zitzler, E.: Scalable multi-objective optimization test problems. In: Proceedings of the Congress on Evolutionary Computation (CEC-2002), pp. 825–830 (2002)
Fliege, J., Svaiter, B.F.: Steepest descent methods for multicriteria optimization. Mathematical Methods of Operations Research 51(3), 479–494 (2000)
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Harada, K., Sakuma, J., Ono, I., Kobayashi, S. (2007). Constraint-Handling Method for Multi-objective Function Optimization: Pareto Descent Repair Operator. In: Obayashi, S., Deb, K., Poloni, C., Hiroyasu, T., Murata, T. (eds) Evolutionary Multi-Criterion Optimization. EMO 2007. Lecture Notes in Computer Science, vol 4403. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-70928-2_15
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DOI: https://doi.org/10.1007/978-3-540-70928-2_15
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