Abstract
The multi-objective covariance matrix adaptation evolution strategy (MO-CMA-ES) combines a mutation operator that adapts its search distribution to the underlying optimization problem with multi-criteria selection. Here, a generational and two steady-state selection schemes for the MO-CMA-ES are compared. Further, a recently proposed method for computationally efficient adaptation of the search distribution is evaluated in the context of the MO-CMA-ES.
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References
Rechenberg, I.: Evolutionsstrategie: Optimierung Technischer Systeme nach Prinzipien der Biologischen Evolution. Werkstatt Bionik und Evolutionstechnik. Frommann-Holzboog, Stuttgart (1973)
Schwefel, H.-P.: Evolution and Optimum Seeking. Sixth-Generation Computer Technology Series. John Wiley & Sons, Chichester (1995)
Hansen, N., Ostermeier, A.: Completely derandomized self-adaptation in evolution strategies. Evolutionary Computation 9(2), 159–195 (2001)
Kern, S., Müller, S., Hansen, N., Büche, D., Ocenasek, J., Koumoutsakos, P.: Learning probability distributions in continuous evolutionary algorithms – A comparative review. Natural Computing 3, 77–112 (2004)
Igel, C., Hansen, N., Roth, S.: Covariance matrix adaptation for multi-objective optimization. Evolutionary Computation (Accepted, 2006)
Deb, K., Agrawal, S., Pratap, A., Meyarivan, T.: A fast and elitist multiobjective genetic algorithm: NSGA-II. IEEE Transactions on Evolutionary Computation 6(2), 182–197 (2002)
Emmerich, M., Beume, N., Naujoks, B.: An EMO algorithm using the hypervolume measure as selection criterion. In: Coello Coello, C.A., Hernández Aguirre, A., Zitzler, E. (eds.) EMO 2005. LNCS, vol. 3410, pp. 62–76. Springer, Heidelberg (2005)
Beume, N., Naujoks, B., Emmerich, M.: SMS-EMOA: Multiobjective selection based on dominated hypervolume. European Journal of Operational Research (In press, 2007)
Igel, C., Suttorp, T., Hansen, N.: A computational efficient covariance matrix update and a (1+1)-CMA for evolution strategies. In: Proceedings of the Genetic and Evolutionary Computation Conference (GECCO 2006), pp. 453–460. ACM Press, New York (2006)
Hansen, N., Müller, S.D., Koumoutsakos, P.: Reducing the time complexity of the derandomized evolution strategy with covariance matrix adaptation (CMA-ES). Evolutionary Computation 11(1), 1–18 (2003)
Grewal, M.S., Andrews, A.P.: Kalman Filtering: Theory and Practice. Prentice-Hall, Englewood Cliffs (1993)
Deb, K.: Multi-Objective Optimization Using Evolutionary Algorithms. Wiley, Chichester (2001)
Zitzler, E., Thiele, L.: Multiobjective optimization using evolutionary algorithms – a comparative case study. In: Eiben, A.E., Bäck, T., Schoenauer, M., Schwefel, H.-P. (eds.) Parallel Problem Solving from Nature - PPSN V. LNCS, vol. 1498, pp. 292–301. Springer, Heidelberg (1998)
Whitley, L.D.: The GENITOR algorithm and selection pressure: Why rank–based allocation of reproductive trials is best. In: Schaffer, J.D. (ed.) Proceedings of the Third International Conference on Genetic Algorithms (ICGA’89), pp. 116–121. Morgan Kaufmann, San Francisco (1989)
Syswerda, G.: Uniform crossover in genetic algorithms. In: Schaffer, J.D. (ed.) Proceedings of the Third International Conference on Genetic Algorithms (ICGA’89), pp. 2–9. Morgan Kaufmann, San Francisco (1989)
Iorio, A., Li, X.: Solving rotated multi-objective optimization problems using differential evolution. In: Webb, G.I., Yu, X. (eds.) AI 2004. LNCS (LNAI), vol. 3339, pp. 861–872. Springer, Heidelberg (2004)
Knowles, J., Thiele, L., Zitzler, E.: A tutorial on the performance assessment of stochastic multiobjective optimizers. TIK-Report 214, Computer Engineering and Networks Laboratory (TIK), Swiss Federal Institute of Technology (ETH) Zurich (2005)
Zitzler, E., Thiele, L., Laumanns, M., Fonseca, C.M., Grunert da Fonseca, V.: Performance assesment of multiobjective optimizers: An analysis and review. IEEE Transactions on Evolutionary Computation 7(2), 117–132 (2003)
Bleuler, S., Laumanns, M., Thiele, L., Zitzler, E.: PISA – A platform and programming language independent interface for search algorithms. In: Fonseca, C.M., Fleming, P.J., Zitzler, E., Deb, K., Thiele, L. (eds.) EMO 2003. LNCS, vol. 2632, pp. 494–508. Springer, Heidelberg (2003)
Fonseca, C.M., Fleming, P.J.: Multiobjective optimization and multiple constraint handling with evolutionary algorithms—Part II: Application example. IEEE Transactions on Systems, Man, and Cybernetics, Part A: Systems and Humans 28(1), 38–47 (1998)
Zitzler, E., Deb, K., Thiele, L.: Comparison of multiobjective evolutionary algorithms: Empirical results. Evolutionary Computation 8(2), 173–195 (2000)
Deb, K., Sinha, A., Kukkonen, S.: Multi-objective test problems, linkages, and evolutionary methodologies. In: Proceedings of the Genetic and Evolutionary Computation Conference (GECCO 2006), pp. 1141–1148. ACM Press, New York (2006)
Iorio, A.W., Li, X.: Rotated test problems for assessing the performance of multi-objective optimization algorithms. In: Proceedings of the Genetic and Evolutionary Computation Conference (GECCO 2006), pp. 683–690. ACM Press, New York (2006)
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Igel, C., Suttorp, T., Hansen, N. (2007). Steady-State Selection and Efficient Covariance Matrix Update in the Multi-objective CMA-ES. 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_16
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DOI: https://doi.org/10.1007/978-3-540-70928-2_16
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