Abstract
Evolutionary multi-objective algorithms (EMOA) using performance indicators for the selection of individuals have turned out to be a successful technique for multi-objective problems. Especially, the selection based on the \(\mathcal{S}\)-metric, as implemented in the SMS-EMOA, seems to be effective. A special feature of this EMOA is the greedy (μ + 1) selection. Based on a pathological example for a population of size two and a discrete Pareto front it has been proven that a (μ + 1)- (or 1-greedy) EMOA may fail in finding a population maximizing the \(\mathcal{S}\)-metric. This work investigates the performance of (μ + 1)-EMOA with small fixed-size populations on Pareto fronts of innumerable size. We prove that an optimal distribution of points can always be achieved on linear Pareto fronts. Empirical studies support the conjecture that this also holds for convex and concave Pareto fronts, but not for continuous shapes in general. Furthermore, the pathological example is generalized to a continuous objective space and it is demonstrated that also (μ + k)-EMOA are not able to robustly detect the globally optimal distribution.
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References
Beume, N., Fonseca, C.M., López-Ibáñez, M., Paquete, L., Vahrenhold, J.: On the Complexity of Computing the Hypervolume Indicator. Technical Report CI-235/07, Reihe CI, SFB 531 (2007)
Beume, N., Naujoks, B., Emmerich, M.: SMS-EMOA: Multiobjective selection based on dominated hypervolume. European Journal of Operational Research 181(3), 1653–1669 (2007)
Deb, K., Pratap, A., Agarwal, S., Meyarivan, T.: A Fast and Elitist Multiobjective Genetic Algorithm: NSGA–II. IEEE Transactions on Evolutionary Computation 6(2), 182–197 (2002)
Deb, K., Thiele, L., Laumanns, M., Zitzler, E.: Scalable Multi-objective Optimization Test Problems. In: Proc. of the 2002 Congress on Evolutionary Computation (CEC 2002), vol. 1, pp. 825–830. IEEE Press, Piscataway (2002)
Hansen, N., Ostermeier, A.: Completely Derandomized Self-Adaptation in Evolution Strategies. IEEE Computational Intelligence Magazine 9(2), 159–195 (2001)
Schaffer, J.D.: Multiple objective optimization with vector evaluated genetic algorithms. In: Grefenstette, J.J. (ed.) Proc. 1st Int’l. Conf. Genetic Algorithms (ICGA), pp. 93–100. Lawrence Erlbaum, Mahwah (1985)
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.) PPSN 1998. LNCS, vol. 1498, pp. 292–301. Springer, Heidelberg (1998)
Zitzler, E., Thiele, L., Bader, J.: On Set-Based Multiobjective Optimization. Technical Report 300, Computer Engineering and Networks Laboratory, ETH Zurich (February 2008)
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Beume, N., Naujoks, B., Preuss, M., Rudolph, G., Wagner, T. (2009). Effects of 1-Greedy \(\mathcal{S}\)-Metric-Selection on Innumerably Large Pareto Fronts. In: Ehrgott, M., Fonseca, C.M., Gandibleux, X., Hao, JK., Sevaux, M. (eds) Evolutionary Multi-Criterion Optimization. EMO 2009. Lecture Notes in Computer Science, vol 5467. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-01020-0_7
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DOI: https://doi.org/10.1007/978-3-642-01020-0_7
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