Abstract
In this work, a new approach to selection in multiobjective evolutionary algorithms (MOEAs) is proposed. It is based on the portfolio selection problem, which is well known in financial management. The idea of optimizing a portfolio of investments according to both expected return and risk is transferred to evolutionary selection, and fitness assignment is reinterpreted as the allocation of capital to the individuals in the population, while taking into account both individual quality and population diversity. The resulting selection procedure, which unifies parental and environmental selection, is instantiated by defining a suitable notion of (random) return for multiobjective optimization. Preliminary experiments on multiobjective multidimensional knapsack problem instances show that such a procedure is able to preserve diversity while promoting convergence towards the Pareto-optimal front.
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References
Bader, J., Zitzler, E.: HypE: An algorithm for fast hypervolume-based many-objective optimization. Evolutionary Computation 19(1), 45–76 (2011)
Baker, J.E.: Reducing bias and inefficiency in the selection algorithm. In: Proc. Second International Conference on Genetic Algorithms, pp. 14–21 (1987)
Baker, J.E.: Adaptive selection methods for genetic algorithms. In: Proc. First International Conference on Genetic Algorithms, pp. 101–111 (1985)
Beume, N., Naujoks, B., Emmerich, M.: SMS-EMOA: Multiobjective selection based on dominated hypervolume. EJOR 181, 1653–1669 (2007)
Cornuejols, G., Tutuncu, R.: Optimization Methods in Finance. Cambridge University Press (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)
Fonseca, C.M., Fleming, P.J.: Multiobjective optimization and multiple constraint handling with evolutionary algorithms—Part I: A unified formulation. IEEE Transactions on Systems, Man and Cybernetics—Part A: Systems and Humans 28(1), 26–37 (1998)
Goldberg, D.: Genetic Algorithms in Search, Optimization, and Machine Learning. Addison-Wesley, Reading (1989)
Guerreiro, A.P.: Portfolio Selection in Evolutionary Algorithms. Ph.D. thesis proposal, University of Coimbra, Coimbra, Portugal (2012)
Hancock, P.J.B.: An empirical comparison of selection methods in evolutionary algorithms. In: Fogarty, T.C. (ed.) AISB-WS 1994. LNCS, vol. 865, pp. 80–94. Springer, Heidelberg (1994)
Knowles, J., Corne, D.: Properties of an adaptive archiving algorithm for storing nondominated vectors. IEEE Transactions on Evolutionary Computation 7(2), 100–116 (2003)
Knowles, J., Corne, D., Fleisher, M.: Bounded archiving using the Lebesgue measure. In: Proc. IEEE Congress on Evolutionary Computation (CEC 2003), vol. 4, pp. 2490–2497. IEEE Press, New York (2003)
Le, K., Landa-Silva, D.: Obtaining better non-dominated sets using volume dominance. In: IEEE Congress on Evolutionary Computation (CEC 2007), pp. 3119–3126 (September 2007)
Liefooghe, A., Paquete, L., Figueira, J.R.: On local search for bi-objective knapsack problems. Evolutionary Computation 21(1), 179–196 (2013)
López-Ibáñez, M., Knowles, J., Laumanns, M.: On sequential online archiving of objective vectors. In: Takahashi, R.H.C., Deb, K., Wanner, E.F., Greco, S. (eds.) EMO 2011. LNCS, vol. 6576, pp. 46–60. Springer, Heidelberg (2011)
Markowitz, H.: Portfolio selection. Journal of Finance 7(1), 77–91 (1952)
Sareni, B., Krahenbuhl, L.: Fitness sharing and niching methods revisited. IEEE Transactions on Evolutionary Computation 2(3), 97–106 (1998)
Zitzler, E., Laumanns, M., Thiele, L.: SPEA2: Improving the strength pareto evolutionary algorithm. In: Evolutionary Methods for Design, Optimization and Control with Applications to Industrial Problems (EUROGEN 2001), pp. 95–100 (2002)
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., Laumanns, M., Fonseca, C., Grunert da Fonseca, V.: Performance assessment of multiobjective optimizers: An analysis and review. IEEE Transactions on Evolutionary Computation 7(2), 117–132 (2003)
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Yevseyeva, I., Guerreiro, A.P., Emmerich, M.T.M., Fonseca, C.M. (2014). A Portfolio Optimization Approach to Selection in Multiobjective Evolutionary Algorithms. In: Bartz-Beielstein, T., Branke, J., Filipič, B., Smith, J. (eds) Parallel Problem Solving from Nature – PPSN XIII. PPSN 2014. Lecture Notes in Computer Science, vol 8672. Springer, Cham. https://doi.org/10.1007/978-3-319-10762-2_66
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DOI: https://doi.org/10.1007/978-3-319-10762-2_66
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