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A Portfolio Optimization Approach to Selection in Multiobjective Evolutionary Algorithms

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Part of the Lecture Notes in Computer Science book series (LNTCS,volume 8672)

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

  1. Bader, J., Zitzler, E.: HypE: An algorithm for fast hypervolume-based many-objective optimization. Evolutionary Computation 19(1), 45–76 (2011)

    Article  Google Scholar 

  2. Baker, J.E.: Reducing bias and inefficiency in the selection algorithm. In: Proc. Second International Conference on Genetic Algorithms, pp. 14–21 (1987)

    Google Scholar 

  3. Baker, J.E.: Adaptive selection methods for genetic algorithms. In: Proc. First International Conference on Genetic Algorithms, pp. 101–111 (1985)

    Google Scholar 

  4. Beume, N., Naujoks, B., Emmerich, M.: SMS-EMOA: Multiobjective selection based on dominated hypervolume. EJOR 181, 1653–1669 (2007)

    Article  MATH  Google Scholar 

  5. Cornuejols, G., Tutuncu, R.: Optimization Methods in Finance. Cambridge University Press (2007)

    Google Scholar 

  6. 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)

    Article  Google Scholar 

  7. 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)

    Article  Google Scholar 

  8. Goldberg, D.: Genetic Algorithms in Search, Optimization, and Machine Learning. Addison-Wesley, Reading (1989)

    MATH  Google Scholar 

  9. Guerreiro, A.P.: Portfolio Selection in Evolutionary Algorithms. Ph.D. thesis proposal, University of Coimbra, Coimbra, Portugal (2012)

    Google Scholar 

  10. 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)

    Chapter  Google Scholar 

  11. Knowles, J., Corne, D.: Properties of an adaptive archiving algorithm for storing nondominated vectors. IEEE Transactions on Evolutionary Computation 7(2), 100–116 (2003)

    Article  Google Scholar 

  12. 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)

    Google Scholar 

  13. 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)

    Google Scholar 

  14. Liefooghe, A., Paquete, L., Figueira, J.R.: On local search for bi-objective knapsack problems. Evolutionary Computation 21(1), 179–196 (2013)

    Article  Google Scholar 

  15. 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)

    Chapter  Google Scholar 

  16. Markowitz, H.: Portfolio selection. Journal of Finance 7(1), 77–91 (1952)

    Google Scholar 

  17. Sareni, B., Krahenbuhl, L.: Fitness sharing and niching methods revisited. IEEE Transactions on Evolutionary Computation 2(3), 97–106 (1998)

    Article  Google Scholar 

  18. 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)

    Google Scholar 

  19. 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)

    Chapter  Google Scholar 

  20. 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)

    Article  Google Scholar 

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© 2014 Springer International Publishing Switzerland

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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

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-10761-5

  • Online ISBN: 978-3-319-10762-2

  • eBook Packages: Computer ScienceComputer Science (R0)

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