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Pareto Set and EMOA Behavior for Simple Multimodal Multiobjective Functions

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Book cover Parallel Problem Solving from Nature - PPSN IX (PPSN 2006)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 4193))

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Abstract

Recent research on evolutionary multiobjective optimization has mainly focused on Pareto fronts. However, we state that proper behavior of the utilized algorithms in decision/search space is necessary for obtaining good results if multimodal objective functions are concerned. Therefore, it makes sense to observe the development of Pareto sets as well. We do so on a simple, configurable problem, and detect interesting interactions between induced changes to the Pareto set and the ability of three optimization algorithms to keep track of Pareto fronts.

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References

  1. Deb, K.: Multi-Objective Optimization using Evolutionary Algorithms. Wiley, Chichester (2001)

    MATH  Google Scholar 

  2. Coello Coello, C.A., Van Veldhuizen, D.A., Lamont, G.B.: Evolutionary Algorithms for Solving Multi-Objective Problems. Kluwer, New York (2002)

    Book  Google Scholar 

  3. Coello, C.A.C.: Evolutionary multi-objective optimization: a historical view of the field. IEEE Computational Intelligence Magazine 1(1), 28–36 (2006)

    Article  Google Scholar 

  4. Neumann, F., Wegener, I.: Minimum spanning trees made easier via multi-objective optimization. In: Beyer, H.G. (ed.) Genetic and evolutionary computation conference (GECCO), pp. 763–769. ACM Press, New York (2005)

    Google Scholar 

  5. Preuss, M., Schönemann, L., Emmerich, M.: Counteracting genetic drift and disruptive recombination in (\(\mu\stackrel{+}{,}\lambda\))-ea on multimodal fitness landscapes. In: Beyer, H.G. (ed.) Genetic and evolutionary computation conference (GECCO), pp. 865–872. ACM Press, New York (2005)

    Google Scholar 

  6. De Jong, K.A.: An analysis of the behavior of a class of genetic adaptive systems. PhD thesis, University of Michigan (1975)

    Google Scholar 

  7. Ehrgott, M.: Multicriteria Optimization, 2nd edn. Springer, Berlin (2005)

    MATH  Google Scholar 

  8. Okabe, T., Jin, Y., Olhofer, M., Sendhoff, B.: On Test Functions for Evolutionary Multi-objective Optimization. In: Yao, X., Burke, E.K., Lozano, J.A., Smith, J., Merelo-Guervós, J.J., Bullinaria, J.A., Rowe, J.E., Tiňo, P., Kabán, A., Schwefel, H.-P. (eds.) PPSN 2004. LNCS, vol. 3242, pp. 792–802. Springer, Heidelberg (2004)

    Chapter  Google Scholar 

  9. Zhou, A., Zhang, Q., Jin, Y., Tsang, E., Okabe, T.: A model-based evolutionary algorithm for bi-objective optimization. In: Congress on Evolutionary Computation (CEC), pp. 2568–2575. IEEE Press, Piscataway (2005)

    Google Scholar 

  10. 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)

    Chapter  Google Scholar 

  11. Naujoks, B., Beume, N., Emmerich, M.: Multi-objective optimisation using S-metric selection: Application to three-dimensional solution spaces. In: Congress on Evolutionary Computation (CEC), pp. 1282–1289. IEEE Press, Piscataway (2005)

    Google Scholar 

  12. Beume, N.: Hypervolumen-basierte Selektion in einem evolutionären Algorithmus zur Mehrzieloptimierung. Diploma thesis, University of Dortmund (2006)

    Google Scholar 

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© 2006 Springer-Verlag Berlin Heidelberg

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Preuss, M., Naujoks, B., Rudolph, G. (2006). Pareto Set and EMOA Behavior for Simple Multimodal Multiobjective Functions. In: Runarsson, T.P., Beyer, HG., Burke, E., Merelo-Guervós, J.J., Whitley, L.D., Yao, X. (eds) Parallel Problem Solving from Nature - PPSN IX. PPSN 2006. Lecture Notes in Computer Science, vol 4193. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11844297_52

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  • DOI: https://doi.org/10.1007/11844297_52

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-38990-3

  • Online ISBN: 978-3-540-38991-0

  • eBook Packages: Computer ScienceComputer Science (R0)

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