Analyzing the Effect of Objective Correlation on the Efficient Set of MNK-Landscapes

  • Sébastien Verel
  • Arnaud Liefooghe
  • Laetitia Jourdan
  • Clarisse Dhaenens
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6683)

Abstract

In multiobjective combinatorial optimization, there exists two main classes of metaheuristics, based either on multiple aggregations, or on a dominance relation. As in the single-objective case, the structure of the search space can explain the difficulty for multiobjective metaheuristics, and guide the design of such methods. In this work we analyze the properties of multiobjective combinatorial search spaces. In particular, we focus on the features related the efficient set, and we pay a particular attention to the correlation between objectives. Few benchmark takes such objective correlation into account. Here, we define a general method to design multiobjective problems with correlation. As an example, we extend the well-known multiobjective NK-landscapes. By measuring different properties of the search space, we show the importance of considering the objective correlation on the design of metaheuristics.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Ehrgott, M., Klamroth, K.: Connectedness of efficient solutions in multiple criteria combinatorial optimization. European Journal of Operational Research 97(1), 159–166 (1997)CrossRefMATHGoogle Scholar
  2. 2.
    Mote, J., Olson, I.M.D.L.: A parametric approach to solving bicriterion shortest path problems. European Journal of Operational Research 53(1), 81–92 (1991)CrossRefMATHGoogle Scholar
  3. 3.
    Paquete, L., Stützle, T.: A study of stochastic local search algorithms for the biobjective QAP with correlated flow matrices. European Journal of Operational Research 169(3), 943–959 (2006)MathSciNetCrossRefMATHGoogle Scholar
  4. 4.
    Knowles, J., Corne, D.: Instance generators and test suites for the multiobjective quadratic assignment problem. In: Fonseca, C.M., Fleming, P.J., Zitzler, E., Deb, K., Thiele, L. (eds.) EMO 2003. LNCS, vol. 2632, pp. 295–310. Springer, Heidelberg (2003)CrossRefGoogle Scholar
  5. 5.
    Aguirre, H.E., Tanaka, K.: Working principles, behavior, and performance of MOEAs on MNK-landscapes. European Journal of Operational Research 181(3), 1670–1690 (2007)CrossRefMATHGoogle Scholar
  6. 6.
    Ehrgott, M.: Multicriteria optimization, 2nd edn. Springer, Heidelberg (2005)MATHGoogle Scholar
  7. 7.
    Paquete, L., Stützle, T.: Stochastic local search algorithms for multiobjective combinatorial optimization: A review. In: Handbook of Approximation Algorithms and Metaheuristics. Computer & Information Science Series, vol. 13, Chapman & Hall / CRC (2007)Google Scholar
  8. 8.
    Knowles, J., Corne, D.: Bounded Pareto archiving: Theory and practice. In: Metaheuristics for Multiobjective Optimisation. LNEMS, vol. 535, pp. 39–64. Springer, Heidelberg (2004)CrossRefGoogle Scholar
  9. 9.
    Gorski, J., Klamroth, K., Ruzika, S.: Connectedness of efficient solutions in multiple objective combinatorial optimization. Technical Report 102/2006, University of Kaiserslautern, Department of Mathematics (2006)Google Scholar
  10. 10.
    Paquete, L., Stützle, T.: Clusters of non-dominated solutions in multiobjective combinatorial optimization: An experimental analysis. In: Multiobjective Programming and Goal Programming. LNEMS, vol. 618, pp. 69–77. Springer, Heidelberg (2009)CrossRefGoogle Scholar
  11. 11.
    Kauffman, S.A.: The Origins of Order. Oxford University Press, New York (1993)Google Scholar
  12. 12.
    Hotelling, H., Pabst, M.R.: Rank correlation and tests of significance involving no assumptions of normality. Ann. Math. Stat. 7, 29–43 (1936)CrossRefMATHGoogle Scholar
  13. 13.
    Weinberger, E.D.: Correlated and uncorrelatated fitness landscapes and how to tell the difference. Biological Cybernetics 63, 325–336 (1990)CrossRefMATHGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  • Sébastien Verel
    • 1
    • 3
  • Arnaud Liefooghe
    • 2
    • 3
  • Laetitia Jourdan
    • 3
  • Clarisse Dhaenens
    • 2
    • 3
  1. 1.CNRSUniversity of Nice Sophia AntipolisFrance
  2. 2.LIFL – CNRSUniversité Lille 1France
  3. 3.INRIA Lille-Nord EuropeFrance

Personalised recommendations