Pareto Local Search Algorithms for Anytime Bi-objective Optimization

  • Jérémie Dubois-Lacoste
  • Manuel López-Ibáñez
  • Thomas Stützle
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7245)

Abstract

Pareto local search (PLS) is an extension of iterative improvement methods for multi-objective combinatorial optimization problems and an important part of several state-of-the-art multi-objective optimizers. PLS stops when all neighbors of the solutions in its solution archive are dominated. If terminated before completion, it may produce a poor approximation to the Pareto front. This paper proposes variants of PLS that improve its anytime behavior, that is, they aim to maximize the quality of the Pareto front at each time step. Experimental results on the bi-objective traveling salesman problem show a large improvement of the proposed anytime PLS algorithm over the classical one.

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References

  1. 1.
    Beume, N., Naujoks, B., Emmerich, M.: SMS-EMOA: Multiobjective selection based on dominated hypervolume. European Journal of Operational Research 181(3), 1653–1669 (2007)MATHCrossRefGoogle Scholar
  2. 2.
    Conover, W.J.: Practical Nonparametric Statistics. John Wiley & Sons (1999)Google Scholar
  3. 3.
    Deb, K., Pratap, A., Agarwal, S., Meyarivan, T.: A fast and elitist multi-objective genetic algorithm: NSGA-II. IEEE Trans. Evol. Comput. 6(2), 181–197 (2002)CrossRefGoogle Scholar
  4. 4.
    Dubois-Lacoste, J., López-Ibáñez, M., Stützle, T.: A hybrid TP+PLS algorithm for bi-objective flow-shop scheduling problems. Computers & Operations Research 38(8), 1219–1236 (2011)MathSciNetMATHCrossRefGoogle Scholar
  5. 5.
    Dubois-Lacoste, J., López-Ibáñez, M., Stützle, T.: Improving the anytime behavior of two-phase local search. Annals of Mathematics and Artificial Intelligence 61(2), 125–154 (2011)CrossRefGoogle Scholar
  6. 6.
    Dubois-Lacoste, J., López-Ibáñez, M., Stützle, T.: Supplementary Material: Pareto Local Search Variants for Anytime Bi-Objective Optimization (2012), http://iridia.ulb.ac.be/supp/IridiaSupp2012-004
  7. 7.
    Ehrgott, M., Gandibleux, X.: Approximative solution methods for combinatorial multicriteria optimization. TOP 12(1), 1–88 (2004)MathSciNetMATHCrossRefGoogle Scholar
  8. 8.
    Liefooghe, A., Mesmoudi, S., Humeau, J., Jourdan, L., Talbi, E.G.: On dominance-based multiobjective local search: design, implementation and experimental analysis on scheduling and traveling salesman problems. Journal of Heuristics (2011)Google Scholar
  9. 9.
    Loudni, S., Boizumault, P.: Combining VNS with constraint programming for solving anytime optimization problems. European Journal of Operational Research 191, 705–735 (2008)MATHCrossRefGoogle Scholar
  10. 10.
    Lust, T., Jaszkiewicz, A.: Speed-up techniques for solving large-scale biobjective TSP. Computers & Operations Research 37(3), 521–533 (2010)MathSciNetMATHCrossRefGoogle Scholar
  11. 11.
    Lust, T., Teghem, J.: The multiobjective multidimensional knapsack problem: a survey and a new approach. Arxiv preprint arXiv:1007.4063 (2010)Google Scholar
  12. 12.
    Lust, T., Teghem, J.: Two-phase Pareto local search for the biobjective traveling salesman problem. Journal of Heuristics 16(3), 475–510 (2010)MATHCrossRefGoogle Scholar
  13. 13.
    Paquete, L., Chiarandini, M., Stützle, T.: Pareto local optimum sets in the biobjective traveling salesman problem: An experimental study. In: Gandibleux, X., et al. (eds.) Metaheuristics for Multiobjective Optimisation. LNEMS, vol. 535, pp. 177–200. Springer (2004)Google Scholar
  14. 14.
    Paquete, L., Stützle, T.: Design and analysis of stochastic local search for the multiobjective traveling salesman problem. Computers & Operations Research 36(9), 2619–2631 (2009)MathSciNetMATHCrossRefGoogle Scholar
  15. 15.
    Zilberstein, S.: Using anytime algorithms in intelligent systems. AI Magazine 17(3), 73–83 (1996)Google Scholar
  16. 16.
    Zitzler, E., Laumanns, M., Thiele, L.: SPEA2: Improving the strength Pareto evolutionary algorithm for multiobjective optimization. In: Giannakoglou, K., et al. (eds.) Evolutionary Methods for Design, Optimisation and Control, pp. 95–100. CIMNE, Barcelona (2002)Google Scholar
  17. 17.
    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 V 1998. LNCS, vol. 1498, pp. 292–301. Springer, Heidelberg (1998)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Jérémie Dubois-Lacoste
    • 1
  • Manuel López-Ibáñez
    • 1
  • Thomas Stützle
    • 1
  1. 1.IRIDIA, CoDEUniversité Libre de BruxellesBrusselsBelgium

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