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Proper balance between search towards and along Pareto front: biobjective TSP case study

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  • Andrzej Jaszkiewicz

    (Poznan University of Technology)

  • Thibaut Lust

    (Sorbonne Universités, UPMC Universités Paris 06)

Abstract

In this paper we propose simple yet efficient version of the two-phase Pareto local search (2PPLS) for solving the biobjective traveling salesman problem (bTSP). In the first phase the powerful Lin–Kernighan heuristic is used to generate some high quality solutions being very close to the Pareto front. Then Pareto local search is used to generate more potentially Pareto efficient solutions along the Pareto front. Instead of previously used method of Aneja and Nair we use uniformly distributed weight vectors in the first phase. We show experimentally that properly balancing the computational effort in the first and second phase we can obtain results better than previous versions of 2PPLS for bTSP and at least comparable to the state-of-the art results of more complex MOMAD method. Furthermore, we propose a simple extension of 2PPLS where some additional solutions are generated by Lin–Kernighan heuristic during the run of PLS. In this way we obtain a method that is more robust with respect to the number of initial solutions generated in the first phase.

Suggested Citation

  • Andrzej Jaszkiewicz & Thibaut Lust, 2017. "Proper balance between search towards and along Pareto front: biobjective TSP case study," Annals of Operations Research, Springer, vol. 254(1), pages 111-130, July.
    • Handle: RePEc:spr:annopr:v:254:y:2017:i:1:d:10.1007_s10479-017-2415-5
    DOI: 10.1007/s10479-017-2415-5
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    References listed on IDEAS

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    1. Y. P. Aneja & K. P. K. Nair, 1979. "Bicriteria Transportation Problem," Management Science, INFORMS, vol. 25(1), pages 73-78, January.
    2. Luis Paquete & Tommaso Schiavinotto & Thomas Stützle, 2007. "On local optima in multiobjective combinatorial optimization problems," Annals of Operations Research, Springer, vol. 156(1), pages 83-97, December.
    3. David Applegate & William Cook & André Rohe, 2003. "Chained Lin-Kernighan for Large Traveling Salesman Problems," INFORMS Journal on Computing, INFORMS, vol. 15(1), pages 82-92, February.
    4. Paquete, Luis & Stutzle, Thomas, 2006. "A study of stochastic local search algorithms for the biobjective QAP with correlated flow matrices," European Journal of Operational Research, Elsevier, vol. 169(3), pages 943-959, March.
    5. S. Lin & B. W. Kernighan, 1973. "An Effective Heuristic Algorithm for the Traveling-Salesman Problem," Operations Research, INFORMS, vol. 21(2), pages 498-516, April.
    6. Andrzej Jaszkiewicz, 2004. "A Comparative Study of Multiple-Objective Metaheuristics on the Bi-Objective Set Covering Problem and the Pareto Memetic Algorithm," Annals of Operations Research, Springer, vol. 131(1), pages 135-158, October.
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    Cited by:

    1. Jaszkiewicz, Andrzej, 2018. "Many-Objective Pareto Local Search," European Journal of Operational Research, Elsevier, vol. 271(3), pages 1001-1013.

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