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Anytime Pareto local search

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  • Dubois-Lacoste, Jérémie
  • López-Ibáñez, Manuel
  • Stützle, Thomas

Abstract

Pareto Local Search (PLS) is a simple and effective local search method for tackling multi-objective combinatorial optimization problems. It is also a crucial component of many state-of-the-art algorithms for such problems. However, PLS may be not very effective when terminated before completion. In other words, PLS has poor anytime behavior. In this paper, we study the effect that various PLS algorithmic components have on its anytime behavior. We show that the anytime behavior of PLS can be greatly improved by using alternative algorithmic components. We also propose Dynagrid, a dynamic discretization of the objective space that helps PLS to converge faster to a good approximation of the Pareto front and continue to improve it if more time is available. We perform a detailed empirical evaluation of the new proposals on the bi-objective traveling salesman problem and the bi-objective quadratic assignment problem. Our results demonstrate that the new PLS variants not only have significantly better anytime behavior than the original PLS, but also may obtain better results for longer computation time or upon completion.

Suggested Citation

  • Dubois-Lacoste, Jérémie & López-Ibáñez, Manuel & Stützle, Thomas, 2015. "Anytime Pareto local search," European Journal of Operational Research, Elsevier, vol. 243(2), pages 369-385.
    • Handle: RePEc:eee:ejores:v:243:y:2015:i:2:p:369-385
    DOI: 10.1016/j.ejor.2014.10.062
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    Cited by:

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    2. Diaz, Juan Esteban & López-Ibáñez, Manuel, 2021. "Incorporating decision-maker’s preferences into the automatic configuration of bi-objective optimisation algorithms," European Journal of Operational Research, Elsevier, vol. 289(3), pages 1209-1222.
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    4. Lamiaa Dahite & Abdeslam Kadrani & Rachid Benmansour & Rym Nesrine Guibadj & Cyril Fonlupt, 2022. "Multi-Objective Model and Variable Neighborhood Search Algorithms for the Joint Maintenance Scheduling and Workforce Routing Problem," Mathematics, MDPI, vol. 10(11), pages 1-37, May.
    5. Pablo A. Miranda-Gonzalez & Javier Maturana-Ross & Carola A. Blazquez & Guillermo Cabrera-Guerrero, 2021. "Exact Formulation and Analysis for the Bi-Objective Insular Traveling Salesman Problem," Mathematics, MDPI, vol. 9(21), pages 1-33, October.
    6. Eduardo Álvarez-Miranda & Camilo Campos-Valdés & Maurcio Morales Quiroga & Matías Moreno-Faguett & Jordi Pereira, 2020. "A Multi-Criteria Pen for Drawing Fair Districts: When Democratic and Demographic Fairness Matter," Mathematics, MDPI, vol. 8(9), pages 1-26, August.
    7. Jaszkiewicz, Andrzej, 2018. "Many-Objective Pareto Local Search," European Journal of Operational Research, Elsevier, vol. 271(3), pages 1001-1013.
    8. Alexandre D. Jesus & Luís Paquete & Arnaud Liefooghe, 2021. "A model of anytime algorithm performance for bi-objective optimization," Journal of Global Optimization, Springer, vol. 79(2), pages 329-350, February.

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