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Generation of the exact Pareto set in multi-objective traveling salesman and set covering problems

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  • Florios, Kostas
  • Mavrotas, George

Abstract

The calculation of the exact set in Multi-Objective Combinatorial Optimization (MOCO) problems is one of the most computationally demanding tasks as most of the problems are NP-hard. In the present work we use AUGMECON2 a Multi-Objective Mathematical Programming (MOMP) method which is capable of generating the exact Pareto set in Multi-Objective Integer Programming (MOIP) problems for producing all the Pareto optimal solutions in two popular MOCO problems: The Multi-Objective Traveling Salesman Problem (MOTSP) and the Multi-Objective Set Covering problem (MOSCP). The computational experiment is confined to two-objective problems that are found in the literature. The performance of the algorithm is slightly better to what is already found from previous works and it goes one step further generating the exact Pareto set to till now unsolved problems. The results are provided in a dedicated site and can be useful for benchmarking with other MOMP methods or even Multi-Objective Meta-Heuristics (MOMH) that can check the performance of their approximate solution against the exact solution in MOTSP and MOSCP problems.

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  • Florios, Kostas & Mavrotas, George, 2014. "Generation of the exact Pareto set in multi-objective traveling salesman and set covering problems," MPRA Paper 105074, University Library of Munich, Germany.
    • Handle: RePEc:pra:mprapa:105074
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    References listed on IDEAS

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    Cited by:

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    3. Mohammed Mahrach & Gara Miranda & Coromoto León & Eduardo Segredo, 2020. "Comparison between Single and Multi-Objective Evolutionary Algorithms to Solve the Knapsack Problem and the Travelling Salesman Problem," Mathematics, MDPI, vol. 8(11), pages 1-23, November.
    4. Lakmali Weerasena & Aniekan Ebiefung & Anthony Skjellum, 2022. "Design of a heuristic algorithm for the generalized multi-objective set covering problem," Computational Optimization and Applications, Springer, vol. 82(3), pages 717-751, July.
    5. David Bergman & Merve Bodur & Carlos Cardonha & Andre A. Cire, 2022. "Network Models for Multiobjective Discrete Optimization," INFORMS Journal on Computing, INFORMS, vol. 34(2), pages 990-1005, March.
    6. Lakmali Weerasena & Margaret M. Wiecek & Banu Soylu, 2017. "An algorithm for approximating the Pareto set of the multiobjective set covering problem," Annals of Operations Research, Springer, vol. 248(1), pages 493-514, January.
    7. Alexandros Nikas & Angelos Fountoulakis & Aikaterini Forouli & Haris Doukas, 2022. "A robust augmented ε-constraint method (AUGMECON-R) for finding exact solutions of multi-objective linear programming problems," Operational Research, Springer, vol. 22(2), pages 1291-1332, April.
    8. Gais Alhadi & Imed Kacem & Pierre Laroche & Izzeldin M. Osman, 2020. "Approximation algorithms for minimizing the maximum lateness and makespan on parallel machines," Annals of Operations Research, Springer, vol. 285(1), pages 369-395, February.
    9. Dinçer Konur & Hadi Farhangi & Cihan H. Dagli, 2016. "A multi-objective military system of systems architecting problem with inflexible and flexible systems: formulation and solution methods," OR Spectrum: Quantitative Approaches in Management, Springer;Gesellschaft für Operations Research e.V., vol. 38(4), pages 967-1006, October.
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    More about this item

    Keywords

    multi-objective; traveling salesman problem; set covering problem; ε-constraint; exact Pareto set;
    All these keywords.

    JEL classification:

    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis
    • C63 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Computational Techniques

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