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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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    2. Mavrotas, George & Florios, Kostas, 2013. "An improved version of the augmented epsilon-constraint method (AUGMECON2) for finding the exact Pareto set in Multi-Objective Integer Programming problems," MPRA Paper 105034, University Library of Munich, Germany.
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    Cited by:

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    2. Justus Bonz, 2021. "Application of a multi-objective multi traveling salesperson problem with time windows," Public Transport, Springer, vol. 13(1), pages 35-57, March.
    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. 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.
    7. Oracio I. Barbosa-Ayala & Jhon A. Montañez-Barrera & Cesar E. Damian-Ascencio & Adriana Saldaña-Robles & J. Arturo Alfaro-Ayala & Jose Alfredo Padilla-Medina & Sergio Cano-Andrade, 2020. "Solution to the Economic Emission Dispatch Problem Using Numerical Polynomial Homotopy Continuation," Energies, MDPI, vol. 13(17), pages 1-15, August.

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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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