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Multi-Objective Integer Programming: An Improved Recursive Algorithm

Author

Listed:
  • Melih Ozlen

    (RMIT University)

  • Benjamin A. Burton

    (University of Queensland)

  • Cameron A. G. MacRae

    (RMIT University)

Abstract

This paper introduces an improved recursive algorithm to generate the set of all nondominated objective vectors for the Multi-Objective Integer Programming (MOIP) problem. We significantly improve the earlier recursive algorithm of Özlen and Azizoğlu by using the set of already solved subproblems and their solutions to avoid solving a large number of IPs. A numerical example is presented to explain the workings of the algorithm, and we conduct a series of computational experiments to show the savings that can be obtained. As our experiments show, the improvement becomes more significant as the problems grow larger in terms of the number of objectives.

Suggested Citation

  • Melih Ozlen & Benjamin A. Burton & Cameron A. G. MacRae, 2014. "Multi-Objective Integer Programming: An Improved Recursive Algorithm," Journal of Optimization Theory and Applications, Springer, vol. 160(2), pages 470-482, February.
    • Handle: RePEc:spr:joptap:v:160:y:2014:i:2:d:10.1007_s10957-013-0364-y
    DOI: 10.1007/s10957-013-0364-y
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    References listed on IDEAS

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    1. Anthony Przybylski & Xavier Gandibleux & Matthias Ehrgott, 2010. "A Recursive Algorithm for Finding All Nondominated Extreme Points in the Outcome Set of a Multiobjective Integer Programme," INFORMS Journal on Computing, INFORMS, vol. 22(3), pages 371-386, August.
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    4. H. P. Benson & E. Sun, 2000. "Outcome Space Partition of the Weight Set in Multiobjective Linear Programming," Journal of Optimization Theory and Applications, Springer, vol. 105(1), pages 17-36, April.
    5. Laumanns, Marco & Thiele, Lothar & Zitzler, Eckart, 2006. "An efficient, adaptive parameter variation scheme for metaheuristics based on the epsilon-constraint method," European Journal of Operational Research, Elsevier, vol. 169(3), pages 932-942, March.
    6. Benson, Harold P. & Sun, Erjiang, 2002. "A weight set decomposition algorithm for finding all efficient extreme points in the outcome set of a multiple objective linear program," European Journal of Operational Research, Elsevier, vol. 139(1), pages 26-41, May.
    7. Özlen, Melih & Azizoglu, Meral, 2009. "Multi-objective integer programming: A general approach for generating all non-dominated solutions," European Journal of Operational Research, Elsevier, vol. 199(1), pages 25-35, November.
    8. Sylva, John & Crema, Alejandro, 2004. "A method for finding the set of non-dominated vectors for multiple objective integer linear programs," European Journal of Operational Research, Elsevier, vol. 158(1), pages 46-55, October.
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    Cited by:

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    2. Natashia Boland & Hadi Charkhgard & Martin Savelsbergh, 2015. "A Criterion Space Search Algorithm for Biobjective Integer Programming: The Balanced Box Method," INFORMS Journal on Computing, INFORMS, vol. 27(4), pages 735-754, November.
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    5. Ceyhan, Gökhan & Köksalan, Murat & Lokman, Banu, 2019. "Finding a representative nondominated set for multi-objective mixed integer programs," European Journal of Operational Research, Elsevier, vol. 272(1), pages 61-77.
    6. Raeesi, Ramin & Zografos, Konstantinos G., 2019. "The multi-objective Steiner pollution-routing problem on congested urban road networks," Transportation Research Part B: Methodological, Elsevier, vol. 122(C), pages 457-485.
    7. Forget, Nicolas & Gadegaard, Sune Lauth & Nielsen, Lars Relund, 2022. "Warm-starting lower bound set computations for branch-and-bound algorithms for multi objective integer linear programs," European Journal of Operational Research, Elsevier, vol. 302(3), pages 909-924.
    8. Seyyed Amir Babak Rasmi & Ali Fattahi & Metin Türkay, 2021. "SASS: slicing with adaptive steps search method for finding the non-dominated points of tri-objective mixed-integer linear programming problems," Annals of Operations Research, Springer, vol. 296(1), pages 841-876, January.
    9. 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.
    10. Kerstin Dächert & Kathrin Klamroth, 2015. "A linear bound on the number of scalarizations needed to solve discrete tricriteria optimization problems," Journal of Global Optimization, Springer, vol. 61(4), pages 643-676, April.
    11. Ozgu Turgut & Evrim Dalkiran & Alper E. Murat, 2019. "An exact parallel objective space decomposition algorithm for solving multi-objective integer programming problems," Journal of Global Optimization, Springer, vol. 75(1), pages 35-62, September.
    12. Özarık, Sami Serkan & Lokman, Banu & Köksalan, Murat, 2020. "Distribution based representative sets for multi-objective integer programs," European Journal of Operational Research, Elsevier, vol. 284(2), pages 632-643.
    13. William Pettersson & Melih Ozlen, 2020. "Multiobjective Integer Programming: Synergistic Parallel Approaches," INFORMS Journal on Computing, INFORMS, vol. 32(2), pages 461-472, April.
    14. Dächert, Kerstin & Klamroth, Kathrin & Lacour, Renaud & Vanderpooten, Daniel, 2017. "Efficient computation of the search region in multi-objective optimization," European Journal of Operational Research, Elsevier, vol. 260(3), pages 841-855.
    15. Doğan, Ilgın & Lokman, Banu & Köksalan, Murat, 2022. "Representing the nondominated set in multi-objective mixed-integer programs," European Journal of Operational Research, Elsevier, vol. 296(3), pages 804-818.
    16. Holzmann, Tim & Smith, J.C., 2018. "Solving discrete multi-objective optimization problems using modified augmented weighted Tchebychev scalarizations," European Journal of Operational Research, Elsevier, vol. 271(2), pages 436-449.
    17. Raimundo, Marcos M. & Ferreira, Paulo A.V. & Von Zuben, Fernando J., 2020. "An extension of the non-inferior set estimation algorithm for many objectives," European Journal of Operational Research, Elsevier, vol. 284(1), pages 53-66.

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