IDEAS home Printed from https://ideas.repec.org/a/eee/ejores/v199y2009i1p25-35.html
   My bibliography  Save this article

Multi-objective integer programming: A general approach for generating all non-dominated solutions

Author

Listed:
  • Özlen, Melih
  • Azizoglu, Meral

Abstract

In this paper we develop a general approach to generate all non-dominated solutions of the multi-objective integer programming (MOIP) Problem. Our approach, which is based on the identification of objective efficiency ranges, is an improvement over classical [epsilon]-constraint method. Objective efficiency ranges are identified by solving simpler MOIP problems with fewer objectives. We first provide the classical [epsilon]-constraint method on the bi-objective integer programming problem for the sake of completeness and comment on its efficiency. Then present our method on tri-objective integer programming problem and then extend it to the general MOIP problem with k objectives. A numerical example considering tri-objective assignment problem is also provided.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:ejores:v:199:y:2009:i:1:p:25-35
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0377-2217(08)00962-4
    Download Restriction: Full text for ScienceDirect subscribers only
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. 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.
    2. Matthias Ehrgott, 2006. "A discussion of scalarization techniques for multiple objective integer programming," Annals of Operations Research, Springer, vol. 147(1), pages 343-360, October.
    3. Sylva, John & Crema, Alejandro, 2007. "A method for finding well-dispersed subsets of non-dominated vectors for multiple objective mixed integer linear programs," European Journal of Operational Research, Elsevier, vol. 180(3), pages 1011-1027, August.
    4. Matthias Ehrgott & Xavier Gandibleux, 2004. "Approximative solution methods for multiobjective combinatorial optimization," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 12(1), pages 1-63, June.
    5. Klein, Dieter & Hannan, Edward, 1982. "An algorithm for the multiple objective integer linear programming problem," European Journal of Operational Research, Elsevier, vol. 9(4), pages 378-385, April.
    6. 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.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Mesquita-Cunha, Mariana & Figueira, José Rui & Barbosa-Póvoa, Ana Paula, 2023. "New ϵ−constraint methods for multi-objective integer linear programming: A Pareto front representation approach," European Journal of Operational Research, Elsevier, vol. 306(1), pages 286-307.
    2. 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.
    3. 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.
    4. Banu Lokman & Murat Köksalan, 2013. "Finding all nondominated points of multi-objective integer programs," Journal of Global Optimization, Springer, vol. 57(2), pages 347-365, October.
    5. Melih Ozlen & Meral Azizoğlu & Benjamin Burton, 2013. "Optimising a nonlinear utility function in multi-objective integer programming," Journal of Global Optimization, Springer, vol. 56(1), pages 93-102, May.
    6. 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.
    7. 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.
    8. 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.
    9. Zhang, Weihua & Reimann, Marc, 2014. "A simple augmented ∊-constraint method for multi-objective mathematical integer programming problems," European Journal of Operational Research, Elsevier, vol. 234(1), pages 15-24.
    10. 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.
    11. S. Razavyan, 2016. "A Method for Generating a Well-Distributed Pareto Set in Multiple Objective Mixed Integer Linear Programs Based on the Decision Maker’s Initial Aspiration Level," Asia-Pacific Journal of Operational Research (APJOR), World Scientific Publishing Co. Pte. Ltd., vol. 33(04), pages 1-23, August.
    12. Kirlik, Gokhan & Sayın, Serpil, 2014. "A new algorithm for generating all nondominated solutions of multiobjective discrete optimization problems," European Journal of Operational Research, Elsevier, vol. 232(3), pages 479-488.
    13. 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.
    14. 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.
    15. Jorge, Jesús M., 2009. "An algorithm for optimizing a linear function over an integer efficient set," European Journal of Operational Research, Elsevier, vol. 195(1), pages 98-103, May.
    16. 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.
    17. 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.
    18. Rong, Aiying & Figueira, José Rui, 2013. "A reduction dynamic programming algorithm for the bi-objective integer knapsack problem," European Journal of Operational Research, Elsevier, vol. 231(2), pages 299-313.
    19. Angelo Aliano Filho & Antonio Carlos Moretti & Margarida Vaz Pato & Washington Alves Oliveira, 2021. "An exact scalarization method with multiple reference points for bi-objective integer linear optimization problems," Annals of Operations Research, Springer, vol. 296(1), pages 35-69, January.
    20. Tolga Bektaş, 2018. "Disjunctive Programming for Multiobjective Discrete Optimisation," INFORMS Journal on Computing, INFORMS, vol. 30(4), pages 625-633, November.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:ejores:v:199:y:2009:i:1:p:25-35. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/locate/eor .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.