IDEAS home Printed from https://ideas.repec.org/a/inm/ormnsc/v56y2010i12p2302-2315.html
   My bibliography  Save this article

An Exact Algorithm for Finding Extreme Supported Nondominated Points of Multiobjective Mixed Integer Programs

Author

Listed:
  • Özgür Özpeynirci

    (Department of Logistics Management, Izmir University of Economics, Izmir 35330, Turkey)

  • Murat Köksalan

    (Industrial Engineering Department, Middle East Technical University, Ankara 06531, Turkey)

Abstract

In this paper, we present an exact algorithm to find all extreme supported nondominated points of multiobjective mixed integer programs. The algorithm uses a composite linear objective function and finds all the desired points in a finite number of steps by changing the weights of the objective functions in a systematic way. We develop further variations of the algorithm to improve its computational performance and demonstrate our algorithm's performance on multiobjective assignment, knapsack, and traveling salesperson problems with three and four objectives.

Suggested Citation

  • Özgür Özpeynirci & Murat Köksalan, 2010. "An Exact Algorithm for Finding Extreme Supported Nondominated Points of Multiobjective Mixed Integer Programs," Management Science, INFORMS, vol. 56(12), pages 2302-2315, December.
    • Handle: RePEc:inm:ormnsc:v:56:y:2010:i:12:p:2302-2315
    DOI: 10.1287/mnsc.1100.1248
    as

    Download full text from publisher

    File URL: http://dx.doi.org/10.1287/mnsc.1100.1248
    Download Restriction: no
    File URL: https://libkey.io/10.1287/mnsc.1100.1248?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    References listed on IDEAS

    as
    1. Y. P. Aneja & K. P. K. Nair, 1979. "Bicriteria Transportation Problem," Management Science, INFORMS, vol. 25(1), pages 73-78, January.
    2. 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.
    3. 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.
    4. Selcen (Pamuk) Phelps & Murat Köksalan, 2003. "An Interactive Evolutionary Metaheuristic for Multiobjective Combinatorial Optimization," Management Science, INFORMS, vol. 49(12), pages 1726-1738, December.
    5. 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.
    6. Solanki, Rajendra S. & Appino, Perry A. & Cohon, Jared L., 1993. "Approximating the noninferior set in multiobjective linear programming problems," European Journal of Operational Research, Elsevier, vol. 68(3), pages 356-373, August.
    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. Britta Schulze & Kathrin Klamroth & Michael Stiglmayr, 2019. "Multi-objective unconstrained combinatorial optimization: a polynomial bound on the number of extreme supported solutions," Journal of Global Optimization, Springer, vol. 74(3), pages 495-522, July.
    2. 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.
    3. 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.
    4. Stephan Helfrich & Tyler Perini & Pascal Halffmann & Natashia Boland & Stefan Ruzika, 2023. "Analysis of the weighted Tchebycheff weight set decomposition for multiobjective discrete optimization problems," Journal of Global Optimization, Springer, vol. 86(2), pages 417-440, June.
    5. Przybylski, Anthony & Gandibleux, Xavier, 2017. "Multi-objective branch and bound," European Journal of Operational Research, Elsevier, vol. 260(3), pages 856-872.
    6. Alves, Maria João & Costa, João Paulo, 2016. "Graphical exploration of the weight space in three-objective mixed integer linear programs," European Journal of Operational Research, Elsevier, vol. 248(1), pages 72-83.
    7. Jyrki Wallenius & James S. Dyer & Peter C. Fishburn & Ralph E. Steuer & Stanley Zionts & Kalyanmoy Deb, 2008. "Multiple Criteria Decision Making, Multiattribute Utility Theory: Recent Accomplishments and What Lies Ahead," Management Science, INFORMS, vol. 54(7), pages 1336-1349, July.
    8. Klamroth, Kathrin & Stiglmayr, Michael & Sudhoff, Julia, 2023. "Ordinal optimization through multi-objective reformulation," European Journal of Operational Research, Elsevier, vol. 311(2), pages 427-443.
    9. Pascal Halffmann & Tobias Dietz & Anthony Przybylski & Stefan Ruzika, 2020. "An inner approximation method to compute the weight set decomposition of a triobjective mixed-integer problem," Journal of Global Optimization, Springer, vol. 77(4), pages 715-742, August.
    10. Piercy, Craig A. & Steuer, Ralph E., 2019. "Reducing wall-clock time for the computation of all efficient extreme points in multiple objective linear programming," European Journal of Operational Research, Elsevier, vol. 277(2), pages 653-666.
    11. Özgür Özpeynirci, 2017. "On nadir points of multiobjective integer programming problems," Journal of Global Optimization, Springer, vol. 69(3), pages 699-712, November.
    12. Soylu, Banu, 2018. "The search-and-remove algorithm for biobjective mixed-integer linear programming problems," European Journal of Operational Research, Elsevier, vol. 268(1), pages 281-299.
    13. Daniel Jornada & V. Jorge Leon, 2020. "Filtering Algorithms for Biobjective Mixed Binary Linear Optimization Problems with a Multiple-Choice Constraint," INFORMS Journal on Computing, INFORMS, vol. 32(1), pages 57-73, January.
    14. 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.
    15. S. Dutta & S. Acharya & Rajashree Mishra, 2016. "Genetic algorithm based fuzzy stochastic transportation programming problem with continuous random variables," OPSEARCH, Springer;Operational Research Society of India, vol. 53(4), pages 835-872, December.
    16. Zhong, Tao & Young, Rhonda, 2010. "Multiple Choice Knapsack Problem: Example of planning choice in transportation," Evaluation and Program Planning, Elsevier, vol. 33(2), pages 128-137, May.
    17. Yang, X. Q. & Goh, C. J., 1997. "A method for convex curve approximation," European Journal of Operational Research, Elsevier, vol. 97(1), pages 205-212, February.
    18. Aritra Pal & Hadi Charkhgard, 2019. "A Feasibility Pump and Local Search Based Heuristic for Bi-Objective Pure Integer Linear Programming," INFORMS Journal on Computing, INFORMS, vol. 31(1), pages 115-133, February.
    19. KIKOMBA KAHUNGU, Michaël & MABELA MAKENGO MATENDO, Rostin & M. NGOIE, Ruffin-Benoît & MAKENGO MBAMBALU, Fréderic & OKITONYUMBE Y.F, Joseph, 2013. "Les fondements mathématiques pour une aide à la décision du réseau de transport aérien : cas de la République Démocratique du Congo [Mathematical Foundation for Air Traffic Network Decision Aid : C," MPRA Paper 68533, University Library of Munich, Germany, revised Mar 2013.
    20. Singh, Preetvanti & Saxena, P. K., 2003. "The multiple objective time transportation problem with additional restrictions," European Journal of Operational Research, Elsevier, vol. 146(3), pages 460-476, May.

    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:inm:ormnsc:v:56:y:2010:i:12:p:2302-2315. 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: Chris Asher (email available below). General contact details of provider: https://edirc.repec.org/data/inforea.html .

    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.