IDEAS home Printed from https://ideas.repec.org/a/wly/navres/v56y2009i2p191-198.html
   My bibliography  Save this article

Approximating the nondominated frontiers of multi‐objective combinatorial optimization problems

Author

Listed:
  • Murat Köksalan
  • Banu Lokman

Abstract

Finding all nondominated vectors for multi‐objective combinatorial optimization (MOCO) problems is computationally very hard in general. We approximate the nondominated frontiers of MOCO problems by fitting smooth hypersurfaces. For a given problem, we fit the hypersurface using a single nondominated reference vector. We experiment with different types of MOCO problems and demonstrate that in all cases the fitted hypersurfaces approximate all nondominated vectors well. We discuss that such an approximation is useful to find the neighborhood of preferred regions of the nondominated vectors with very little computational effort. Further computational effort can then be spent in the identified region to find the actual nondominated vectors the decision maker will prefer. © 2009 Wiley Periodicals, Inc. Naval Research Logistics, 2009

Suggested Citation

  • Murat Köksalan & Banu Lokman, 2009. "Approximating the nondominated frontiers of multi‐objective combinatorial optimization problems," Naval Research Logistics (NRL), John Wiley & Sons, vol. 56(2), pages 191-198, March.
    • Handle: RePEc:wly:navres:v:56:y:2009:i:2:p:191-198
    DOI: 10.1002/nav.20336
    as

    Download full text from publisher

    File URL: https://doi.org/10.1002/nav.20336
    Download Restriction: no
    File URL: https://libkey.io/10.1002/nav.20336?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. Murat Köksalan & Selcen (Pamuk) Phelps, 2007. "An Evolutionary Metaheuristic for Approximating Preference-Nondominated Solutions," INFORMS Journal on Computing, INFORMS, vol. 19(2), pages 291-301, May.
    2. Pekka Korhonen & Seppo Salo & Ralph E. Steuer, 1997. "A Heuristic for Estimating Nadir Criterion Values in Multiple Objective Linear Programming," Operations Research, INFORMS, vol. 45(5), pages 751-757, October.
    3. 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)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Tezcaner Öztürk, Diclehan & Köksalan, Murat, 2023. "Biobjective route planning of an unmanned air vehicle in continuous space," Transportation Research Part B: Methodological, Elsevier, vol. 168(C), pages 151-169.
    2. Nail Karabay & Murat Köksalan & Diclehan Tezcaner Öztürk, 2023. "Biobjective UAV routing for a mission to visit multiple mobile targets," OR Spectrum: Quantitative Approaches in Management, Springer;Gesellschaft für Operations Research e.V., vol. 45(3), pages 925-954, September.
    3. 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.
    4. 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.
    5. 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.
    6. 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.

    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. A.P. Wierzbicki, 1998. "Reference Point Methods in Vector Optimization and Decision Support," Working Papers ir98017, International Institute for Applied Systems Analysis.
    2. Murat Köksalan & Banu Lokman, 2015. "Finding nadir points in multi-objective integer programs," Journal of Global Optimization, Springer, vol. 62(1), pages 55-77, May.
    3. Satya Tamby & Daniel Vanderpooten, 2021. "Enumeration of the Nondominated Set of Multiobjective Discrete Optimization Problems," INFORMS Journal on Computing, INFORMS, vol. 33(1), pages 72-85, January.
    4. Ibrahim Muter & Tevfik Aytekin, 2017. "Incorporating Aggregate Diversity in Recommender Systems Using Scalable Optimization Approaches," INFORMS Journal on Computing, INFORMS, vol. 29(3), pages 405-421, August.
    5. Lacour, Renaud, 2014. "Approches de résolution exacte et approchée en optimisation combinatoire multi-objectif, application au problème de l'arbre couvrant de poids minimal," Economics Thesis from University Paris Dauphine, Paris Dauphine University, number 123456789/14806 edited by Vanderpooten, Daniel.
    6. Alves, Maria João & Costa, João Paulo, 2009. "An exact method for computing the nadir values in multiple objective linear programming," European Journal of Operational Research, Elsevier, vol. 198(2), pages 637-646, October.
    7. Villacorta, Kely D.V. & Oliveira, P. Roberto, 2011. "An interior proximal method in vector optimization," European Journal of Operational Research, Elsevier, vol. 214(3), pages 485-492, November.
    8. 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.
    9. 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.
    10. Granat, Janusz & Guerriero, Francesca, 2003. "The interactive analysis of the multicriteria shortest path problem by the reference point method," European Journal of Operational Research, Elsevier, vol. 151(1), pages 103-118, November.
    11. Boland, Natashia & Charkhgard, Hadi & Savelsbergh, Martin, 2017. "The Quadrant Shrinking Method: A simple and efficient algorithm for solving tri-objective integer programs," European Journal of Operational Research, Elsevier, vol. 260(3), pages 873-885.
    12. Murat Köksalan & Banu Soylu, 2010. "Bicriteria p -Hub Location Problems and Evolutionary Algorithms," INFORMS Journal on Computing, INFORMS, vol. 22(4), pages 528-542, November.
    13. 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.
    14. Boland, Natashia & Charkhgard, Hadi & Savelsbergh, Martin, 2017. "A new method for optimizing a linear function over the efficient set of a multiobjective integer program," European Journal of Operational Research, Elsevier, vol. 260(3), pages 904-919.
    15. 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.
    16. Jiapeng Liu & Miłosz Kadziński & Xiuwu Liao & Xiaoxin Mao, 2021. "Data-Driven Preference Learning Methods for Value-Driven Multiple Criteria Sorting with Interacting Criteria," INFORMS Journal on Computing, INFORMS, vol. 33(2), pages 586-606, May.
    17. 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.
    18. Sun, Minghe, 2005. "Some issues in measuring and reporting solution quality of interactive multiple objective programming procedures," European Journal of Operational Research, Elsevier, vol. 162(2), pages 468-483, April.
    19. De Santis, Marianna & Grani, Giorgio & Palagi, Laura, 2020. "Branching with hyperplanes in the criterion space: The frontier partitioner algorithm for biobjective integer programming," European Journal of Operational Research, Elsevier, vol. 283(1), pages 57-69.
    20. 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.

    More about this item

    Statistics

    Access and download statistics

    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:wly:navres:v:56:y:2009:i:2:p:191-198. 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: Wiley Content Delivery (email available below). General contact details of provider: https://doi.org/10.1002/(ISSN)1520-6750 .

    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.