IDEAS home Printed from https://ideas.repec.org/a/eee/ejores/v248y2016i1p72-83.html
   My bibliography  Save this article

Graphical exploration of the weight space in three-objective mixed integer linear programs

Author

Listed:
  • Alves, Maria João
  • Costa, João Paulo

Abstract

In this paper we address the computation of indifference regions in the weight space for multiobjective integer and mixed-integer linear programming problems and the graphical exploration of this type of information for three-objective problems. We present a procedure to compute a subset of the indifference region associated with a supported nondominated solution obtained by the weighted-sum scalarization. Based on the properties of these regions and their graphical representation for problems with up to three objective functions, we propose an algorithm to compute all extreme supported nondominated solutions adjacent to a given solution and another one to compute all extreme supported nondominated solutions to a three-objective problem. The latter is suitable to characterize solutions in delimited nondominated areas or to be used as a final exploration phase. A computer implementation is also presented.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:ejores:v:248:y:2016:i:1:p:72-83
    DOI: 10.1016/j.ejor.2015.06.072
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0377221715006268
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.ejor.2015.06.072?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
    ---><---

    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. 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.
    2. Alves, Maria Joao & Climaco, Joao, 2000. "An interactive reference point approach for multiobjective mixed-integer programming using branch-and-bound," European Journal of Operational Research, Elsevier, vol. 124(3), pages 478-494, August.
    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. P. L. Yuf & M. Zeleny, 1976. "Linear Multiparametric Programming by Multicriteria Simplex Method," Management Science, INFORMS, vol. 23(2), pages 159-170, 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. 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.
    2. Pedro Correia & Luís Paquete & José Rui Figueira, 2021. "Finding multi-objective supported efficient spanning trees," Computational Optimization and Applications, Springer, vol. 78(2), pages 491-528, March.
    3. 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.
    4. 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.

    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. 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.
    2. 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.
    3. 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.
    4. 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.
    5. 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.
    6. Jamain, Florian, 2014. "Représentations discrètes de l'ensemble des points non dominés pour des problèmes d'optimisation multi-objectifs," Economics Thesis from University Paris Dauphine, Paris Dauphine University, number 123456789/14002 edited by Bazgan, Cristina.
    7. 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.
    8. M. Turkensteen (Marcel) & van den Heuvel, W., 2019. "The trade-off between costs and carbon emissions from lot-sizing decisions," Econometric Institute Research Papers EI2019-19, Erasmus University Rotterdam, Erasmus School of Economics (ESE), Econometric Institute.
    9. 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.
    10. Alves, Maria Joao & Climaco, Joao, 2004. "A note on a decision support system for multiobjective integer and mixed-integer programming problems," European Journal of Operational Research, Elsevier, vol. 155(1), pages 258-265, May.
    11. Filippi, C. & Guastaroba, G. & Speranza, M.G., 2016. "A heuristic framework for the bi-objective enhanced index tracking problem," Omega, Elsevier, vol. 65(C), pages 122-137.
    12. Xie, Chi & Travis Waller, S., 2012. "Parametric search and problem decomposition for approximating Pareto-optimal paths," Transportation Research Part B: Methodological, Elsevier, vol. 46(8), pages 1043-1067.
    13. Koutras, V.P. & Platis, A.N. & Gravvanis, G.A., 2009. "Optimal server resource reservation policies for priority classes of users under cyclic non-homogeneous markov modeling," European Journal of Operational Research, Elsevier, vol. 198(2), pages 545-556, October.
    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. Ustun, Ozden & DemI[dot above]rtas, Ezgi Aktar, 2008. "An integrated multi-objective decision-making process for multi-period lot-sizing with supplier selection," Omega, Elsevier, vol. 36(4), pages 509-521, August.
    16. Demirtas, Ezgi Aktar & Üstün, Özden, 2008. "An integrated multiobjective decision making process for supplier selection and order allocation," Omega, Elsevier, vol. 36(1), pages 76-90, February.
    17. Osman Ou{g}uz, 2000. "Bounds on the Opportunity Cost of Neglecting Reoptimization in Mathematical Programming," Management Science, INFORMS, vol. 46(7), pages 1009-1012, July.
    18. Alves, Maria Joao & Climaco, Joao, 2007. "A review of interactive methods for multiobjective integer and mixed-integer programming," European Journal of Operational Research, Elsevier, vol. 180(1), pages 99-115, July.
    19. Matthias Ehrgott & Andreas Löhne & Lizhen Shao, 2012. "A dual variant of Benson’s “outer approximation algorithm” for multiple objective linear programming," Journal of Global Optimization, Springer, vol. 52(4), pages 757-778, April.
    20. 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.

    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:248:y:2016:i:1:p:72-83. 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.