IDEAS home Printed from https://ideas.repec.org/a/eee/ejores/v277y2019i2p653-666.html
   My bibliography  Save this article

Reducing wall-clock time for the computation of all efficient extreme points in multiple objective linear programming

Author

Listed:
  • Piercy, Craig A.
  • Steuer, Ralph E.

Abstract

This paper describes an approach for markedly reducing the time required to obtain all efficient extreme points of a multiple objective linear program (MOLP) with three objectives. The approach is particularly useful when working with such MOLPs possessing large numbers of efficient extreme points. By subdividing the criterion cone into sub-cones, the paper shows how the task of computing all efficient extreme points can be broken down into parts so that the parts can be solved concurrently, thus allowing all efficient extreme points to be computed in much reduced elapsed time. The paper investigates several schemes for conducting this task and reports on a volume of computational experience.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:ejores:v:277:y:2019:i:2:p:653-666
    DOI: 10.1016/j.ejor.2019.02.042
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0377221719301900
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.ejor.2019.02.042?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. Lizhen Shao & Matthias Ehrgott, 2008. "Approximating the nondominated set of an MOLP by approximately solving its dual problem," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 68(3), pages 469-492, December.
    2. Lizhen Shao & Matthias Ehrgott, 2008. "Approximately solving multiobjective linear programmes in objective space and an application in radiotherapy treatment planning," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 68(2), pages 257-276, October.
    3. 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.
    4. Abbas, Moncef & Chaabane, Djamal, 2006. "Optimizing a linear function over an integer efficient set," European Journal of Operational Research, Elsevier, vol. 174(2), pages 1140-1161, October.
    5. Kaisa Miettinen & Dmitry Podkopaev & Francisco Ruiz & Mariano Luque, 2015. "A new preference handling technique for interactive multiobjective optimization without trading-off," Journal of Global Optimization, Springer, vol. 63(4), pages 633-652, December.
    6. Steuer, Ralph E. & Piercy, Craig A., 2005. "A regression study of the number of efficient extreme points in multiple objective linear programming," European Journal of Operational Research, Elsevier, vol. 162(2), pages 484-496, April.
    7. 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.
    8. 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.
    9. Miettinen, Kaisa & Eskelinen, Petri & Ruiz, Francisco & Luque, Mariano, 2010. "NAUTILUS method: An interactive technique in multiobjective optimization based on the nadir point," European Journal of Operational Research, Elsevier, vol. 206(2), pages 426-434, October.
    10. 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.
    11. 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.
    12. Löhne, Andreas & Weißing, Benjamin, 2017. "The vector linear program solver Bensolve – notes on theoretical background," European Journal of Operational Research, Elsevier, vol. 260(3), pages 807-813.
    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. Hadjer Belkhiri & Mohamed El-Amine Chergui & Fatma Zohra Ouaïl, 2022. "Optimizing a linear function over an efficient set," Operational Research, Springer, vol. 22(4), pages 3183-3201, September.

    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. Özgür Özpeynirci, 2017. "On nadir points of multiobjective integer programming problems," Journal of Global Optimization, Springer, vol. 69(3), pages 699-712, November.
    3. Fereshteh Akbari & Mehrdad Ghaznavi & Esmaile Khorram, 2018. "A Revised Pascoletti–Serafini Scalarization Method for Multiobjective Optimization Problems," Journal of Optimization Theory and Applications, Springer, vol. 178(2), pages 560-590, August.
    4. 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.
    5. Kaisa Miettinen & Francisco Ruiz, 2016. "NAUTILUS framework: towards trade-off-free interaction in multiobjective optimization," Journal of Business Economics, Springer, vol. 86(1), pages 5-21, January.
    6. Andreas Löhne & Birgit Rudloff & Firdevs Ulus, 2014. "Primal and dual approximation algorithms for convex vector optimization problems," Journal of Global Optimization, Springer, vol. 60(4), pages 713-736, December.
    7. Nghe, Philippe & Mulder, Bela M. & Tans, Sander J., 2018. "A graph-based algorithm for the multi-objective optimization of gene regulatory networks," European Journal of Operational Research, Elsevier, vol. 270(2), pages 784-793.
    8. 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.
    9. 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.
    10. 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.
    11. 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.
    12. Ana B. Ruiz & Francisco Ruiz & Kaisa Miettinen & Laura Delgado-Antequera & Vesa Ojalehto, 2019. "NAUTILUS Navigator: free search interactive multiobjective optimization without trading-off," Journal of Global Optimization, Springer, vol. 74(2), pages 213-231, June.
    13. Matthias Ehrgott & Çiğdem Güler & Horst Hamacher & Lizhen Shao, 2010. "Mathematical optimization in intensity modulated radiation therapy," Annals of Operations Research, Springer, vol. 175(1), pages 309-365, March.
    14. 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.
    15. 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.
    16. 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.
    17. Koenen, Melissa & Balvert, Marleen & Fleuren, H.A., 2023. "A Renewed Take on Weighted Sum in Sandwich Algorithms : Modification of the Criterion Space," Discussion Paper 2023-012, Tilburg University, Center for Economic Research.
    18. Koenen, Melissa & Balvert, Marleen & Fleuren, H.A., 2023. "A Renewed Take on Weighted Sum in Sandwich Algorithms : Modification of the Criterion Space," Other publications TiSEM 795b6c0c-c7bc-4ced-9d6b-a, Tilburg University, School of Economics and Management.
    19. Gokhan Kirlik & Serpil Sayın, 2015. "Computing the nadir point for multiobjective discrete optimization problems," Journal of Global Optimization, Springer, vol. 62(1), pages 79-99, May.
    20. Shuang Yao & Donghua Yu & Yan Song & Hao Yao & Yuzhen Hu & Benhai Guo, 2018. "Dry Bulk Carrier Investment Selection through a Dual Group Decision Fusing Mechanism in the Green Supply Chain," Sustainability, MDPI, vol. 10(12), pages 1-19, 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:277:y:2019:i:2:p:653-666. 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.