IDEAS home Printed from https://ideas.repec.org/a/eee/ejores/v266y2018i2p415-425.html
   My bibliography  Save this article

A one direction search method to find the exact nondominated frontier of biobjective mixed-binary linear programming problems

Author

Listed:
  • Fattahi, Ali
  • Turkay, Metin

Abstract

The nondominated frontier (NDF) of a biobjective optimization problem is defined as the set of feasible points in the objective function space that cannot be improved in one objective function value without worsening the other. For a biobjective mixed-binary linear programming problem (BOMBLP), the NDF consists of some combination of isolated points and open, closed, or half-open/half-closed line segments. Some algorithms have been proposed in the literature to find an approximate or exact representation of the NDF. We present a one direction search (ODS) method to find the exact NDF of BOMBLPs. We provide a theoretical analysis of the ODS method and show that it generates the exact NDF. We also conduct a comprehensive experimental study on a set of benchmark problems and show the solution quality and computational efficacy of our algorithm.

Suggested Citation

  • Fattahi, Ali & Turkay, Metin, 2018. "A one direction search method to find the exact nondominated frontier of biobjective mixed-binary linear programming problems," European Journal of Operational Research, Elsevier, vol. 266(2), pages 415-425.
    • Handle: RePEc:eee:ejores:v:266:y:2018:i:2:p:415-425
    DOI: 10.1016/j.ejor.2017.09.026
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0377221717308470
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.ejor.2017.09.026?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. 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.
    2. Y. P. Aneja & K. P. K. Nair, 1979. "Bicriteria Transportation Problem," Management Science, INFORMS, vol. 25(1), pages 73-78, January.
    3. Thomas Stidsen & Kim Allan Andersen & Bernd Dammann, 2014. "A Branch and Bound Algorithm for a Class of Biobjective Mixed Integer Programs," Management Science, INFORMS, vol. 60(4), pages 1009-1032, April.
    4. 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.
    5. Natashia Boland & Hadi Charkhgard & Martin Savelsbergh, 2015. "A Criterion Space Search Algorithm for Biobjective Mixed Integer Programming: The Triangle Splitting Method," INFORMS Journal on Computing, INFORMS, vol. 27(4), pages 597-618, November.
    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. Nathan Adelgren & Akshay Gupte, 2022. "Branch-and-Bound for Biobjective Mixed-Integer Linear Programming," INFORMS Journal on Computing, INFORMS, vol. 34(2), pages 909-933, March.
    2. Alvaro Sierra Altamiranda & Hadi Charkhgard, 2019. "A New Exact Algorithm to Optimize a Linear Function over the Set of Efficient Solutions for Biobjective Mixed Integer Linear Programs," INFORMS Journal on Computing, INFORMS, vol. 31(4), pages 823-840, October.
    3. Tyler Perini & Natashia Boland & Diego Pecin & Martin Savelsbergh, 2020. "A Criterion Space Method for Biobjective Mixed Integer Programming: The Boxed Line Method," INFORMS Journal on Computing, INFORMS, vol. 32(1), pages 16-39, January.
    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.
    5. Acuna, Jorge A. & Zayas-Castro, José L. & Charkhgard, Hadi, 2020. "Ambulance allocation optimization model for the overcrowding problem in US emergency departments: A case study in Florida," Socio-Economic Planning Sciences, Elsevier, vol. 71(C).
    6. Guillermo Cabrera-Guerrero & Matthias Ehrgott & Andrew J. Mason & Andrea Raith, 2022. "Bi-objective optimisation over a set of convex sub-problems," Annals of Operations Research, Springer, vol. 319(2), pages 1507-1532, December.

    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. Yıldız, Gazi Bilal & Soylu, Banu, 2019. "A multiobjective post-sales guarantee and repair services network design problem," International Journal of Production Economics, Elsevier, vol. 216(C), pages 305-320.
    2. Masar Al-Rabeeah & Santosh Kumar & Ali Al-Hasani & Elias Munapo & Andrew Eberhard, 2019. "Bi-objective integer programming analysis based on the characteristic equation," International Journal of System Assurance Engineering and Management, Springer;The Society for Reliability, Engineering Quality and Operations Management (SREQOM),India, and Division of Operation and Maintenance, Lulea University of Technology, Sweden, vol. 10(5), pages 937-944, October.
    3. Przybylski, Anthony & Gandibleux, Xavier, 2017. "Multi-objective branch and bound," European Journal of Operational Research, Elsevier, vol. 260(3), pages 856-872.
    4. 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.
    5. Cacchiani, Valentina & D’Ambrosio, Claudia, 2017. "A branch-and-bound based heuristic algorithm for convex multi-objective MINLPs," European Journal of Operational Research, Elsevier, vol. 260(3), pages 920-933.
    6. 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.
    7. Miriam Enzi & Sophie N. Parragh & Jakob Puchinger, 2022. "The bi-objective multimodal car-sharing problem," OR Spectrum: Quantitative Approaches in Management, Springer;Gesellschaft für Operations Research e.V., vol. 44(2), pages 307-348, June.
    8. Soylu, Banu & Katip, Hatice, 2019. "A multiobjective hub-airport location problem for an airline network design," European Journal of Operational Research, Elsevier, vol. 277(2), pages 412-425.
    9. 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.
    10. Hadi Charkhgard & Mahdi Takalloo & Zulqarnain Haider, 2020. "Bi-objective autonomous vehicle repositioning problem with travel time uncertainty," 4OR, Springer, vol. 18(4), pages 477-505, December.
    11. 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.
    12. Sierra-Altamiranda, Alvaro & Charkhgard, Hadi & Eaton, Mitchell & Martin, Julien & Yurek, Simeon & Udell, Bradley J., 2020. "Spatial conservation planning under uncertainty using modern portfolio theory and Nash bargaining solution," Ecological Modelling, Elsevier, vol. 423(C).
    13. Konur, Dinçer & Campbell, James F. & Monfared, Sepideh A., 2017. "Economic and environmental considerations in a stochastic inventory control model with order splitting under different delivery schedules among suppliers," Omega, Elsevier, vol. 71(C), pages 46-65.
    14. 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.
    15. Guillermo Cabrera-Guerrero & Matthias Ehrgott & Andrew J. Mason & Andrea Raith, 2022. "Bi-objective optimisation over a set of convex sub-problems," Annals of Operations Research, Springer, vol. 319(2), pages 1507-1532, December.
    16. Esmaeili, Somayeh & Bashiri, Mahdi & Amiri, Amirhossein, 2023. "An exact criterion space search algorithm for a bi-objective blood collection problem," European Journal of Operational Research, Elsevier, vol. 311(1), pages 210-232.
    17. Atashpaz Gargari, Masoud & Sahraeian, Rashed, 2023. "An exact criterion space search method for a bi-objective nursing home location and allocation problem," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 206(C), pages 166-180.
    18. Di Martinelly, Christine & Meskens, Nadine, 2017. "A bi-objective integrated approach to building surgical teams and nurse schedule rosters to maximise surgical team affinities and minimise nurses' idle time," International Journal of Production Economics, Elsevier, vol. 191(C), pages 323-334.
    19. Hongming Li & Xintao Li, 2022. "A Branch-and-Bound Algorithm for the Bi-Objective Quay Crane Scheduling Problem Based on Efficiency and Energy," Mathematics, MDPI, vol. 10(24), pages 1-20, December.
    20. 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.

    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:266:y:2018:i:2:p:415-425. 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.