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A dual variant of Benson’s “outer approximation algorithm” for multiple objective linear programming

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  • Matthias Ehrgott
  • Andreas Löhne
  • Lizhen Shao

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  • 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.
    • Handle: RePEc:spr:jglopt:v:52:y:2012:i:4:p:757-778
    DOI: 10.1007/s10898-011-9709-y
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    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. 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.
    3. 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.
    4. H. P. Benson, 1998. "Further Analysis of an Outcome Set-Based Algorithm for Multiple-Objective Linear Programming," Journal of Optimization Theory and Applications, Springer, vol. 97(1), pages 1-10, April.
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    Cited by:

    1. László Csirmaz, 2016. "Using multiobjective optimization to map the entropy region," Computational Optimization and Applications, Springer, vol. 63(1), pages 45-67, January.
    2. Kellner, Florian & Lienland, Bernhard & Utz, Sebastian, 2019. "An a posteriori decision support methodology for solving the multi-criteria supplier selection problem," European Journal of Operational Research, Elsevier, vol. 272(2), pages 505-522.
    3. Daniel Ciripoi & Andreas Löhne & Benjamin Weißing, 2018. "A vector linear programming approach for certain global optimization problems," Journal of Global Optimization, Springer, vol. 72(2), pages 347-372, October.
    4. 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.
    5. 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.
    6. Julius Bauß & Michael Stiglmayr, 2024. "Augmenting bi-objective branch and bound by scalarization-based information," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 100(1), pages 85-121, August.
    7. 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.
    8. 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.
    9. 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.
    10. Zachary Feinstein & Birgit Rudloff, 2017. "A recursive algorithm for multivariate risk measures and a set-valued Bellman’s principle," Journal of Global Optimization, Springer, vol. 68(1), pages 47-69, May.
    11. Victor Blanco & Justo Puerto & Safae El Haj Ben Ali, 2014. "A Semidefinite Programming approach for solving Multiobjective Linear Programming," Journal of Global Optimization, Springer, vol. 58(3), pages 465-480, March.
    12. Zachary Feinstein & Birgit Rudloff, 2015. "A recursive algorithm for multivariate risk measures and a set-valued Bellman's principle," Papers 1508.02367, arXiv.org, revised Jul 2016.
    13. Fritz Bökler & Sophie N. Parragh & Markus Sinnl & Fabien Tricoire, 2024. "An outer approximation algorithm for generating the Edgeworth–Pareto hull of multi-objective mixed-integer linear programming problems," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 100(1), pages 263-290, August.

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