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Further Analysis of an Outcome Set-Based Algorithm for Multiple-Objective Linear Programming

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  • H. P. Benson

    (Warrington College of Business Administration, University of Florida)

Abstract

Various difficulties have been encountered in using decision set-based vector maximization methods to solve a multiple-objective linear programming problem (MOLP). Motivated by these difficulties, Benson recently developed a finite, outer-approximation algorithm for generating the set of all efficient extreme points in the outcome set, rather than in the decision set, of problem (MOLP). In this article, we show that the Benson algorithm also generates the set of all weakly efficient points in the outcome set of problem (MOLP). As a result, the usefulness of the algorithm as a decision aid in multiple objective linear programming is further enhanced.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:joptap:v:97:y:1998:i:1:d:10.1023_a:1022614814789
    DOI: 10.1023/A:1022614814789
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    References listed on IDEAS

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    1. Gal, Tomas, 1977. "A general method for determining the set of all efficient solutions to a linear vectormaximum problem," European Journal of Operational Research, Elsevier, vol. 1(5), pages 307-322, September.
    2. Gerald W. Evans, 1984. "An Overview of Techniques for Solving Multiobjective Mathematical Programs," Management Science, INFORMS, vol. 30(11), pages 1268-1282, November.
    3. Harold P. Benson, 1985. "Multiple Objective Linear Programming with Parametric Criteria Coefficients," Management Science, INFORMS, vol. 31(4), pages 461-474, April.
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    Cited by:

    1. Henri Bonnel & Julien Collonge, 2015. "Optimization over the Pareto outcome set associated with a convex bi-objective optimization problem: theoretical results, deterministic algorithm and application to the stochastic case," Journal of Global Optimization, Springer, vol. 62(3), pages 481-505, July.
    2. Zhenqiang Zhang & Sile Ma & Xiangyuan Jiang, 2022. "Research on Multi-Objective Multi-Robot Task Allocation by Lin–Kernighan–Helsgaun Guided Evolutionary Algorithms," Mathematics, MDPI, vol. 10(24), pages 1-17, December.
    3. 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.
    4. 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.
    5. Henri Bonnel & Julien Collonge, 2014. "Stochastic Optimization over a Pareto Set Associated with a Stochastic Multi-Objective Optimization Problem," Journal of Optimization Theory and Applications, Springer, vol. 162(2), pages 405-427, August.
    6. 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.
    7. 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.

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