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Outcome Space Partition of the Weight Set in Multiobjective Linear Programming

Author

Listed:
  • H. P. Benson

    (University of Florida)

  • E. Sun

    (University of Florida)

Abstract

Approaches for generating the set of efficient extreme points of the decision set of a multiple-objective linear program (P) that are based upon decompositions of the weight set W0 suffer from one of two special drawbacks. Either the required computations are redundant, or not all of the efficient extreme point set is found. This article shows that the weight set for problem (P) can be decomposed into a partition based upon the outcome set Y of the problem, where the elements of the partition are in one-to-one correspondence with the efficient extreme points of Y. As a result, the drawbacks of the decompositions of W0 based upon the decision set of problem (P) disappear. The article explains also how this new partition offers the potential to construct algorithms for solving large-scale applications of problem (P) in the outcome space, rather than in the decision space.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:joptap:v:105:y:2000:i:1:d:10.1023_a:1004605810296
    DOI: 10.1023/A:1004605810296
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    References listed on IDEAS

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    8. 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.
    9. 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.
    10. 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.
    11. M. Ehrgott & J. Puerto & A. M. Rodríguez-Chía, 2007. "Primal-Dual Simplex Method for Multiobjective Linear Programming," Journal of Optimization Theory and Applications, Springer, vol. 134(3), pages 483-497, September.
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