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Computational Approach to Essential and Nonessential Objective Functions in Linear Multicriteria Optimization

Author

Listed:
  • A. B. Malinowska

    (Białystok Technical University)

  • D. F. M. Torres

    (University of Aveiro)

Abstract

The question of obtaining well-defined criteria for multiple-criteria decision making problems is well known. One of the approaches dealing with this question is the concept of nonessential objective functions. A certain objective function is called nonessential if the set of efficient solutions is the same with or without that objective function. We present two methods for determining nonessential objective functions. A computational implementation is done using a computer algebra system.

Suggested Citation

  • A. B. Malinowska & D. F. M. Torres, 2008. "Computational Approach to Essential and Nonessential Objective Functions in Linear Multicriteria Optimization," Journal of Optimization Theory and Applications, Springer, vol. 139(3), pages 577-590, December.
    • Handle: RePEc:spr:joptap:v:139:y:2008:i:3:d:10.1007_s10957-008-9397-z
    DOI: 10.1007/s10957-008-9397-z
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    References listed on IDEAS

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    1. Gal, Tomas & Hanne, Thomas, 2006. "Nonessential objectives within network approaches for MCDM," European Journal of Operational Research, Elsevier, vol. 168(2), pages 584-592, January.
    2. Gal, Tomas & Leberling, Heiner, 1977. "Redundant objective functions in linear vector maximum problems and their determination," European Journal of Operational Research, Elsevier, vol. 1(3), pages 176-184, May.
    3. Gal, Tomas & Hanne, Thomas, 1999. "Consequences of dropping nonessential objectives for the application of MCDM methods," European Journal of Operational Research, Elsevier, vol. 119(2), pages 373-378, December.
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    Cited by:

    1. Nguyen Thoai, 2012. "Criteria and dimension reduction of linear multiple criteria optimization problems," Journal of Global Optimization, Springer, vol. 52(3), pages 499-508, March.
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