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Sensitivity of Pareto Solutions in Multiobjective Optimization

Author

Listed:
  • A. Balbás

    (Universidad Carlos III)

  • E. Galperin

    (Université du Québec à Montréal)

  • P. Jiménez. Guerra

    (Universidad Nacional de Educación a Distancia)

Abstract

The paper presents a sensitivity analysis of Pareto solutions on the basis of the Karush-Kuhn-Tucker (KKT) necessary conditions applied to nonlinear multiobjective programs (MOP) continuously depending on a parameter. Since the KKT conditions are of the first order, the sensitivity properties are considered in the first approximation. An analogue of the shadow prices, well known for scalar linear programs, is obtained for nonlinear MOPs. Two types of sensitivity are investigated: sensitivity in the state space (on the Pareto set) and sensitivity in the cost function space (on the balance set) for a vector cost function. The results obtained can be used in applications for sensitivity computation under small variations of parameters. Illustrative examples are presented.

Suggested Citation

  • A. Balbás & E. Galperin & P. Jiménez. Guerra, 2005. "Sensitivity of Pareto Solutions in Multiobjective Optimization," Journal of Optimization Theory and Applications, Springer, vol. 126(2), pages 247-264, August.
    • Handle: RePEc:spr:joptap:v:126:y:2005:i:2:d:10.1007_s10957-005-4713-3
    DOI: 10.1007/s10957-005-4713-3
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    Cited by:

    1. Balbás, Alejandro & Balbás, Beatriz & Balbás, Raquel, 2016. "Good deals and benchmarks in robust portfolio selection," European Journal of Operational Research, Elsevier, vol. 250(2), pages 666-678.
    2. Mansouri, S. Afshin & Aktas, Emel & Besikci, Umut, 2016. "Green scheduling of a two-machine flowshop: Trade-off between makespan and energy consumption," European Journal of Operational Research, Elsevier, vol. 248(3), pages 772-788.

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