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Utility Function Programs and Optimization over the Efficient Set in Multiple-Objective Decision Making

Author

Listed:
  • R. Horst

    (University of Trier)

  • N. V. Thoai

    (Institute of Mathematics, Bo Ho
    University of Trier)

Abstract

Natural basic concepts in multiple-objective optimization lead to difficult multiextremal global optimization problems. Examples include detection of efficient points when nonconvexities occur, and optimization of a linear function over the efficient set in the convex (even linear) case. Assuming that a utility function exists allows one to replace in general the multiple-objective program by a single, nonconvex optimization problem, which amounts to a minimization over the efficient set when the utility function is increasing. A new algorithm is discussed for this utility function program which, under natural mild conditions, converges to an ∈-approximate global solution in a finite number of iterations. Applications include linear, convex, indefinite quadratic, Lipschitz, and d.c. objectives and constraints.

Suggested Citation

  • R. Horst & N. V. Thoai, 1997. "Utility Function Programs and Optimization over the Efficient Set in Multiple-Objective Decision Making," Journal of Optimization Theory and Applications, Springer, vol. 92(3), pages 605-631, March.
    • Handle: RePEc:spr:joptap:v:92:y:1997:i:3:d:10.1023_a:1022659523991
    DOI: 10.1023/A:1022659523991
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    References listed on IDEAS

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    1. Dessouky, M. I. & Ghiassi, M. & Davis, W. J., 1986. "Estimates of the minimum nondominated criterion values in multiple-criteria decision-making," Engineering Costs and Production Economics, Elsevier, vol. 10(2), pages 95-104, June.
    2. Benson, Harold P., 1986. "An algorithm for optimizing over the weakly-efficient set," European Journal of Operational Research, Elsevier, vol. 25(2), pages 192-199, May.
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    Cited by:

    1. Horst, Reiner & Thoai, Nguyen V., 1999. "Maximizing a concave function over the efficient or weakly-efficient set," European Journal of Operational Research, Elsevier, vol. 117(2), pages 239-252, September.
    2. Thoai, Nguyen V., 2000. "A class of optimization problems over the efficient set of a multiple criteria nonlinear programming problem," European Journal of Operational Research, Elsevier, vol. 122(1), pages 58-68, April.
    3. Le Thi, Hoai An & Pham, Dinh Tao & Thoai, Nguyen V., 2002. "Combination between global and local methods for solving an optimization problem over the efficient set," European Journal of Operational Research, Elsevier, vol. 142(2), pages 258-270, October.
    4. S.T. Hackman & U. Passy, 2002. "Maximizing a Linear Fractional Function on a Pareto Efficient Frontier," Journal of Optimization Theory and Applications, Springer, vol. 113(1), pages 83-103, April.
    5. R. Horst & N. V. Thoai & Y. Yamamoto & D. Zenke, 2007. "On Optimization over the Efficient Set in Linear Multicriteria Programming," Journal of Optimization Theory and Applications, Springer, vol. 134(3), pages 433-443, September.
    6. H.A. Le Thi & T. Pham Dinh & L.D. Muu, 2003. "Simplicially-Constrained DC Optimization over Efficient and Weakly Efficient Sets," Journal of Optimization Theory and Applications, Springer, vol. 117(3), pages 503-531, June.
    7. J. Fülöp & L. D. Muu, 2000. "Branch-and-Bound Variant of an Outcome-Based Algorithm for Optimizing over the Efficient Set of a Bicriteria Linear Programming Problem," Journal of Optimization Theory and Applications, Springer, vol. 105(1), pages 37-54, April.
    8. Nguyen, Duy Van, 2013. "Global maximization of UTA functions in multi-objective optimization," European Journal of Operational Research, Elsevier, vol. 228(2), pages 397-404.
    9. Tu, Ta Van, 2000. "Optimization over the efficient set of a parametric multiple objective linear programming problem," European Journal of Operational Research, Elsevier, vol. 122(3), pages 570-583, May.
    10. Ehrgott, Matthias & Tenfelde-Podehl, Dagmar, 2003. "Computation of ideal and Nadir values and implications for their use in MCDM methods," European Journal of Operational Research, Elsevier, vol. 151(1), pages 119-139, November.

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