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Nonlinear and unconstrained multiple‐objective optimization: Algorithm, computation, and application

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  • Asim Roy
  • Jyrki Wallenius

Abstract

An extension of Zionts‐Wallenius procedure, providing a unified approach to solving several classes of multiple‐objective optimization problems, is presented. The classes of problems addressed are linear programming, nonlinear programming, and unconstrained optimization. The method and its extensions are described, implemented for computer, subjected to extensive computational testing, and applied to a quality‐control problem.

Suggested Citation

  • Asim Roy & Jyrki Wallenius, 1991. "Nonlinear and unconstrained multiple‐objective optimization: Algorithm, computation, and application," Naval Research Logistics (NRL), John Wiley & Sons, vol. 38(4), pages 623-635, August.
    • Handle: RePEc:wly:navres:v:38:y:1991:i:4:p:623-635
    DOI: 10.1002/1520-6750(199108)38:43.0.CO;2-W
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    References listed on IDEAS

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    1. K. Musselman & Joseph Talavage, 1980. "A Tradeoff Cut Approach to Multiple Objective Optimization," Operations Research, INFORMS, vol. 28(6), pages 1424-1435, December.
    2. Stanley Zionts & Jyrki Wallenius, 1983. "An Interactive Multiple Objective Linear Programming Method for a Class of Underlying Nonlinear Utility Functions," Management Science, INFORMS, vol. 29(5), pages 519-529, May.
    3. Sadagopan, S. & Ravindran, A., 1986. "Interactive algorithms for multiple criteria nonlinear programming problems," European Journal of Operational Research, Elsevier, vol. 25(2), pages 247-257, May.
    4. G. V. Loganathan & Hanif D. Sherali, 1987. "A Convergent Interactive Cutting-Plane Algorithm for Multiobjective Optimization," Operations Research, INFORMS, vol. 35(3), pages 365-377, June.
    5. Asim Roy & L. S. Lasdon & J. Lordeman, 1986. "Extending Planning Languages to Include Optimization Capabilities," Management Science, INFORMS, vol. 32(3), pages 360-373, March.
    6. Stanley Zionts & Jyrki Wallenius, 1976. "An Interactive Programming Method for Solving the Multiple Criteria Problem," Management Science, INFORMS, vol. 22(6), pages 652-663, February.
    7. Hannele Wallenius & Jyrki Wallenius & Pentti Vartia, 1978. "An Approach to Solving Multiple Criteria Macroeconomic Policy Problems and an Application," Management Science, INFORMS, vol. 24(10), pages 1021-1030, June.
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    Cited by:

    1. Asim Roy & Patrick Mackin & Jyrki Wallenius & James Corner & Mark Keith & Gregory Schymik & Hina Arora, 2008. "An Interactive Search Method Based on User Preferences," Decision Analysis, INFORMS, vol. 5(4), pages 203-229, December.

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