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Direction-Specific Gradient Scaling for Interactive Multicriterion Optimization Using an Abstract Mass Concept

Author

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  • Marvin D. Troutt

    (Southern Illinois University, Carbondale, Illinois)

Abstract

In the Method of Abstract Forces for the direction finding (or tradeoff cut) subproblems of interactive multicriterion optimization, it is necessary to scale criterion gradients. Previously, an ad hoc, analyst assisted, but nevertheless effective scaling method was used. This paper introduces a concept of abstract mass. It is shown that the previous ad hoc scaling method may be considered an approximation to the present direction-specific approach. Also, the abstract mass approach provides a strengthening of the original Newton's Second Law of Motion analogy motivation for the Method of Abstract Forces. A method for automatic and direction-specific scaling is proposed which depends on the solution of a continuous piecewise polynomial system of equations. The method is illustrated on an example with three criterion functions. In this example, Newton's method for solving simultaneous nonlinear systems converges to a solution. More generally, restart homotopy methods may be required.

Suggested Citation

  • Marvin D. Troutt, 1994. "Direction-Specific Gradient Scaling for Interactive Multicriterion Optimization Using an Abstract Mass Concept," Operations Research, INFORMS, vol. 42(6), pages 1110-1119, December.
    • Handle: RePEc:inm:oropre:v:42:y:1994:i:6:p:1110-1119
    DOI: 10.1287/opre.42.6.1110
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    Cited by:

    1. Parag Pendharkar & Marvin Troutt, 2014. "Interactive classification using data envelopment analysis," Annals of Operations Research, Springer, vol. 214(1), pages 125-141, March.
    2. Pendharkar, Parag C. & Troutt, Marvin D., 2011. "DEA based dimensionality reduction for classification problems satisfying strict non-satiety assumption," European Journal of Operational Research, Elsevier, vol. 212(1), pages 155-163, July.

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