Direction-specific gradient scaling for interactive multicriterion optimization using an abstract mass concept

Direction-specific gradient scaling for interactive multicriterion optimization using an abstract mass concept

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Article ID: iaor19961290
Country: United States
Volume: 42
Issue: 6
Start Page Number: 1110
End Page Number: 1119
Publication Date: Nov 1994
Journal: Operations Research
Authors:
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 as 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.

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