DIRECTION-SPECIFIC GRADIENT SCALING FOR INTERACTIVE MULTICRITERION OPTIMIZATION USING AN ABSTRACT MASS CONCEPT
成果类型：
Article
署名作者：
TROUTT, MD
刊物名称：
OPERATIONS RESEARCH
ISSN/ISSBN：
0030-364X
DOI：
10.1287/opre.42.6.1110
发表日期：
1994
页码：
1110-1119
关键词：
摘要：
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.