A closer look at drawbacks of minimizing weighted sums of objectives for Pareto set generation in multicriteria optimization problems

被引：753

作者：

Das, I

Dennis, JE

机构：

[1] Dept. of Compl. and Appl. Math., Rice University, Houston

来源：

STRUCTURAL OPTIMIZATION | 1997年 / 14卷 / 01期

关键词：

Civil Engineer; Standard Technique; Uneven Distribution; Objective Space; Frequent Observation;

D O I：

10.1007/BF01197559

中图分类号：

TP39 [计算机的应用];

学科分类号：

081203 ; 0835 ;

摘要：

A standard technique for generating the Pareto set in multicriteria optimization problems is to minimize (convex) weighted sums of the different objectives for various different settings of the weights. However, it is well-known that this method succeeds in getting points from all parts of the Pareto set only when the Pareto curve is convex. This article provides a geometrical argument as to why this is the case. Secondly, it is a frequent observation that even for convex Pareto curves, an evenly distributed set of weights fails to produce an even distribution of points from all parts of the Pareto set. This article aims to identify the mechanism behind this observation. Roughly, the weight is related to the slope of the Pareto curve in the objective space in a way such that an even spread of Pareto points actually corresponds to often very uneven distributions of weights. Several examples are provided showing assumed shapes of Pareto curves and the distribution of weights corresponding to an even spread of points on those Pareto curves.

引用

页码：63 / 69

页数：7