Pareto analysis in multiobjective optimization using the collinearity theorem and scaling method
Pareto analysis in multiobjective optimization using the collinearity theorem and scaling method
复制标题
DOI：
10.1007/s001580100138
复制
发表时间：
2001-10-01
影响因子：
3.9
通讯作者：
Lewis, KE
中科院分区：
文献类型：
--
作者：
Kasprzak, EM;Lewis, KE
本文提出了一种预测使Pareto解集中任意成员成为最优所必需的相对客观加权格式的方法。首先，利用仿真和高性能计算构造了Pareto集的多项式描述。然后，利用所讨论的帕累托集合的成员，乌托邦点的位置和多项式系数之间的几何关系，确定导致帕累托集合中特定成员成为最优的性能指标的权重。通过车辆动力学优化领域的一个示例问题来检验这种称为缩放法的技术的使用。标度方法基于共线性定理，文中也给出了该定理。
This paper presents a method to predict the relative objective weighting scheme necessary to cause arbitrary members of a Pareto solution set to become optimal. First, a polynomial description of the Pareto set is constructed utilizing simulation and high performance computing. Then, using geometric relationships between the member of the Pareto set in question, the location of the utopia point and the polynomial coefficients, the weighting of the performance metrics which causes a particular member of the Pareto set to become optimal is determined. The use of this technique, termed the scaling method, is examined via using a sample problem from the field of vehicle dynamics optimization. The scaling method is based on the collinearity theorem which is also presented in the paper.