基于模式搜索的渴求函数法在多响应优化中的应用

渴求函数法是处理多响应参数优化的常用方法之一,它通过最大化总体渴求值获得因子的最佳水平组合.然而,随着因子个数和响应个数的增加,渴求函数往往变得多约束、多峰分布、高度非线性,传统的基于梯度的优化算法不适用.根据因子及响应个数等问题复杂程度不同,提出了以模式搜索算法为基础,用重叠等值线图或遗传算法设定模式搜索的起始点,对总体渴求函数进行寻优的新方法.算例验证了该方法的有效性.

Application of Pattern Search Algorithm to Multiresponse Optimization Based on Desirability Functions

The desirability function method is widely used for multiresponse optimization by maximizing the overall desirability function. However, the overall desirability function is usually with multi-constraints, multi-peak distribution and high nonlinearity, especially when there are quite a number of factors and output responses. The traditional gradient-based procedures are not suitable for searching the maxima of overall desirability function. Therefore, this paper employs the pattern search algorithm (PS) which is gradient-free to deal with this kind of problems. The starting point of PS can be set either by the overlaid contour plot or by the genetic algorithm, depending on the complexity of the problem. Two numerical examples from literatures are presented for illustration.