在Nelder-Mead优化算法中选择初始单纯形 [英] Choosing the initial simplex in the Nelder-Mead optimization algorithm

问题描述

初始化从用户猜测"顶点进行Nelder-Mead单纯形搜索的单纯形的最佳方法是什么?

What's the best way to initialize a simplex for use in a Nelder-Mead simplex search from a user's 'guess' vertex?

推荐答案

我不确定在Nelder-Mead方法中是否存在最佳选择初始单纯形的方法，但是以下方法是通常的做法.

I'm not sure if there is a best way to choose the initial simplex in the Nelder-Mead method, but the following is what is done in common practice.

初始单纯形S的构造是通过在N维度空间中围绕您称为用户的猜测"顶点xin的位置生成n+1顶点x0,..,xn来获得的.最常见的选择是

The construction of the initial simplex S is obtained from generating n+1 vertices x0,..,xn around what you call a user's "guess" vertex xin in a N dimensional space. The most frequent choice is

x0=xin 

然后生成

和其余的n顶点，以便

and the remaining n vertices are then generated so that

xj=x0+hj*ej 

其中，ej是R^n中第j个坐标轴的单位矢量，hj是在ej方向上的步长.

where ej is the unit vector of the j-th coordinate axis in R^n and hj is a step-size in the direction of ej.

hj = 0.05    if (x0)j is non-zero
hj = 0.00025 if (x0)j=0

带有(x0)j的

x0的第j个分量.请注意，这是Matlab的 fminsearch 例程中的选择，该例程基于Nelder-Mead方案.

with (x0)j the j-th component of x0. Note that this is the choice in Matlab's fminsearch routine, which is based on the Nelder-Mead scheme.

您可以在以下找到更多信息

You can find some more information in

F. Gao，L.Han，用自适应参数实现Nelder-Mead单纯形算法"，计算机.最佳.应用，DOI 10.1007/s10589-010-9329-3

F. Gao, L. Han, "Implementing the Nelder-Mead simplex algorithm with adaptive parameters", Comput. Optim. Appl., DOI 10.1007/s10589-010-9329-3

这篇关于在Nelder-Mead优化算法中选择初始单纯形的文章就介绍到这了，希望我们推荐的答案对大家有所帮助，也希望大家多多支持IT屋！