求解全局优化问题的填充函数法

求解全局优化问题的填充函数法

姜志侠¹,², 花秋玲²

1. 吉林大学数学学院，长春 130012； 2. 长春理工大学理学院应用数学系, 长春 130022

收稿日期:2006-11-30 修回日期:1900-01-01 出版日期:2007-09-26 发布日期:2007-09-26
通讯作者: 姜志侠

A Filled Function Method for Solving Global Optimization Problem

JIANG Zhixia¹,², HUA Qiuling²

1. College of Mathematics, Jilin University, Changchun 130012, China; 2. Department of Applied Mathematics, College of Science, Changchun University of Science and Technology， Changchun 130022, China

Received:2006-11-30 Revised:1900-01-01 Online:2007-09-26 Published:2007-09-26
Contact: JIANG Zhixia

摘要/Abstract

摘要： 给出一类基于目标函数和变量与极值点距离平方的填充函数, 应用此函数可从一个极小值点出发, 找到函数值小于此极值的另一极值点；证明了适当选取参数r可使函数达到总体极小值而非鞍点值或极大值，并给出了具体的算法步骤及算例.

关键词: 填充函数, 盆地, 极小值

Abstract: A filled function is proposed based on the objective function and the square of the distance between variate and extremum point. With the filled function, from a minimum point we can find another minimum point at which the value of the function is less than the former value. We have proven it can make the function reach to the global minimum but not maximum or saddle point value to select r properly. Finally steps and examples of the algorithm are given.

Key words: filled function, basin, minimum

中图分类号:

O221.2

姜志侠,, 花秋玲. 求解全局优化问题的填充函数法[J]. J4, 2007, 45(05): 733-737.

JIANG Zhixia,, HUA Qiuling. A Filled Function Method for Solving Global Optimization Problem[J]. J4, 2007, 45(05): 733-737.