两种平滑优化算法在一维情况下的比较研究

北京大学学报（自然科学版）

两种平滑优化算法在一维情况下的比较研究

崔鹏¹,张立昂¹,吉利久¹,高立²

¹北京大学信息科学技术学院，北京，100871；²北京大学数学学院，北京，100871

收稿日期:2002-10-09 出版日期:2003-09-20 发布日期:2003-09-20

Comparisons of Two Smoothing Algorithms for Optimization in One-Dimensional Space

CUI Peng¹，ZHANG Li'ang¹，JI Lijiu¹，GAO Li²

¹School of Electronic Engineering & Computer Science, Peking University, Beijing,100871; ²School of Mathematical Sciences, Peking University, Beijing, 100871

Received:2002-10-09 Online:2003-09-20 Published:2003-09-20

摘要/Abstract

摘要： 平滑方法是全局优化的一种启发式方法，在分子构像优化问题中得到大量应用。扩散方程法和邻域平均法是平滑方法的两种实现方式。在一维情况下给出了邻域平均法的性质，通过数值实验比较了两种方法的性能。对类似Griewank函数的测试函数，发现邻域平均法的优化结果在总体上优于扩散方程法。

关键词: 平滑方法, 全局优化, 扩散方程法, 邻域平均法, Griewank函数

Abstract: The smoothing method is a heuristic method for global optimization, which is much applicable in the research area of molecular conformations. The diffusion equation method (DEM) and the neighborhood averaging method (NAM) are two kinds of implementations of the smoothing method. The properties of the neighborhood averaging method and the efficiency of the two implementations in one-dimensional space are given. For Griewank-like functions, the optimization results of NAM as a whole excel DEM.

Key words: smoothing method, global optimization, diffusion equation method, neighborhood averaging method, Griewank function

中图分类号:

TP301.6

崔鹏,张立昂,吉利久,高立. 两种平滑优化算法在一维情况下的比较研究[J]. 北京大学学报（自然科学版）.

CUI Peng,ZHANG Li'ang,JI Lijiu,GAO Li. Comparisons of Two Smoothing Algorithms for Optimization in One-Dimensional Space[J]. Acta Scientiarum Naturalium Universitatis Pekinensis.

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https://xbna.pku.edu.cn/CN/Y2003/V39/I5/681