多水平直接搜索全局优化方法  

GLOBAL OPTIMIZATION BY MULTILEVEL DIRECT SEARCH

作　　者：刘群锋[1] 陈景周 徐钦桂[1] 

机构地区：[1]东莞理工学院计算机学院,广东东莞523808

出　　处：《数值计算与计算机应用》2017年第4期297-311,共15页Journal on Numerical Methods and Computer Applications

基　　金：国家自然科学基金(#61773119);广东省自然科学基金(#2015A030313648)资助

摘　　要：直接搜索是数值最优化中的重要思想.DIRECT算法是基于直接搜索思想的一个流行的全局优化算法.本文首先回顾了新近提出来的一个具有三水平直接搜索框架的全局优化算法MrDIRECT,着重回顾了MrDIRECT算法是怎样消除DIRECT算法的"渐近无效"行为的,并为此提供了更多的数值证据.然后,本文提出了一个具有四水平直接搜索框架的MrDIRECT算法,讨论了其收敛性,并对之进行了大量的数值测试.我们的目的是检验水平数的增加对算法效率的影响.结果表明,水平数的增加带来的数值效果的改善并不足以抵消计算成本的增加,总体数值效果不如三水平MrDIRECT算法.最后,本文指出MrDIRECT算法采用的多水平直接搜索框架的重要优势是,能够很灵活地平衡局部搜索和全局搜索,从而可用于设计更多的多水平直接搜索全局优化算法.本文验证的水平数增加未必带来整体数值效果的改善这一结论也可用于指导这类算法的设计.Direct search is an important method in numerical optimization. The DIRECT algo- rithm is a popular global optimization algorithm based on direct search. In this paper, we review firstly a recently proposed multilevel robust DIRECT （MrDIRECT） algorithm, espe- cially how it can eliminate the ＂eventually inefficient behavior＂ of the DIRECT algorithm through adopting three levels of search spaces. We provide some more numerical experi- ments to support MrDIRECT＇s such ability. Then we propose a new version of MrDIRECT which adopts four levels of search spaces. Our main purpose is to verify the affection of the number of search levels. Extensive numerical results show that four search levels bring no significant improvement but consumes much more computational cost. Therefore, our con- clusion is that large number of search levels are not suitable for multilevel search in global optimization. Finally, we pointed out that the idea of multilevel direct search spaces is very convenient in balancing between local search and global search, and therefore can be used to design other global optimization algorithms. Moreover, the numerical result obtained inthis paper is helpful for the choice of the number of search levels in multilevel direct search global optimization algorithms.

关 键 词：全局优化 直接搜索 多水平算法 MrDIRECT算法 

分 类 号：O224[理学—运筹学与控制论]