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 数值计算与计算机应用  2017, Vol. 38 Issue (4): 297-311    DOI:
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GLOBAL OPTIMIZATION BY MULTILEVEL DIRECT SEARCH
Liu Qunfeng, Chen Jingzhou, Xu Qingui
College of Computer Science and Network Security, Dongguan University of Technology, Dongguan 523808, China
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Abstract： Direct search is an important method in numerical optimization. The DIRECT algorithm is a popular global optimization algorithm based on direct search. In this paper, we review firstly a recently proposed multilevel robust DIRECT (MrDIRECT) algorithm, especially how it can eliminate the "eventually inefficient behavior" of the DIRECT algorithm through adopting three levels of search spaces. We provide some more numerical experiments 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 conclusion 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 in this paper is helpful for the choice of the number of search levels in multilevel direct search global optimization algorithms.

 引用本文: . 多水平直接搜索全局优化方法[J]. 数值计算与计算机应用, 2017, 38(4): 297-311. . GLOBAL OPTIMIZATION BY MULTILEVEL DIRECT SEARCH[J]. Journal of Numerical Methods and Computer Applicat, 2017, 38(4): 297-311.

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