Interactive model-based search with reactive resource allocation
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- 作者：Yue Sun ; Alfredo Garcia
- 关键词：Model ; based search ; Parallel algorithms ; Reactive resource allocation
- 刊名：Journal of Global Optimization
- 出版年：2017
- 出版时间：January 2017
- 年：2017
- 卷：67
- 期：1-2
- 页码：135-149
- 全文大小：
- 刊物类别：Business and Economics
- 刊物主题：Optimization; Operation Research/Decision Theory; Real Functions; Computer Science, general;
- 出版者：Springer US
- ISSN：1573-2916
- 卷排序：67
文摘
We revisit the interactive model-based approach to global optimization proposed in Wang and Garcia (J Glob Optim 61(3):479–495, 2015) in which parallel threads independently execute a model-based search method and periodically interact through a simple acceptance-rejection rule aimed at preventing duplication of search efforts. In that paper it was assumed that each thread successfully identifies a locally optimal solution every time the acceptance-rejection rule is implemented. Under this stylized model of computational time, the rate of convergence to a globally optimal solution was shown to increase exponentially in the number of threads. In practice however, the computational time required to identify a locally optimal solution varies greatly. Therefore, when the acceptance-rejection rule is implemented, several threads may fail to identify a locally optimal solution. This situation calls for reallocation of computational resources in order to speed up the identification of local optima when one or more threads repeatedly fail to do so. In this paper we consider an implementation of the interactive model-based approach that accounts for real time, that is, it takes into account the possibility that several threads may fail to identify a locally optimal solution whenever the acceptance-rejection rule is implemented. We propose a modified acceptance-rejection rule that alternates between enforcing diverse search (in order to prevent duplication) and reallocation of computational effort (in order to speed up the identification of local optima). We show that the rate of convergence in real-time increases with the number of threads. This result formalizes the idea that in parallel computing, exploitation and exploration can be complementary provided relatively simple rules for interaction are implemented. We report the results from extensive numerical experiments which are illustrate the theoretical analysis of performance.