期刊
EUROPEAN JOURNAL OF OPERATIONAL RESEARCH
卷 220, 期 3, 页码 684-694出版社
ELSEVIER
DOI: 10.1016/j.ejor.2012.02.028
关键词
Simulation; Direct search method; Nelder-Mead simplex
资金
- Advanced Manufacturing and Service Management Center at National Tsing Hua University [100NN2074E1/101N2074E1]
- National Science Council in Taiwan [NSC99-2221-E-007-038-MY1]
Nelder-Mead simplex method (NM), originally developed in deterministic optimization, is an efficient direct search method that optimizes the response function merely by comparing function values. While successful in deterministic settings, the application of NM to simulation optimization suffers from two problems: (1) It lacks an effective sample size scheme for controlling noise; consequently the algorithm can be misled to the wrong direction because of noise, and (2) it is a heuristic algorithm; the quality of estimated optimal solution cannot be quantified. We propose a new variant, called Stochastic Nelder-Mead simplex method (SNM), that employs an effective sample size scheme and a specially-designed global and local search framework to address these two problems. Without the use of gradient information, SNM can handle problems where the response functions are nonsmooth or gradient does not exist. This is complementary to the existing gradient-based approaches. We prove that SNM can converge to the true global optima with probability one. An extensive numerical study also shows that the performance SNM is promising and is worthy of further investigation. (C) 2012 Elsevier B.V. All rights reserved.
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