Authors: Zhao, Qiu Hong
Urošević, Dragan 
Mladenović, Nenad 
Hansen, Pierre
Affiliations: Mathematical Institute of the Serbian Academy of Sciences and Arts 
Title: A restarted and modified simplex search for unconstrained optimization
Journal: Computers and Operations Research
Volume: 36
Issue: 12
First page: 3263
Last page: 3271
Issue Date: 1-Dec-2009
Rank: M21a
ISSN: 0305-0548
DOI: 10.1016/j.cor.2009.03.005
In this paper we propose a simple but efficient modification of the well-known Nelder-Mead (NM) simplex search method for unconstrained optimization. Instead of moving all n simplex vertices at once in the direction of the best vertex, our "shrink" step moves them in the same direction but one by one until an improvement is obtained. In addition, for solving non-convex problems, we simply restart the so-modified NM (MNM) method by constructing an initial simplex around the solution obtained in the previous phase. We repeat restarts until there is no improvement in the objective function value. Thus, our restarted modified NM (RMNM) is a descent and deterministic method and may be seen as an extended local search for continuous optimization. In order to improve computational complexity and efficiency, we use the heap data structure for storing and updating simplex vertices. Extensive empirical analysis shows that: our modified method outperforms in average the original version as well as some other recent successful modifications; in solving global optimization problems, it is comparable with the state-of-the-art heuristics.
Keywords: Direct search methods | Global optimization | Metaheuristics | Nelder-Mead method | Restarted modified simplex search | Unconstrained optimization
Publisher: Elsevier
Project: National Natural Science Foundation of China (under Project nos. 70771001 and 70821061)
New Century Excellent Talents in University of China under Project no. NCET-07-0049
Serbian Ministry of Science, Project no. 144007

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