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Less is more: simplified Nelder-Mead method for large unconstrained optimization

Kayo Gonçalves-e-Silva, Daniel Aloise, Samuel Xavier-De-Souza, Nenad Mladenović

Article (2018)

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Abstract

Nelder-Mead method (NM) for solving continuous non-linear optimization problem is probably the most cited and the most used method in the optimization literature and in practical applications, too. It belongs to the direct search methods, those which do not use the first and the second order derivatives. The popularity of NM is based on its simplicity. In this paper we propose even more simple algorithm for larger instances that follows NM idea. We call it Simplified NM (SNM): instead of generating all n + 1 simplex points in Rn, we perform search using just q + 1 vertices, where q is usually much smaller than n. Though the results cannot be better than after performing calculations in n+1 points as in NM, significant speed-up allows to run many times SNM from different starting solutions, usually getting better results than those obtained by NM within the same cpu time. Computational analysis is performed on 10 classical convex and non-convex instances, where the number of variables n can be arbitrarily large. The obtained results show that SNM is more effective than the original NM, confirming that LIMA yields good results when solving a continuous optimization problem.

Uncontrolled Keywords

continuous optimization; direct search methods; Nelder Mead method; less is more approach

Subjects: 2700 Information technology > 2706 Software engineering
2700 Information technology > 2715 Optimization
Department: Department of Computer Engineering and Software Engineering
Funders: CNPq-Brazil, RSF, NPAD/UFRN
Grant number: 308887/2014-0, 400350/2014-9, 14-41-00039
PolyPublie URL: https://publications.polymtl.ca/3562/
Journal Title: Yugoslav Journal of Operations Research (vol. 28, no. 2)
Publisher: Faculty of Organizational Sciences, Belgrade, Mihajlo Pupin Institute, Belgrade, Faculty of Transport and Traffic Engineering, Belgrade, Faculty of Mining and Geology – Department of Mining, Belgrade, Mathematical Institute SANU, Belgrade
DOI: 10.2298/yjor180120014g
Official URL: https://doi.org/10.2298/yjor180120014g
Date Deposited: 27 Mar 2020 08:32
Last Modified: 08 Nov 2022 14:59
Cite in APA 7: Gonçalves-e-Silva, K., Aloise, D., Xavier-De-Souza, S., & Mladenović, N. (2018). Less is more: simplified Nelder-Mead method for large unconstrained optimization. Yugoslav Journal of Operations Research, 28(2), 153-169. https://doi.org/10.2298/yjor180120014g

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