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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. | Yugoslav Journal of Operations Research 28 (2018), Number 2, 153–169 DOI: https://doi.org/10.2298/YJOR180120014G LESS IS MORE: SIMPLIFIED NELDER-MEAD METHOD FOR LARGE UNCONSTRAINED OPTIMIZATION Kayo GONC ¸ ALVES-E-SILVA Digital Metropolis Institute, Universidade Federal do Rio Grande do Norte, Natal, Brazil kayo@imd.ufrn.br Daniel ALOISE ´ Department of Computer and Software Engineering, Ecole Polytechnique de Montral, Montr´eal, Canada daniel.aloise@polymtl.ca Samuel XAVIER-DE-SOUZA Department of Computation and Automation, Universidade Federal do Rio Grande do Norte, Natal, Brazil samuel@dca.ufrn.br ´ Nenad MLADENOVIC Mathematical Institiute, Serbian Academy of Sciences and Arts, Belgrade, Serbia nenad@mi.sanu.ac.rs Received: January 2018 / Accepted: March 2018 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 con- 154 K. Gon¸calves-e-Silva, et al. / Less is more: Simplified Nelder-Mead Method vex 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 .
