Geometric generalization of the nelder-mead algorithm

Authors:
Alberto Moraglio;Colin G. Johnson
Affiliations:
School of Computing, University of Kent, Canterbury, UK;School of Computing, University of Kent, Canterbury, UK
Venue:
EvoCOP'10 Proceedings of the 10th European conference on Evolutionary Computation in Combinatorial Optimization
Year:
2010

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Abstract

The Nelder-Mead Algorithm (NMA) is an almost half-century old method for numerical optimization, and it is a close relative of Particle Swarm Optimization (PSO) and Differential Evolution (DE). Geometric Particle Swarm Optimization (GPSO) and Geometric Differential Evolution (GDE) are recently introduced formal generalization of traditional PSO and DE that apply naturally to both continuous and combinatorial spaces. In this paper, we generalize NMA to combinatorial search spaces by naturally extending its geometric interpretation to these spaces, analogously as what was done for the traditional PSO and DE algorithms, obtaining the Geometric Nelder-Mead Algorithm (GNMA).