Multi-direction-based Nelder–Mead method

Abstract

The original Nelder–Mead (NM) method tends to be used to optimize low-dimensional functions. This article provides a modified NM that has the capability of large-scale optimization. The modification of NM is characterized by (a) working with a population of points, (b) mining multiple search directions through two strategies – point-grouping and variable-centroid multi-direction (VCMD), thus giving rise to VCMD plus grouping (VCMD_g) and (c) introducing random coefficients into NM and performing mutation on best-points, producing a random NM (NM_r). The combination of NM_r and VCMD_g, NM_r-VCMD_g, is just the modified NM in this work.

Keywords:

• large-scale global optimization
• Nelder–Mead method
• multi-direction search
• random search

Acknowledgements

Hong Feng Xiao gratefully acknowledges the support from Starup Fund for doctorial Programm of Hunan Normal University, Programme Fundation for the Excellent Youth Scholars of Hunan Normal University and the National Natural Science Foundation of China (51005074).