Parameter sensitivity study of the Nelder-Mead Simplex Method

摘要

This paper presents a parameter sensitivity study of the Nelder-Mead Simplex Method for unconstrained optimization. Nelder-Mead Simplex Method is very easy to implement in practice, because it does not require gradient computation; however, it is very sensitive to the choice of initial points selected. Fan-Zahara conducted a sensitivity study using a select set of test cases and suggested the best values for the parameters based on the highest percentage rate of successful minimization. Begambre-Laier used a strategy to control the Particle Swarm Optimization parameters based on the Nelder Mead Simplex Method in identifying structural damage. The main purpose of the paper is to extend their parameter sensitivity study to better understand the parameter's behavior. The comprehensive parameter sensitivity study was conducted on seven test functions: B2, Beale, Booth, Wood, Rastrigin, Rosen-brock and Sphere Functions to search for common patterns and relationships each parameter has in producing the optimum solution. The results show important relations of the Nelder-Mead Simplex parameters: reflection, expansion, contraction, and Simplex size and how they impact the optimum solutions. This study is crucial, because better understanding of the parameters behavior can motivate current and future research using Nelder-Mead Simplex in creating an intelligent algorithm, which can be more effective, efficient, and save computational time.