Improved Nelder–Mead algorithm in high dimensions with adaptive parameters based on Chebyshev spacing points

Abstract

In spite of being one of the most popular optimization methods, Nelder–Mead's simplex search algorithm with the default choice of parameters performs poorly on high-dimensional problems. The work presented here concerns such values of the Nelder–Mead algorithm's parameters that help improve the convergence and success rate of the algorithm in high dimensions. In this work, a novel way of assigning parameters to the Nelder–Mead simplex search algorithm is proposed. The proposed scheme is based on Chebyshev spacing points and adapts itself to the dimension of the problem. The numerical experiments conducted for this study show that the proposed scheme is better not just in comparison with the original Nelder–Mead algorithm but it outperforms the other existing adaptive schemes as well.