A Simplex Nelder Mead Genetic Algorithm for Minimizing Molecular Potential Energy Function

Abstract

In this paper, we propose a new algorithm, namely genetic Nelder Mead algorithm (GNMA), for minimizing molecular potential energy function. The minimization of molecular potential energy function problem is very challenging, since the number of local minima grows exponentially with the molecular size. The new algorithm combines a global search genetic algorithm with a local search Nelder-Mead algorithm in order to search for the global minimum of molecular potential energy function. Such hybridization enhances the power of the search technique by combining the wide exploration capabilities of genetic algorithm and the deep exploitation capabilities of Nelder-Mead algorithm. The proposed algorithm can reach the global or near-global optimum for the molecular potential energy function with up to 200\(^\circ \) of freedom. We compared the proposed GNMA results with the results of 9 existing algorithms from the literature. Experimental results show efficiency of the proposed GNMA to have more accurate solutions with low computational costs.