Minimizing molecular potential energy function using genetic Nelder-Mead algorithm

Abstract

This paper presents a new algorithm for minimizing the molecular potential energy function. 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. 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 is called GNMA (Genetic Nelder-Mead Algorithm). Such hybridization enhances the power of the search technique by combining the wide exploration capabilities of Genetic Algorithm (GA) 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 degrees of freedom. The performance of the proposed algorithm has been compared with other 9 existing methods from the literature. The numerical results show that the proposed algorithm is promising and produce high quality solutions with low computational costs.