A GA-Simplex Hybrid Algorithm for Global Minimization of Molecular Potential Energy Functions

Abstract

In this paper we propose a hybrid genetic algorithm for minimizing molecular potential energy functions. Experimental evidence shows that the global minimum of the potential energy of a molecule corresponds to its most stable conformation, which dictates its properties. The search for the global minimum of a potential energy function is very difficult since the number of local minima grows exponentially with molecule size. The proposed approach was successfully applied to two cases: (i) a simplified version of more general molecular potential energy functions in problems with up to 100 degrees of freedom, and (ii) a realistic potential energy function modeling two different molecules.

Minimization of Molecular Potential Energy Function Using newly developed Real Coded Genetic Algorithms

“…The potential energy function E is minimized in the specified search space [0,5] n , where n is the total number of beads in a system. Table 1 reproduces the global minimum values of [6] attained for the function E corresponding to different chain sizes i.e. corresponding to n equal to 20, 40, 60, 80 and 100. top edge indicated.…”

“…Computational results are presented in Table 3 in terms of function evaluations: average, minimum, maximum, and standard deviations of successful runs as well as the computational time of all new RCGAs. These are compared with the existing results of Bansal et al [14] and Barobosa et al [6]. In Table 3 rHYB [2] denotes the staged hybrid GA with a reduced simplex and a fixed limit for simplex iterations and qPSO [14] is a hybrid PSO in which quadratic approximation operator is hybridized with PSO.…”

“…Computational results for simplified molecular model for n=20 to 100 using WX-PM, LX-PM, WX-LLM, LX-LLM, rHYB [6] and qPSO [14]. [6], ** Bansal et al, [14] To further analyze the relative performance of all RCGAs in terms of average function evaluations, a graphical representation in the form of box plot is shown in Figure 3, where the best performer is marked with star. The average function evaluation is directly proportional to the computational cost of the method.…”

“…As given in [6] it can also be shown that for all value of n the difference between the global minimum value E * and second best value of (3) i.e. E 2 always satisfies the following relation…”

“…Further, a function [5] has been developed to test methods applied to global minimization of potential energy of molecules. In literature, many researchers for example [6][7][8][9] have applied computational intelligence methods for minimizing the potential energy function.…”