On one approach to hybridization in the multi-start method

Abstract

One of the approaches to hybridization and selection of parameters of minimization methods used in the multi-start method is proposed and experimentally tested. The approach consists in a combination of one-dimensional search methods depending on the values of the minimized function obtained in the calculation process. The multi-start method consists in repeatedly launching the methods of searching for a local minimum from various starting points. Therefore, we can assume that the problems of local minimization arising at each iteration of the method have similar characteristics. By using this feature of the multi-start method, it was possible to ensure the selection of parameters in the process of work. Numerical experiments were carried out to determine the dependence of the speed of local descent methods on the parameters and an algorithm was proposed for choosing the optimal parameter value. It has been experimentally shown that the interval of optimality of parameters has wide enough boundaries. Numerical experiments were carried out on the problem of finding the global minimum of the energy of a set of atoms of a fragment of a flat crystal lattice. To calculate the interatomic interaction energy, the Tersoff potential was used.