Multi-start method with deterministic restart mechanism

The work is devoted to the development and study of a method for solving global optimization problems with interval constraints. The paper proposes a global optimization algorithm based on a deterministic method of selecting starting points for local search methods. The starting points are the extremum points of functions of one variable, obtained by restricting the objective function to straight, collinear coordinate vectors. The effectiveness of the proposed algorithm is demonstrated by the example of the problem of minimizing the energy of a fragment of a flat crystal lattice. The energy of interatomic interaction is calculated using the Tersoff potential. An experimental comparison is made of the developed algorithm with the classical version of the multi-start method, in which pseudo-random points uniformly distributed in the parallelepiped are used to select starting points. As a local search method, in both cases, one of the modifications of the coordinate wise descent method is used. The developed method can be applied to problems with an unknown analytical expression for an objective function that is often encountered in practice.