Global Optimization Using a Multi-point Type Discrete Inertial Time-varying Model

Abstract

In this paper, we propose a new global optimization model which is described as discrete time-varying inertial gradient dynamics. The proposed model has a autonomous damping term adjustment structure which takes the search history into consideration. In the proposed model, its dynamics destabilizes autonomously when its search point approaches to the best point in the search history. Thus, stagnation of search around the neighborhood of the best point is restrained, in consequence, global search is continued. Furthermore, in this paper, we analytically explain a characteristic of the search trajectory generated by the inertial gradient system. The characteristic is the implementation of intensive and diverse search in the attracting region for the inertial gradient system. Consequently, we propose a multi-point type search model in which search points are attracted to a promising region, where objective function value is small, by a coupling structure in order to make the attracting region the promising region. We confirm effectiveness of the proposed model through numerical experiments using several benchmark problems.