On Using the Decision Trees to Identify the Local Extrema in Parallel Global Optimization Algorithm

Abstract

In the present work, the solving of the multidimensional global optimization problems using decision tree to reveal the attractor regions of the local minima is considered. The objective function of the problem is defined as a “black box”, may be non-differentiable, multi-extremal and computational costly. We assume that the function satisfies the Lipschitz condition with a priory unknown constant. Global search algorithm is applied for the search of global minimum in the problems of such type. It is well known that the solution complexity essentially depends on the presence of multiple local extrema. Within the framework of the global search algorithm, we propose a method for selecting the vicinity of local extrema of the objective function based on analysis of accumulated search information. Conducting such an analysis using machine learning techniques allows making a decision to run a local method, which can speed up the convergence of the algorithm. This suggestion was confirmed by the results of numerical experiments demonstrating the speedup when solving a series of test problems.