Global Optimization by Generalized Random Tunneling Algorithm and Its Application to System Identification and Control Problems Using Neural Networks

Abstract

Recently, new global optimization procedure called Random Tunneling Algorithm has been proposed for the problems which have differential objective functions. In this paper, we generalize it and propose a method which can also solve the problems which have non-differentiable objective functions. We apply the proposed method to system identification and control problems using neural networks in order to show its effectiveness.There exist two phases in the tunneling algorithm for global minimization problems, 1) minimization phase and 2) tunneling phase. The local minimum is searched in the minimization phase and the point in the lower valley is searched in the tunneling phase.In the proposed algorithm, we use the random search which generates the increments according to Cauchy distribution in the minimization phase. Likewise, in the tunneling phase, we generate the increments from the local minimum at some temperature according to Cauchy distribution and search the points in the lower valley. The wide range of search becomes possible owing to the property of Cauchy distribution and temperature cooling.In addition to numerical test problems, system identification and adaptive control problems using neural networks are solved. The proposed method works very well for these application problems and is very promising for many types of global optimization problems.