Global optimization using chaos in a quasi-steepest descent method
Hiroyuki Sugata, Kiyotaka Shimizu · Electronics and Communications in Japan (Part III Fundamental Electronic Science) · 1997
In the continuous time model of the Hopfield neural network, which is one of the recurrent-type neural networks, the minimization of a quadratic objective function is carried out by the quasi-steepest descent method with decision variables in the upper and lower limits. This paper describes a quasi-steepest descent method in which arbitrary objective functions are selected. It is shown also that when a quasi-steepest descent method is made discrete under a certain sampling condition, the trajectory becomes chaotic. In addition, a method of applying the chaotic characteristics to the global optimization for a constrained optimization problem with upper and lower limits will be shown. The effectiveness of this method will be demonstrated numerically. © 1997 Scripta Technica, Inc. Electron Comm Jpn Pt 3, 80(4): 60–70, 1997