Transactions of the Institute of Systems, Control and Information Engineers
Online ISSN : 2185-811X
Print ISSN : 1342-5668
ISSN-L : 1342-5668
Constrained Global Optimization Methods by Using Inner State Models with Nonlinear Dissipative Dynamics
Takashi OKAMOTOEitaro AIYOSHI
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2003 Volume 16 Issue 12 Pages 662-669

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Abstract

Optimization methods by using chaos dynamics are interesting as a class of global optimization methods by which the global minimum can be obtained without trapping in local minima. The chaos dynamics are classfied into discretized gradient models and continuous dissipative models with a nonlinear damping term. In this paper, two types of constrained optimization problems are considered in order to present nonlinear dissipative dynamics embedded in their constraints. One of types of the constraints is upper and lower bounds on each variable, and the other type is a simplex. For the each type of constraints, the inner state model with nonlinear dissipative dynamics w.r.t.inner states is introduced, which is composed of a nonlinear inertial model with the gradient and a nonlinear output function. As the nonlinear dissipative dynamics, Fujita-Yasuda's Model [6] and Tani's Model [7] are adopted. Especially, their revised models are proposed newly for the simplex type. The numerical simulations for a few constrained optimization problems demonstrate effectiveness of presented constrained global optimization methods.

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