Global Optimization Constrained on the Hypersphere by Using Continuous Dissipative Chaos

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 classified into discretized gradient models and continuous dissipative models with a nonlinear damping term. In this paper, optimization problems with hyperspherical constraints are considered in order to present nonlinear dissipative dynamics embedded in their constraints. As the nonlinear dissipative dynamics, Fujita-Yasuda’s Model⁽²⁾ and Tani’s Model⁽³⁾ are adopted. Especially, their revised models are proposed newly for the hyperspherical constraints. The numerical simulations for a few constrained optimization problems demonstrate effectiveness of presented constrained global optimization methods.