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This paper proposes a global optimization method based on thoroughly searching for equilibrium points of gradient-based dynamical systems. Such a method is possible due to the linkage between equilibrium points of nonlinear systems and the outstanding properties of gradient dynamics. As the essence of this study, a general form of computational procedure for efficiently finding equilibrium points of nonlinear dynamical system based on the use of trajectories initiating from already known points into their eigen-directions is provided. Then, optimization is realized by incorporating the procedure to gradient-based models for obtaining various local optima as their stable equilibrium points. Its application to constrained global optimization is also discussed, and the effectiveness of our method is demonstrated through numerical simulations.

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This paper proposes a global optimization method based on searching for multiple equilibrium points of gradient-based dynamical systems. We are motivated to construct the method with significant mathematical properties of gradient systems from the viewpoint of optimization and nonlinear science. As the essence of this study, we propose a computational procedure for finding equilibrium points of nonlinear dynamical system with ascending or descending trajectories. The computation requires to generate trajectories from known equilibrium points to various directions. In this paper, we will further discuss the simplification of the procedure to reduce calculation by using a certain set of vectors. We will also show the effectiveness of our method through numerical simulations.

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