Global Optimization Method by Equilibrium Points Search of Gradient-Based Dynamical Systems
Kazuaki Masuda, Kenzo Kurihara · IEEJ Transactions on Electronics Information and Systems · 2006
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.