关键词: Julia集, 分形, 混沌, 全局优化

Abstract: Newton optimization technique is an important optimization technique and a nonlinear discrete dynamic process that exhibits sensitive dependence on initial guess point. This sensitivity has a fractal nature. The Julia set of Newton optimization iterative function is the sensitive area. A method to find Julia set point is proposed. The Julia set which is the boundaries of basins of attractions (optima) display the intricate fractal structures and chaos phenomena. A novel global optimization method based on utilizing sensitive fractal areas to locate the Julia set point to find all the local optima of the nonlinear optimization problems is proposed. The developed technique uses an important feature of fractals to preserve shape of basins of attraction (optima) on infinitely small scales. The numerical simulation results show that the method is effective.

Key words: Chaos, Fractals, Global optimzation, Julia sets