混沌分形优化方法及其应用

Chaos & fractals optimization method and its application

混沌分形是动力系统普遍出现的一种现象.牛顿优化技术是重要的一维及多维优化迭代技术,其迭代本身对初始点非常敏感,该敏感区是牛顿优化技术所构成的非线性离散动力系统Julia集.在Julia集中迭代函数会呈现出混沌分形现象,论文提出了一种寻找牛顿优化迭代函数的Julia点的求解方法,利用非线性离散动力系统在其Julia集出现混沌分形现象的特点,提出了一种基于牛顿优化技术的全局优化新方法,数值试验表明了该方法的有效性和正确性.

Chaos & fractals are universal phenomena in dynamic systems. Newton optimization method is an important optimization technique whose iterative process itself is heavily sensitive to the initial guess point. 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) displays the intricate fractal structures and chaos phenomena. A novel global optimization method that utilizes sensitive fractal areas to locate the Julia set point to find all the local optima of the nonlinear optimization problems is proposed. The numerical simulation results show that the method is effective.