一个新的单参数填充函数算法

A New One-parameter Filled Function Algorithm

本文研究连续全局最优化问题的确定性求解方法.构造了一个单参数填充函数并证明了该填充函数的性质.该填充函数算法由极小化阶段和填充阶段两个阶段构成.其中极小化阶段利用局部优化方法获得填充函数的局部极小点,对填充函数的无约束极小化使得算法离开原目标函数的任何局部极小点.填充阶段依据原目标函数的局部极小点构造填充函数.极小化阶段和填充阶段交替重复实施直到终止准则满足.最后,给出了填充函数算法的数值结果.

This paper is concerned a deterministic solution method for global optimization of functions with continuous variables. A filled function with one parameter is presented and the theoretical properties of the filled function are proved. Moreover, a filled function algorithm is proposed for continuous global optimization problem. The filled function algorithm consists of two phases： a local search phase and a function filling phase. In the local search phase, we apply local minimization methods to obtain a local minimizer of the filled function. The unconstrained minimization of the filled function allows to escape from any local minima of the original objective function. In the function filling phase, based on the current local minimizer, we construct a filled function. The two phases repeat alternatively until the termination criterion is met. Finally, the numerical results of the proposed filled function algorithm are presented.