关于求解全局优化的途径:从局部到全局(英文)

On the Solving Global Optimization Approach from Local to Global

在实际应用中常常要求求解全局优化问题,而用有效的求解全局优化问题是非常困难的。填充函数方法和打洞函数方法是两种全局优化的函数变换方法,有关文献的计算说明这些方法是有效的。本文将给出这两种全局优化方法最近的发展。首先分析原先由葛仁溥提出的填充函数和Levy与Montalvo提出的打洞函数方法的缺点。其次给出在箱子集或者全空间上无约束或者不等式约束的全局优化问题的单参数的新填充函数和变形打洞函数的定义,并构造出相应的填充函数和变形打洞函数。此外亦讨论整数全局优化问题的填充函数和变形打洞函数方法。最近还讨论了全空间上等式约束全局优化问题。最后给出综述,指出非线性规划的一个主要发展方向:混合整数非线性规划,给出用填充函数和变形打洞函数的求解途径。

Frequently practitioners need to solve global optimization problems. These problems can be extremely difficult to solve without computationally efficient methods. Filled function methods and tunneling function methods are two kinds of function transformation methods in global optimization, and are computationally efficient as illustrated by numerous papers. In this paper, some advances in these two kinds of global optimization methods are reported. Firstly, we investigate the disadvantages of the early filled function proposed by Ge and the tunneling function proposed by Levy and Montalvo. Secondly, we propose definitions of novel filled functions and modified tunneling functions with one parameter for unconstraint and inequality constraint global optimization on box X or R^n, and construct the corresponding functions. Furthermore, we have discussed the filled functions and modified tunneling function in integer global optimization. Recently we have discussed the equality constraint global optimization on R^n. Finally, we give a survey, where we point out one of the main trends for nonlinear programming--the mixed integer nonlinear programming and we propose some solving approaches in the use of filled function or modified tunneling functions.