从随机到确定性的积分型全局优化方法

An Integral Global Optimization Method from Random to Deterministic

郑权等于1978年提出了积分水平集求总极值的方法,其主要特点有判别总极值的收敛准则,但其概念算法与Monte Carlo随机投点的实现算法不匹配,易遗失总极值外,其实现算法收敛性至今未解决.该文在张连生、邬冬华等提出的修正算法的基础上,将积分型方法中的Monte Carlo随机投点与确定性的数论方法相结合,以提高修正算法的计算效率,并在文中给出了这种从随机到确定性的积分型全局优化方法全局收敛性的证明.

In 1978, Zheng presented an integral-level set method to solve global optimization pro-(blems.) The method is characterized by a convergence criterion to distinguish the global optimal value. However the conceptual algorithm does not match the implementation algorithm based on the Monte-Carlo method. Implementation of Zheng's algorithm may lose the global optimal property, and its convergence has not yet been resolved. In order to improve the efficiency of the algorithm for practical computation, this paper is based on a modified algorithm proposed by Lian-sheng Zhang, et al. and the combination of Monte-Carlo method and the number theory. Finally, the global convergence of the integral global optimization method from random to deterministic is proved.