基于局部填充函数的混合优化算法的改进

填充函数算法是求解全局优化问题的常用算法,其应用效果依赖于如何合理地选择算法参数。为了方便地选择参数,该文提出了局部填充函数的概念,讨论了基于局部填充函数的混合优化算法的改进策略。对于给定的参数,混合优化算法寻找一个包含极小点的区域,使得所构造的函数在该区域上满足局部填充函数的定义,从而利用局部填充函数的性质简化寻优过程,减少优化过程中参数调整的次数和难度,提高算法的效率和稳定性。此外,针对填充函数算法研究中简单盆存在性问题,该文给出了一个实例,说明二次连续可微的函数在一定条件下其孤立极小点附近可以不存在简单盆。

Modified hybrid optimization algorithm based on locally filled functions

The filled function method is a well known optimization method for global optimization.The method's efficiency relies on properly choosing algorithmic parameters.The filled function parameters can more easily be adjusted by using the locally filled function defined in this paper.The properties of locally filled functions and cluster analysis can be used to improve the performance of the hybrid optimization algorithms.Usually,the existence of a simple basin is assumed in the study of filled function methods.An instance of twice differential functions is also given in the paper,which illustrates the nonexistence of a simple basin for a certain objective function.Finally,some numerical results are presented for the modified hybrid optimization algorithms.