一种无约束优化的无参数填充函数算法

Parametric-free Filled Function Algorithm for Unconstrained Optimization

填充函数法是求解无约束全局优化问题的重要方法,其核心工作在于构建具有良好性质、形式简单而且容易求解极小值的填充函数。基于填充函数的定义,针对无约束的全局优化问题的目标函数满足条件的基础上,构建了一个无参数的填充函数。此函数形式简单,便于计算。针对此填充函数,首先,在满足合适的假设条件下,研究并证明了填充函数的某些性质;其次,在遵照这些相关性质的基础上,设计了适合此填充函数的算法,该填充函数算法主要包含极小化过程与填充过程,这两个过程循环交替进行,直至满足终止条件;最后,利用经典算例,进行了算例实验并与其他文献结果比较。结果显示,不仅此填充函数可行,算法有效;而且计算结果准确,计算迭代次数较少。

Filled function method is a kind of important method for solving unconstrained optimization problem.The key of the method is to construct a filled function with good properties,simple form and easy to solve the minimum value.Based on the definition of filled function and certain conditions of the obJective function for unconstrained global optimization problem,a non-parameter filled function is proposed for solving this problem,which is simple and easy to be calculated.For the filled function,firstly,under suitable assumptions,some properties of filled function are studied and proved.Secondly,according to the related pro-perties,an algorithm suitable for this filled function algorithm is established.The filled function algorithm consists of two phases:the minimization phase and the filling phase.The two phases alternate until the termination criterion is met.Finally,through classical examples,numerical experiments are carried out and compared with the results of other literatures.Experiments results show that not only the filled function is feasible and the algorithm is effective,but also the results are accurate and the number of iterations is less.