一个求解无约束优化的单参数填充函数算法

A Filled Function Algorithm with One Parameter for Unconstrained Optimization Problems

填充函数法被称为求解无约束的全局优化问题的重要方法,此方法的核心之处在于构建具有性质良好、形式简单而且容易求解极小值的填充函数。严格按照填充函数的定义,在目标函数符合条件的基础上,鉴于全局优化问题,构建了一个新的单参数填充函数。此函数具有形式简单、计算简便的特点。在合理的假设条件下,探究并且证明了该填充函数的填充性质和其他的必要性质。并在遵循这些相关性质的基础上,设计了适合该填充函数的算法;此填充函数的算法的主要过程是极小化过程和填充过程;极小化过程和填充过程循环交替运行,直到满足终止条件。最后,通过经典算例,进行了算例实验并与其他文献的结果比较。结果表明,该填充函数是可行的,算法是有效的。结果精确度较高,迭代次数较少。

The filled function method is known as an important method for solving unconstrained optimization problem,the key of which is to construct a filled function whose minimum is easy to solve with excellent properties and simple form. Strictly following the definition of the fill function,in view of the global optimization problem,we construct a new single parameter filling function on the basis of the qualified objective function with simple form and simple calculation. Under reasonable assumptions,the filled properties and other necessary properties of the function are explored and proved. Besides,according to these related properties,an algorithm suitable for the filling function is designed,which consists of two phases:a local search phase and function filled phase. The two phases repeat alternatively until the termination criterion is met. Finally,through classical examples,numerical experiments are carried out and compared with the other literatures. It is showed that the function is feasible and the algorithm is effective,with higher accuracy and fewer iterations.