一个新的非线性整数规划问题的单参数填充函数算法

非线性整数规划问题是一类复杂的优化问题,填充函数算法是求解整数规划问题的一类有效方法.构造一个新的单参数填充函数,分析并证明了其填充性质;然后,基于该填充函数并结合离散最速下降法提出了一种新的填充函数算法;最后,采用新算法对6个测试函数进行数值实验,结果表明该算法具有良好的计算效果,是有效可行的.

A new single parameter filled function method for nonlinear integer programming

Nonlinear integer programming problem is a kind of complex optimization problem. The filled function algorithm is an effective method for solving integer programming problems. It involves an auxiliary function to move successively from one local minimum to another better one. At the same time, the method for using only the local minimization algorithm of mature and popular. However, most of the existing filled functions contain one or two interdependent parameters, which makes it difficult to select and adjust the parameters. And the filled function is a composite function of the objective function, and the objective function itself is more complex. Therefore, it is important to construct a filled function which is simple in form, with fewer parameters and good properties. To solve such problems, in this paper, firstly, we construct a new filled function with one parameter, analyze and prove its filling properties; then, the filled function combined with discrete steepest descent method and proposes a new filled function algorithm; finally, the implementation of the algorithms on six test problems show that the algorithm has good effect and is effective and feasible.