整数规划问题的滤子填充函数算法  

A filled-filter function algorithm for solving unconstrained integer programming

作　　者：石礼堂 陈伟[1] SHI Litang;CHEN Wei(College of Sciences,Shanghai University,Shanghai 200444,China)

机构地区：[1]上海大学理学院,上海200444

出　　处：《应用数学与计算数学学报》2018年第2期331-342,共12页Communication on Applied Mathematics and Computation

摘　　要：全局优化是最优化的一个分支,非线性整数规划问题的全局优化在各个方面都有广泛的应用.填充函数是解决全局优化问题的方法之一,它可以帮助目标函数跳出当前的局部极小点找到下一个更好的极小点.滤子方法的引入可以使得目标函数和填充函数共同下降,省却了以往算法要设置两个循环的麻烦,提高了算法的效率.本文提出了一个求解无约束非线性整数规划问题的无参数填充函数,并分析了其性质.同时引进了滤子方法,在此基础上设计了整数规划的无参数滤子填充函数算法.数值实验证明该算法是有效的.The global optimization is a branch of optimization, and the nonlinear integer programming is widely used in all aspects. The filled function method is one of the methods for solving the global optimization problems. It can help the objective functions out of the current local minima to find a better one. The use of filter technology can make the objective functions and filled functions decline together, avoid the previous algorithm to set up two cycle processes, and improve the efficiency of the algorithm. In this article, we propose a parameter-free filled function for solving unconstrained nonlinear integer programming problems, at the same time analyze its properties. Besides, the filter method is introduced.Later, we construct a filter-filled function algorithm based on this idea. Numerical experiments show that the algorithm is effective.

关 键 词：无参数填充函数 全局优化 滤子方法 无约束整数规划 

分 类 号：O221.4[理学—运筹学与控制论]