A Smoothing Approach for Minimizing A Linear Function Subject to Fuzzy Relation Inequalities with Addition-Min Composition
A Smoothing Approach for Minimizing A Linear Function Subject to Fuzzy Relation Inequalities with Addition-Min Composition
复制标题
最小化加法最小组合模糊关系不等式线性函数的平滑方法
DOI：
10.1007/s40815-018-0530-3
复制
发表时间：
2019
影响因子：
4.3
通讯作者：
Shen Jie
中科院分区：
文献类型：
--
作者：
Guo Fang Fang;Shen Jie
本文主要关注最小化受模糊关系不等式影响的线性函数与加法最小组合。尽管该问题已被证明等价于线性规划，但当约束和变量数量达到 200 左右时，仍然很难有效求解。在本文中，我们致力于构建一种平滑方法来求解问题的近似解。利用最大熵方法，我们通过连续可微函数来近似约束，并证明近似解序列的任何簇都是原问题的最优点。数值实验表明，近似解的误差在合理范围内。同时，与线性规划方法相比，平滑方法花费的计算时间要少得多，特别是对于大规模问题。
This paper mainly focuses on minimizing a linear function subject to fuzzy relation inequalities with addition–min composition. Although the problem has been proved to be equivalent to a linear programming, it is still difficult to efficiently solve when the numbers of constrains and variables come to about 200. In this paper, we devotes to constructing a smoothing approach for solving approximate solutions of the problem. Utilizing maximum entropy method, we approximate the constraints by continuously differentiable functions and prove that any cluster of an approximate solution sequence is an optimal point of the original problem. Numerical experiments show that the error of the approximate solutions is within a reasonable range. At the same time, compared to the linear programming approach, the smoothing approach costs much less computation time, especially for large-scale problems.