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Branch-and-price algorithm for fuzzy integer programming problems with block angular structure

机译：具有块角结构的模糊整数规划问题的分支价格算法

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摘要

This paper deals with fuzzy integer linear programming problems with block angular structure in which the fuzzy constraints are simplified by using possibility and necessity relations. This main fuzzy problem is efficiently decomposed and is solved by a branch-and-price algorithm. In the nodes of the branch-and-price tree, the linear relaxation of the problem is solved by applying a column generation method. Also, the relationship between the optimal solutions of this problem under possibility and necessity relations is derived. To show the validation of the proposed algorithm, some results are proved. In addition, the application of this algorithm is illustrated on fuzzy multicommodity flow problem. For this case, a new branching scheme is proposed to preserve the network structure of the subproblems which are produced in the column generation method. Some examples are solved and their results are compared with the previous works. Also, the results of the proposed algorithm are reported on some large-scale benchmark instances. (C) 2015 Elsevier B.V. All rights reserved.
机译：本文研究了具有块角结构的模糊整数线性规划问题，通过利用可能性和必要性关系简化了模糊约束。该主要模糊问题得到了有效分解，并通过分支定价算法得以解决。在分支价格树的节点中，通过应用列生成方法解决了问题的线性松弛问题。另外，推导了在可能性和必要性关系之间该问题的最优解之间的关系。为了证明该算法的有效性，证明了一些结果。另外，说明了该算法在模糊多商品流问题上的应用。对于这种情况，提出了一种新的分支方案，以保留列生成方法中产生的子问题的网络结构。解决了一些示例，并将其结果与以前的工作进行了比较。此外，在一些大型基准实例上报告了该算法的结果。 （C）2015 Elsevier B.V.保留所有权利。

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