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首页> 外文期刊>RAIRO Operation Research >A BRANCH-AND-PRICE-AND-CUT ALGORITHM FOR THE PATTERN MINIMIZATION PROBLEM
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A BRANCH-AND-PRICE-AND-CUT ALGORITHM FOR THE PATTERN MINIMIZATION PROBLEM

机译：图案最小化问题的分支-价格-切割算法

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摘要

In cutting stock problems, after an optimal (minimal stock usage) cutting plan has been devised, one might want to further reduce the operational costs by minimizing the number of setups. A setup operation occurs each time a different cutting pattern begins to be produced. The related optimization problem is known as the Pattern Minimization Problem, and it is particularly hard to solve exactly. In this paper, we present different techniques to strengthen a formulation proposed in the literature. Dual feasible functions are used for the first time to derive valid inequalities from different constraints of the model, and from linear combinations of constraints. A new arc flow formulation is also proposed. This formulation is used to define the branching scheme of our branch-and-price-and-cut algorithm, and it allows the generation of even stronger cuts by combining the branching constraints with other constraints of the model. The computational experiments conducted on instances from the literature show that our algorithm finds optimal integer solutions faster than other approaches. A set of computational results on random instances is also reported.
机译：在减少库存问题时，在制定了最佳的（最小的库存使用量）切割计划后，人们可能希望通过减少设置数量来进一步降低运营成本。每次开始产生不同的切割图案时，都会进行设置操作。相关的优化问题称为“模式最小化问题”，很难精确地解决。在本文中，我们提出了各种技术来加强文献中提出的配方。首次使用对偶可行函数从模型的不同约束以及约束的线性组合得出有效不等式。还提出了一种新的电弧流公式。此公式用于定义我们的“分支和价格并剪切”算法的分支方案，并且通过将分支约束与模型的其他约束组合在一起，可以生成更强大的剪切。对文献中的实例进行的计算实验表明，我们的算法比其他方法更快地找到最佳整数解。还报告了一组有关随机实例的计算结果。

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