Previous research shows that a cardinality reasoning can improve the pruning of the bin-packing constraint. We first introduce a new algorithm, called BPCFlow, that filters both load and cardinality bounds on the bins, using a flow reasoning similar to the Global Cardinality Constraint. Moreover, we detect impossible assignments of items by combining the load and cardinality of the bins, using a method to detect items that are either ”too-big” or ”too-small”. This method is adapted to two previously existing filtering techniques along with BPCFlow, creating three new propagators. We then experiment the four new algorithms on Balanced Academic Curriculum Problem and Tank Allocation Problem instances. BPCFlow is shown to be stronger than previously existing filtering, and more computationally intensive. We show that the new filtering is useful on a small number of hard instances, while being too expensive for general use. Our results show that the introduced ”too-big/too-small” filtering can most of the time drastically reduce the size of the search tree and the computation time. This method is profitable in 88% of the tested instances.

中文翻译：

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具有基数约束的装箱改进过滤

先前的研究表明，基数推理可以改善对bin-packing约束的修剪。我们首先介绍一种称为BPCFlow的新算法，该算法使用类似于Global Cardinality Constraint的流推理来过滤垃圾箱上的负载和基数范围。此外，我们通过组合垃圾箱的负荷和基数来检测不可能分配的物品，使用一种方法来检测“太大”或“太小”的物品。该方法与BPCFlow一起适用于两种先前存在的过滤技术，从而创建了三个新的传播器。然后，我们在平衡学术课程问题和坦克分配问题实例上试验了四种新算法。事实证明，BPCFlow比以前的现有过滤功能更强大，并且计算量更大。我们表明，新的过滤对少量的硬实例很有用，而对于一般用途来说太昂贵了。我们的结果表明，引入的“太大/太小”过滤可以在大多数情况下极大地减少搜索树的大小和计算时间。该方法在88％的测试实例中有利可图。