Memorization, as an algorithm design technique, enables to speed up algorithms at the price of increased space usage. In this work, we focus on search tree algorithms applied to sequencing problems. In these algorithms, on lower branching levels, isomorphic sub-problems may appear exponentially many times and the use of memorization is twofold: on the one hand it avoids repetitive solutions, as they correspond to identical sub-problems; on the other hand, it allows to check for dominance conditions among permutations of the same subset of elements. The idea of memorization appeared for a long time, however, to the best of the authors’ knowledge, it was only seldom applied in the number of branching algorithms proposed in the literature. In this paper, we propose a unifying framework for implementing memorization in exact branching algorithms dedicated to sequencing problems. Our proposal leads to the paradigm of Branch & Memorize and its implementation to three classical single machine problems is validated by an extensive computational experimentation that shows that the mentioned paradigm consistently improves existing exact branching algorithms. These results emphasize the idea of more systematically embedding memorization in branching algorithms.

记忆作为一种算法设计技术，能够以增加空间使用为代价来加速算法。在这项工作中，我们专注于应用于排序问题的搜索树算法。在这些算法中，在较低的分支级别上，同构子问题可能会以指数形式出现多次，并且记忆的用途是双重的：一方面，它避免了重复的解决方案，因为它们对应于相同的子问题；另一方面，它允许检查元素的同一子集的排列之间的主导条件。记忆的想法出现了很长一段时间，但是，据作者所知，它很少被应用于文献中提出的分支算法中。在本文中，我们提出了一个统一的框架，用于在专门用于排序问题的精确分支算法中实现记忆。我们的建议导致了范式广泛的计算实验验证了Branch＆Memorize及其对三个经典单机问题的实现，该实验表明上述范式不断改进了现有的精确分支算法。这些结果强调了在分支算法中更系统地嵌入存储的想法。