Primal heuristics play a crucial role in exact solvers for Mixed Integer Programming (MIP). While solvers are guaranteed to find optimal solutions given sufficient time, real-world applications typically require finding good solutions early on in the search to enable fast decision-making. While much of MIP research focuses on designing effective heuristics, the question of how to manage multiple MIP heuristics in a solver has not received equal attention. Generally, solvers follow hard-coded rules derived from empirical testing on broad sets of instances. Since the performance of heuristics is instance-dependent, using these general rules for a particular problem might not yield the best performance. In this work, we propose the first data-driven framework for scheduling heuristics in an exact MIP solver. By learning from data describing the performance of primal heuristics, we obtain a problem-specific schedule of heuristics that collectively find many solutions at minimal cost. We provide a formal description of the problem and propose an efficient algorithm for computing such a schedule. Compared to the default settings of a state-of-the-art academic MIP solver, we are able to reduce the average primal integral by up to 49% on a class of challenging instances.
Shuttling Compiler for Trapped-Ion Quantum Computers Based on Fine-Tuned Large Language Models
Institute of Computer Science, Johannes Gutenberg University（计算机科学研究所，约翰内斯·古特堡大学）；Institute of Physics, Johannes Gutenberg University（物理研究所，约翰内斯·古特堡大学）；Department of Computer Science, Saarland University（计算机科学系，萨尔兰大学）
University of Toronto（多伦多大学）；Polytechnique Montréal（蒙特利尔理工学院）；University of Oxford（牛津大学）；Mila（米拉（魁北克人工智能研究所））；Université de Montréal（蒙特利尔大学）；The Alan Turing Institute（阿兰·图灵研究所）；Cornell Tech（康奈尔科技校区）；Technion - IIT（以色列理工学院）
Learning Branching Heuristics for Propositional Model Counting
University of Toronto（多伦多大学）；UC Berkeley（加州大学伯克利分校）；Vector Institute（向量研究所）
命题模型计数（Propositional Model Counting），或#SAT，是计算布尔公式的满意赋值的数量的问题。来自不同应用领域的许多问题，包括许多离散概率推理问题，可以转化为模型计数问题，由#SAT求解器来解决。然而，精确的#SAT求解器通常不能扩展到工业规模的实例。在本文中，我们提出了Neuro#，一种用于学习分支算法的方法，以提高给定问题族实例上的精确SAT求解器的性能。我们的实验表明，我们的方法减少了类似的分布式举行了实例的步骤数，并推广到更大的实例，从同一个问题的家庭。它是能够实现这些结果对一些不同的问题家庭具有非常不同的结构。除了步数改进之外，Neuro#还可以在某些问题族中的较大实例上实现比vanilla求解器高出几个数量级的挂钟加速，尽管查询模型的运行时开销很大。
A Learning based Branch and Bound for Maximum Common Subgraph Problems
Huazhong university of science and technology（华中科技大学）；Wuhan university of science and technology（武汉科技大学）；University of Picardie Jules Verne（皮卡第儒勒·凡尔纳大学）
分支定界算法（Branch-and-Bound，BnB）是求解组合问题的一种常用算法，其分支启发式是BnB算法性能的关键，本文研究了一类典型的最大公共子图（Maximum Common Subgraph，MCS）问题，并提出了一种启发自强化学习的分支启发式算法，目标是尽可能早地到达树叶，以大大减少搜索树的大小。大量的实验表明，我们的方法是有益的，并且优于MCS的当前最佳BnB算法。
