Branch-and-bound is a typical way to solve combinatorial optimization problems. This paper proposes a graph pointer network model for learning the variable selection policy in the branch-and-bound. We extract the graph features, global features and historical features to represent the solver state. The proposed model, which combines the graph neural network and the pointer mechanism, can effectively map from the solver state to the branching variable decisions. The model is trained to imitate the classic strong branching expert rule by a designed top-k Kullback-Leibler divergence loss function. Experiments on a series of benchmark problems demonstrate that the proposed approach significantly outperforms the widely used expert-designed branching rules. Our approach also outperforms the state-of-the-art machine-learning-based branch-and-bound methods in terms of solving speed and search tree size on all the test instances. In addition, the model can generalize to unseen instances and scale to larger instances.

翻译：分支定界法是求解组合优化问题的典型方法。本文提出了一种图指针网络模型，用于学习分支定界中的变量选择策略。我们提取图特征、全局特征和历史特征来表征求解器状态。所提出的模型结合了图神经网络与指针机制，能够有效将求解器状态映射为分支变量决策。该模型通过设计基于top-k KL散度的损失函数，以模仿经典强分支专家规则进行训练。在一系列基准问题上的实验表明，所提方法显著优于广泛使用的专家设计分支规则。在所有测试实例上，我们的方法在求解速度和搜索树规模方面均优于当前基于机器学习的分支定界方法。此外，该模型能够泛化到未见实例并扩展到更大规模问题。