Many real-world problems can be efficiently modeled as Mixed Integer Programs (MIPs) and solved with the Branch-and-Bound method. Prior work has shown the existence of MIP backdoors, small sets of variables such that prioritizing branching on them when possible leads to faster running times. However, finding high-quality backdoors that improve running times remains an open question. Previous work learns to estimate the relative solver speed of randomly sampled backdoors through ranking and then decide whether to use it. In this paper, we utilize the Monte-Carlo tree search method to collect backdoors for training, rather than relying on random sampling, and adapt a contrastive learning framework to train a Graph Attention Network model to predict backdoors. Our method, evaluated on four common MIP problem domains, demonstrates performance improvements over both Gurobi and previous models.

翻译：许多现实世界的问题可以高效地建模为混合整数规划（MIP），并通过分支定界法求解。已有研究表明，MIP 后门（即一组关键变量）的存在使得优先对其分支可能缩短求解时间。然而，寻找能提升求解速度的高质量后门仍是一个未解难题。以往研究通过排序学习随机采样后门的相对求解器速度，进而决定是否采用该后门。本文利用蒙特卡洛树搜索方法收集训练用后门，而非依赖随机采样，并采用对比学习框架训练图注意力网络模型以预测后门。在四个常见 MIP 问题域上的评估表明，本方法在性能上优于 Gurobi 及既有模型。