Recent advancements have introduced machine learning frameworks to enhance the Branch and Bound (B\&B) branching policies for solving Mixed Integer Linear Programming (MILP). These methods, primarily relying on imitation learning of Strong Branching, have shown superior performance. However, collecting expert samples for imitation learning, particularly for Strong Branching, is a time-consuming endeavor. To address this challenge, we propose \textbf{C}ontrastive Learning with \textbf{A}ugmented \textbf{M}ILPs for \textbf{Branch}ing (CAMBranch), a framework that generates Augmented MILPs (AMILPs) by applying variable shifting to limited expert data from their original MILPs. This approach enables the acquisition of a considerable number of labeled expert samples. CAMBranch leverages both MILPs and AMILPs for imitation learning and employs contrastive learning to enhance the model's ability to capture MILP features, thereby improving the quality of branching decisions. Experimental results demonstrate that CAMBranch, trained with only 10\% of the complete dataset, exhibits superior performance. Ablation studies further validate the effectiveness of our method.

通过引入机器学习框架加强了解决混合整数线性规划（MILP）的分支策略，特别是通过模仿学习强分支方法，提出了一种新的框架CAMBranch，借助变量转移生成增强MILPs（AMILPs），并利用对比学习提高模型的能力从而改善分支决策质量。

CAMBranch：使用增强型MILP进行区分学习的分支