Dynamic Stratified Contrastive Learning with Upstream Augmentation for MILP Branching

TL;DR

This paper introduces extsc{Ours}, a novel contrastive learning framework for MILP branching that improves node discrimination and solving efficiency by leveraging stratified grouping and upstream data augmentation.

Contribution

The paper proposes a dynamic stratified contrastive training method with upstream augmentation, addressing data scarcity and semantic variation in MILP branching.

Findings

Enhances branching accuracy significantly.

Reduces overall MILP solving time.

Generalizes well to unseen instances.

Abstract

Mixed Integer Linear Programming (MILP) is a fundamental class of NP-hard problems that has garnered significant attention from both academia and industry. The Branch-and-Bound (B\&B) method is the dominant approach for solving MILPs and the branching plays an important role in B\&B methods. Neural-based learning frameworks have recently been developed to enhance branching policies and the efficiency of solving MILPs. However, these methods still struggle with semantic variation across depths, the scarcity of upstream nodes, and the costly collection of strong branching samples. To address these issues, we propose \ours, a Dynamic \underline{\textbf{S}}tratified \underline{\textbf{C}}ontrastive Training Framework for \underline{\textbf{MILP}} Branching. It groups branch-and-bound nodes based on their feature distributions and trains a GCNN-based discriminative model to progressively separate nodes across groups, learning finer-grained node representations throughout the tree. To address data scarcity and imbalance at upstream nodes, we introduce an upstream-augmented MILP derivation procedure that generates both theoretically equivalent and perturbed instances. \ours~effectively models subtle semantic differences between nodes, significantly enhancing branching accuracy and solving efficiency, particularly for upstream nodes. Extensive experiments on standard MILP benchmarks demonstrate that our method enhances branching accuracy, reduces solving time, and generalizes effectively to unseen instances.