CoCo-MILP: Inter-Variable Contrastive and Intra-Constraint Competitive MILP Solution Prediction

TL;DR

CoCo-MILP introduces a novel GNN-based approach that explicitly models inter-variable contrast and intra-constraint competition, significantly improving MILP solution prediction accuracy over existing methods.

Contribution

The paper proposes CoCo-MILP, a new framework with contrastive loss and specialized GNN layers to better capture variable relationships in MILP problems, advancing solution prediction accuracy.

Findings

Reduces solution gap by up to 68.12% compared to traditional solvers.

Outperforms existing learning-based approaches on standard benchmarks.

Effectively models variable competition within constraints.

Abstract

Mixed-Integer Linear Programming (MILP) is a cornerstone of combinatorial optimization, yet solving large-scale instances remains a significant computational challenge. Recently, Graph Neural Networks (GNNs) have shown promise in accelerating MILP solvers by predicting high-quality solutions. However, we identify that existing methods misalign with the intrinsic structure of MILP problems at two levels. At the leaning objective level, the Binary Cross-Entropy (BCE) loss treats variables independently, neglecting their relative priority and yielding plausible logits. At the model architecture level, standard GNN message passing inherently smooths the representations across variables, missing the natural competitive relationships within constraints. To address these challenges, we propose CoCo-MILP, which explicitly models inter-variable Contrast and intra-constraint Competition for advanced MILP solution prediction. At the objective level, CoCo-MILP introduces the Inter-Variable Contrastive Loss (VCL), which explicitly maximizes the embedding margin between variables assigned one versus zero. At the architectural level, we design an Intra-Constraint Competitive GNN layer that, instead of homogenizing features, learns to differentiate representations of competing variables within a constraint, capturing their exclusionary nature. Experimental results on standard benchmarks demonstrate that CoCo-MILP significantly outperforms existing learning-based approaches, reducing the solution gap by up to 68.12% compared to traditional solvers. Our code is available at https://github.com/happypu326/CoCo-MILP.