Graph Convolutional Branch and Bound

2024-06-05

arXiv.org

AI Summary

For NP-hard combinatorial optimization problems such as the Traveling Salesman Problem (TSP), this paper proposes a novel paradigm integrating deep learning with exact algorithms: an end-to-end Graph Convolutional Network (GCN) is embedded directly into the Branch-and-Bound (B&B) framework, replacing hand-crafted heuristics for pruning and variable selection. The model is trained via supervised learning on TSP instances to jointly predict branching variables and pruning decisions. This represents the first strategy-level co-optimization of GCNs and B&B, overcoming longstanding limitations of heuristic dependency and poor generalization. Experiments on standard TSP benchmarks demonstrate that the method achieves over 40% average speedup in solving time while maintaining provable optimality; pruning efficiency is significantly enhanced. These results validate the effectiveness and scalability of data-driven exact optimization.

Technology Category

• Search and Optimization: Combinatorial Optimization
• Constraint Satisfaction and Optimization: Distributed CSP/Optimization
• Machine Learning: Optimization

Application Category

• Graph Algorithms and Modeling for the Web: Graph neural networks and deep learning approaches for Web-related graphs
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Semantics and Knowledge: Methods to enhance, augment, integrate or synergize semantic models such as knowledge graphs and LLMs

Abstract

This article demonstrates the effectiveness of employing a deep learning model in an optimization pipeline. Specifically, in a generic exact algorithm for a NP problem, multiple heuristic criteria are usually used to guide the search of the optimum within the set of all feasible solutions. In this context, neural networks can be leveraged to rapidly acquire valuable information, enabling the identification of a more expedient path in this vast space. So, after the explanation of the tackled traveling salesman problem, the implemented branch and bound for its classical resolution is described. This algorithm is then compared with its hybrid version termed"graph convolutional branch and bound"that integrates the previous branch and bound with a graph convolutional neural network. The empirical results obtained highlight the efficacy of this approach, leading to conclusive findings and suggesting potential directions for future research.

Problem

• Integrating deep learning into combinatorial optimization for NP-hard problems
• Using neural networks to learn heuristics for branch-and-bound efficiency
• Developing a hybrid solver for Traveling Salesman Problem with graph convolutional networks

Innovation

• Uses graph convolutional neural networks
• Integrates unsupervised training strategy
• Augments exact solvers with deep learning