Learning Node Selection via Tripartite Graph Representation in Mixed Integer Linear Programming

Sijia Zhang, Fei Shang, Feng Wu, Shaoang Li, Xiangyang Li

Primary Area: optimization

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Keywords: Mixed Integer Linear Programming, Branch-and-Bound, Node Selection

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TL;DR: This paper presents a new graph representation for intermediate states of search trees and employs reinforcement learning for enhanced node selection in MILPs.

Abstract: Branch-and-bound methods are pivotal in solving Mixed Integer Linear Programs (MILPs), where the challenge of node selection arises, necessitating the prioritization of different regions of the space for subsequent exploration. While machine learning techniques have been proposed to address this, our paper resolves two crucial and open questions concerning \textbf{(P1)} the representation of the MILP solving process and \textbf{(P2)} the qualification of nodes in node selection. We present a novel tripartite graph representation for the branch-and-bound search tree, which, through theoretical validation, proves to effectively encapsulate the essential information of the search tree for node selection. To further this, we introduce three innovative metrics for node selection and formulate a GNN-based model, DQN-GNN, utilizing reinforcement learning to derive node selection policies. Empirical evaluations illustrate that DQN-GNN markedly enhances the efficiency of solving MILPs, surpassing the existing human-designed and learning-based models. compared to other AI methods, our experiments substantiate that DQN-GNN exhibits commendable generalization to MILPs that are substantially larger than those encountered during training.

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Submission Number: 7602