Graph Transformer based Large Neighborhood Search via Expert Guided Reinforcement Learning
Abstract: Mixed-Integer Linear Programs (MILPs) have wide-ranging applications across various fields. Recently, significant research efforts have been directed towards developing learning-based Large Neighborhood Search (LNS) methods for efficiently identifying high-quality MILP solutions. Most existing works focus on imitation learning, which faces two major challenges: (i) the performance is limited by the expert policy itself, and (ii) learning the graph representation of MILPs cannot effectively explore the global graph structure due to the limited receptive field of Graph Convolutional Networks (GCNs). To address these issues, we propose a novel expert-guided reinforcement learning model to design the destroy operator in LNS. In our approach, the expert provides weighted guidance to assist the learning agent efficiently. Additionally, we introduce a novel graph transformer-based network, which captures both local and global information efficiently. We prove that our graph transformer-based network is more expressive than 1-WL test and can distinguish non-isomorphic MILP graphs successfully. We conduct extensive evaluations to demonstrate the effectiveness of our proposed algorithm, showing significant improvements in the performance of LNS for MILPs.
Submission Length: Long submission (more than 12 pages of main content)
Assigned Action Editor: ~Baoxiang_Wang1
Submission Number: 4722
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