Reinforcement Learning for Node Selection in Branch-and-Bound

• URL: http://arxiv.org/abs/2310.00112v2
• Date: Wed, 5 Jun 2024 12:36:39 GMT
• Title: Reinforcement Learning for Node Selection in Branch-and-Bound
• Authors: Alexander Mattick, Christopher Mutschler,
• Abstract summary: Current state-of-the-art selectors utilize either hand-crafted ensembles that automatically switch between naive sub-node selectors, or learned node selectors that rely on individual node data. We propose a novel simulation technique that uses reinforcement learning (RL) while considering the entire tree state, rather than just isolated nodes.
• Score: 52.2648997215667
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: A big challenge in branch and bound lies in identifying the optimal node within the search tree from which to proceed. Current state-of-the-art selectors utilize either hand-crafted ensembles that automatically switch between naive sub-node selectors, or learned node selectors that rely on individual node data. We propose a novel simulation technique that uses reinforcement learning (RL) while considering the entire tree state, rather than just isolated nodes. To achieve this, we train a graph neural network that produces a probability distribution based on the path from the model's root to its "to-be-selected" leaves. Modelling node-selection as a probability distribution allows us to train the model using state-of-the-art RL techniques that capture both intrinsic node-quality and node-evaluation costs. Our method induces a high quality node selection policy on a set of varied and complex problem sets, despite only being trained on specially designed, synthetic travelling salesmen problem (TSP) instances. Using such a fixed pretrained policy shows significant improvements on several benchmarks in optimality gap reductions and per-node efficiency under strict time constraints.

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