A Symmetry-Aware Learning Approach for Solving Mixed-Integer Linear Programs
Keywords: mixed-integer linear programming, symmetry, machine learning, graph neural networks
Abstract: Recently, machine learning techniques have been widely utilized for solving mixed-integer linear programs (MILPs). Notably, learning-based approaches that encode MILPs as bipartite graphs and then leverage graph neural networks (GNNs) to identify high-quality solutions have shown remarkable potential. Symmetry as an intrinsic property of many MILPs leads to multiple equivalent solutions, which incurs noticeable computational challenges and hence is treated with care in classic optimization algorithms. However, to the best of our knowledge, none of the learning-based methods take special care of symmetry within MILPs such that their computational performance might be jeopardized. To mitigate this issue, we propose a symmetry-aware learning approach that includes (i) position embeddings as node features to differentiate interchangeable variable nodes, and (ii) a novel loss function to alleviate ambiguity caused by equivalent solutions. We conduct extensive experiments on public datasets and the computational results demonstrate that our proposed approach significantly outperforms existing ones in both computational efficiency and solution quality.
Primary Area: optimization
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Submission Number: 6748
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