aiqbench analysis
This research introduces a fully differentiable Message-Passing Neural Network (MPNN) designed to solve the Uniform Facility Location problem while maintaining provable approximation guarantees. By integrating algorithmic principles directly into the model architecture without relying on discrete relaxations or solver supervision, the approach bridges the gap between classical worst-case bounds and adaptive learning-based heuristics. The method demonstrates improved empirical performance over standard algorithms, offering a robust framework for combinatorial optimization in logistics and clustering applications.
Learning to Approximate Uniform Facility Location via Graph Neural Networks
arXiv:2602.13155v3 Announce Type: replace Abstract: Neural networks, particularly message-passing neural networks (MPNNs), are increasingly used as heuristics for hard combinatorial optimization problems. Yet many learning-based methods rely on supervision, reinforcement learning, or gradient estimators, causing high computational cost, unstable training, or limited guarantees. Classical approximation algorithms provide worst-case guarantees but are non-differentiable and cannot adapt to structure in natural input distributions. We study this tradeoff through Uniform Facility Location (UniFL), a problem with applications in clustering, summarization, logistics, and supply chains. We propose a fully differentiable MPNN that incorporates approximation-algorithmic principles without solver supervision or discrete relaxations. The model has provable approximation guarantees and empirically improves on standard approximation algorithms, narrowing the gap to integer linear programming.
Abstract:Neural networks, particularly message-passing neural networks (MPNNs), are increasingly used as heuristics for hard combinatorial optimization problems. Yet many learning-based methods rely on supervision, reinforcement learning, or gradient estimators, causing high computational cost, unstable training, or limited guarantees. Classical approximation algorithms provide worst-case guarantees but are non-differentiable and cannot adapt to structure in natural input distributions. We study this tradeoff through Uniform Facility Location (UniFL), a problem with applications in clustering, summarization, logistics, and supply chains. We propose a fully differentiable MPNN that incorporates approximation-algorithmic principles without solver supervision or discrete relaxations. The model has provable approximation guarantees and empirically improves on standard approximation algorithms, narrowing the gap to integer linear programming.
Machine Learning (cs.LG); Data Structures and Algorithms (cs.DS); Neural and Evolutionary Computing (cs.NE); Machine Learning (stat.ML)
arXiv:2602.13155 [cs.LG]
(or arXiv:2602.13155v3 [cs.LG] for this version)
https://doi.org/10.48550/arXiv.2602.13155 Focus to learn more arXiv-issued DOI via DataCite
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Full text under the publisher's open licence · 217 words
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