通过预热启动MCMC微调学习求解二次指派问题
Learning to Solve the Quadratic Assignment Problem with Warm-Started MCMC Finetuning
AI总结：
本文提出PLMA框架，通过预热启动MCMC微调提升求解性能，结合能量基模型和交叉图注意力机制，有效解决二次指派问题。
摘要：
二次指派问题（QAP）是一个NP难任务，传统启发式和现代学习方法均面临挑战。本文提出PLMA框架，采用预热启动MCMC微调，利用短马尔可夫链锚定已有探索区域。设计加性能量基模型实现O(1)时间2交换Metropolis-Hastings采样步骤，并结合可扩展的交叉图注意力机制建模设施与地点交互。实验表明PLMA在各类基准上均优于现有方法，尤其在QAPLIB上接近零平均最优解差距，在Taixxeyy实例上表现出色，且在带宽最小化中有效。
英文摘要：
The quadratic assignment problem (QAP) is a fundamental NP-hard task that poses significant challenges for both traditional heuristics and modern learning-based solvers. Existing QAP solvers still struggle to achieve consistently competitive performance across structurally diverse real-world instances. To bridge this performance gap, we propose PLMA, an innovative permutation learning framework. PLMA features an efficient warm-started MCMC finetuning procedure to enhance deployment-time performance, leveraging short Markov chains to anchor the adaptation to the promising regions previously explored. For rapid exploration via MCMC over the permutation space, we design an additive energy-based model (EBM) that enables an $O(1)$-time 2-swap Metropolis-Hastings sampling step. Moreover, the neural network used to parameterize the EBM incorporates a scalable and flexible cross-graph attention mechanism to model interactions between facilities and locations in the QAP. Extensive experiments demonstrate that PLMA consistently outperforms state-of-the-art baselines across various benchmarks. In particular, PLMA achieves a near-zero average optimality gap on QAPLIB, exhibits remarkably superior robustness on the notoriously difficult Taixxeyy instances, and also serves as an effective QAP solver in bandwidth minimization.
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