Given a network, allocating resources at clusters level, rather than at each node, enhances efficiency in resource allocation and usage. In this paper, we study the problem of finding fully connected disjoint clusters to minimize the intra-cluster distances and maximize the number of nodes assigned to the clusters, while also ensuring that no two nodes within a cluster exceed a threshold distance. While the problem can easily be formulated using a binary linear model, traditional combinatorial optimization solvers struggle when dealing with large-scale instances. We propose an approach to solve this constrained clustering problem via reinforcement learning. Our method involves training an agent to generate both feasible and (near) optimal solutions. The agent learns problem-specific heuristics, tailored to the instances encountered in this task. In the results section, we show that our algorithm finds near optimal solutions, even for large scale instances.

翻译：给定一个网络，在聚类层面而非单个节点层面分配资源，能够提升资源分配与使用的效率。本文研究在确保聚类内任意两节点距离不超过阈值的前提下，寻找全连通不相交聚类，以最小化类内距离并最大化分配到聚类的节点数量的难题。尽管该问题可轻易通过二元线性模型进行形式化表述，但传统组合优化求解器在处理大规模实例时困难重重。我们提出了一种通过强化学习求解该约束聚类问题的方法。该方法训练一个智能体生成可行且（近）最优解，该智能体能够学习针对任务中遇到实例量身定制的问题特异性启发式策略。在结果部分，我们证明了即便对于大规模实例，我们的算法也能找到近最优解。