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NeuroPrim:An attention-based model for solving NP-hard spanning tree problems

Science China Mathematics 2024年第6期67卷 1359-1376页

作者： Yuchen Shi Congying Han Tiande Guo School of Mathematical Sciences University of Chinese Academy of SciencesBeijing100049China

spanning tree problems with specialized constraints can be difficult to solve in real-world scenarios,often requiring intricate algorithmic design and exponential ***,there has been growing interest in end-to-end deep neural networks for solving routing ***,such methods typically produce sequences of vertices,which make it difficult to apply them to general combinatorial optimization problems where the solution set consists of edges,as in various spanning tree *** this paper,we propose NeuroPrim,a novel framework for solving various spanning tree problems by defining a Markov decision process for general combinatorial optimization problems on *** approach reduces the action and state space using Prim's algorithm and trains the resulting model using *** apply our framework to three difficult problems on the Euclidean space:the degree-constrained minimum spanning tree problem,the minimum routing cost spanning tree problem and the Steiner tree problem in *** results on literature instances demonstrate that our model outperforms strong heuristics and achieves small optimality gaps of up to 250 ***,we find that our model has strong generalization ability with no significant degradation observed on problem instances as large as 1,*** results suggest that our framework can be effective for solving a wide range of combinatorial optimization problems beyond spanning tree problems.

关键词： degree-constrained minimum spanning tree problem minimum routing cost spanning tree problem Steiner tree problem in graphs Prim's algorithm reinforcement learning

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