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

作　　者：Yuchen Shi Congying Han Tiande Guo 

机构地区：[1]School of Mathematical Sciences,University of Chinese Academy of Sciences,Beijing,100049,China

出　　处：《Science China Mathematics》2024年第6期1359-1376,共18页中国科学（数学）（英文版）

基　　金：supported by National Key R&D Program of China(Grant No.2021YFA1000403);National Natural Science Foundation of China(Grant No.11991022);the Strategic Priority Research Program of Chinese Academy of Sciences(Grant No.XDA27000000);the Fundamental Research Funds for the Central Universities。

摘　　要：Spanning tree problems with specialized constraints can be difficult to solve in real-world scenarios,often requiring intricate algorithmic design and exponential time.Recently,there has been growing interest in end-to-end deep neural networks for solving routing problems.However,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 problems.In 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 graphs.Our approach reduces the action and state space using Prim's algorithm and trains the resulting model using REINFORCE.We 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 graphs.Experimental results on literature instances demonstrate that our model outperforms strong heuristics and achieves small optimality gaps of up to 250 vertices.Additionally,we find that our model has strong generalization ability with no significant degradation observed on problem instances as large as 1,000.Our 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 

分 类 号：O157.5[理学—数学] O224[理学—基础数学]