Deep Reinforcement Learning for Solving Directed Steiner Tree Problems

The design of approximation algorithms for solving NP-hard Combinatorial Optimization (CO) problems is usually challenging. In recent years, deep learning has demonstrated the power to solve specific CO problems, such as Travelling Salesman problem and Minimum Vertex Cover problem. In this paper, we propose a deep reinforcement learning approach based on graph neural networks (GNN) to tackle Directed Steiner Tree (DST) problem. Simulations are conducted to evaluate the proposed approach compared to benchmarks upon approximation ratios and execution time respectively. The results reveal the potential of our approach in solving DST problems in practice and the scalability that can be smoothly applied to disparate graphs after enough off-line training.