Nearly Optimal Steiner Trees using Graph Neural Network Assisted Monte Carlo Tree Search
This work addresses a combinatorial optimization problem with applications in network design, offering a novel hybrid approach that improves upon classical methods.
The paper tackles the Steiner Tree problem by combining a graph neural network with Monte Carlo Tree Search to propose nodes for partial solutions, consistently outperforming the standard 2-approximation algorithm and often finding optimal solutions.
Graph neural networks are useful for learning problems, as well as for combinatorial and graph problems such as the Subgraph Isomorphism Problem and the Traveling Salesman Problem. We describe an approach for computing Steiner Trees by combining a graph neural network and Monte Carlo Tree Search. We first train a graph neural network that takes as input a partial solution and proposes a new node to be added as output. This neural network is then used in a Monte Carlo search to compute a Steiner tree. The proposed method consistently outperforms the standard 2-approximation algorithm on many different types of graphs and often finds the optimal solution.