Learning to Variable Selection with Hybrid Convolutional and Attentional Graph Neural Networks

Solving Mixed Integer Linear Programming (MILP) problems is of considerable practical importance. The Branch and bound (B&B) method is widely used to solve MILP problems. In this paper, we propose a Hybrid Convolutional and Attentional Graph Neural Network (HCAGNN), which integrates graph convolution and attention mechanisms to enhance node embeddings and reduce computational time. The B&B solving process is modeled as a Tree Markov Decision Process (MDP), and we employ reinforcement learning to train a more effective branching strategy. We demonstrate the model’s ability to learn branching rules by solving a series of MILP problems. The results show that the proposed model outperforms existing methods and exhibits strong generalization, allowing it to scale to problems of varying sizes.