ECB-GNN: Edge-Conditioned Bipartite Graph Neural Networks for Efficient Isolated Microgrid Scheduling

Isolated industrial microgrids impose extremely high requirements on the reliability of physical constraints and the response speed of real-time scheduling schemes. While traditional mixed-integer linear programming (MILP) can rigorously guarantee physical constraints, the computational latency caused by its NP-hard nature fails to meet the requirements of real-time management. Conversely, although existing end-to-end deep learning methods achieve rapid inference, they often face the risk of physical constraint violations. To this end, this article proposes an Edge-conditioned bipartite graph neural network (ECB-GNN), aiming to achieve efficient and robust branching decisions within the MILP solution framework. Through an edge-conditioned multihead attention mechanism, ECB-GNN models physical coefficients as edge features for bi-directional message passing, consistently enhancing the perception of strong coupling constraints in microgrids. Furthermore, we release a standardized microgrid MILP benchmark of 225 typical instances, incorporating dual-source perturbations and multilevel difficulty categorizations. Experimental results demonstrate that ECB-GNN consistently outperforms existing solvers and branching strategies in both accuracy and speed. It exhibits superior robustness against parametric fluctuations and topological changes, maintaining consistent acceleration even for large-scale instances with 10⁶ variables.