Stable Variable Fixation for Accelerated Unit Commitment via Graph Neural Network and Linear Programming Hybrid Learning

The Unit Commitment Problem (UCP) is a critical component of power market decision-making and is typically formulated as Mixed Integer Programming (MIP). Given the complexity of solving MIPs, efficiently solving large-scale UCPs remains a significant challenge. This paper presents a hybrid Graph Neural Network (GNN)–Linear Programming (LP) framework to accelerate the solution of large-scale Unit Commitment Problems (UCPs) while maintaining the quality of solutions. By analyzing variable stability through historical branch-and-bound (B&B) trajectories, we classify MIP variables into dynamically adjustable stable and unstable groups. We adopt an MIP formulation that includes multiple types of binary variables—such as commitment, startup, and shutdown variables—and extract additional information from these auxiliary binary variables. This enriched representation provides more candidates for stable variable fixation, helping to improve variable refinement, mitigate suboptimality, and enhance computational efficiency. A bipartite GNN is trained offline to predict stable variables based on system topology and historical operational patterns. During online optimization, instance-specific root LP solutions refine these predictions, enabling adaptive variable fixation via a dual-threshold mechanism that integrates GNN confidence and LP relaxations. To mitigate suboptimality risks, we introduce temporally flexible fixation strategies—hard fixation for variables with persistent stability and soft fixation allowing limited temporal adjustments—alongside a GNN-guided branching rule to prioritize unstable variables. Numerical experiments demonstrate that jointly fixing commitment, startup, and shutdown variables yields better performance compared to fixing only commitment variables. Ablation studies further validate the importance of hard fixation and customized branching strategies, especially for large-scale systems.