Surrogate Models in Power System Scheduling Problems: Learning Active Constraints via Graph Neural Networks

Power system scheduling problems are solved repeatedly and require fast computation for real time deployment of asset setpoints. Bilevel optimization is often employed due to its ability to capture the hierarchical structure between network operators and end users. However, the inherent complexity of bilevel models makes repeated solutions computationally expensive. To address this, we propose a surrogate modeling approach that predicts the set of active constraints in the full bilevel formulation, thereby significantly reducing computational effort. Rather than relying on extensive sampling over uncertain parameters, we exploit the bipartite graph structure of optimization problems and apply Graph Neural Networks (GNNs) to learn constraint activity directly by leveraging the intrinsic geometric dependencies of the optimization models. We evaluate the end to end approach by comparing the surrogate objective values and computational speedup against the original problem, benchmarking against Random Forest (RF) and Feed-foward Neural Network (FNN) classifiers across a range of increasingly complex test cases, from linear programming problems to mixed integer linear programming and bilevel problems. Results show that GNN based models, which encode mathematical properties like complementary slackness and binary activations to reduce model complexity, achieve up to 10-20x speedup with an objective deviation under 4% and a 99% optimality ratio. This represents superior performance to RFs and FNN, highlighting the suitability of GNNs for directly encoding the mathematical structure of optimization models, thanks to its inherent topology awareness to solve complex constraint activity prediction tasks in power system scheduling.