WARP: A Benchmark for Primal-Dual Warm-Starting of Interior-Point Solvers
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Abstract (arXiv)
Solving AC Optimal Power Flow (AC-OPF) is of central importance in electricity market operations, where interior-point methods (IPMs) such as IPOPT are the standard solvers. A growing body of work uses machine learning to predict primal warm-start iterates, reporting iteration reductions of 30-46%. We show that these reported gains rest on an inappropriate evaluation baseline: prior methods benchmark against the flat start Vm = 1, Va = 0, whereas the solver's actual default - the variable-bound midpoint (l+u)/2 - is near-optimal for log-barrier centrality. Against this corrected baseline, no primal-only warm-start method reduces solver iterations. We trace the failure to a geometric property of interior-point methods: primal prediction accuracy is anticorrelated with convergence speed, and providing the ground-truth optimal solution x^* without dual variables causes the solver to diverge. Oracle experiments establish that the complete primal-dual-barrier state (x^*, λ^*, z^*, μ^*) reduces IPOPT iterations from 23 to 3 - an 85% reduction that is structurally inaccessible to primal-only methods. To enable rigorous evaluation of warm-start methods on this task, we release a benchmark suite comprising dual-labeled AC-OPF datasets with IPOPT-extracted solutions, a corrected evaluation protocol, and WARP - a topology-conditioned encode-process-decode interaction network that predicts the full interior-point state (hatx, hatλ, hatz, hatμ) on the heterogeneous constraint graph. WARP achieves a 76% reduction in IPOPT iterations while natively accommodating N-1 contingency topology variations without retraining.
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References · 23
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11 more
- 2019Learning for DC-OPF: Classifying active sets using neural netscited by 31
- 2022Topology-aware Graph Neural Networks for Learning Feasible and Adaptive ac-OPF Solutionscited by 28
- 2024CANOS: A Fast and Scalable Neural AC-OPF Solver Robust To N-1 Perturbationscited by 27
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- 2024Learning Constrained Optimization with Deep Augmented Lagrangian Methodscited by 16
- 2019Data-Driven Screening of Network Constraints for Unit Commitmentcited by 11
- 2020Hybrid Learning Aided Inactive Constraints Filtering Algorithm to Enhance AC OPF Solution Timecited by 7
- 2023Constraint-Informed Learning for Warm Starting Trajectory Optimizationcited by 7
- 2020Deep learning architectures for inference of AC-OPF solutionscited by 4
- 2024Dual Interior Point Optimization Learningcited by 4
- 2024IPM-LSTM: A Learning-Based Interior Point Method for Solving Nonlinear Programscited by 4
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