# Strong NP-hardness of AC power flows feasibility

arXiv: https://arxiv.org/abs/1512.07315 · HTML: https://mlsanity.com/paper/1512.07315/

## Key facts

- Cited by 14 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 23 Dec 2015.

## Built on by (most cited first, 14 of 14)

- [Modeling the AC Power Flow Equations with Optimally Compact Neural Networks: Application to Unit Commitment](https://mlsanity.com/paper/2110.11269/) (2021)
- [Unsupervised Optimal Power Flow Using Graph Neural Networks](https://mlsanity.com/paper/2210.09277/) (2022)
- [A Reinforcement Learning Approach to Parameter Selection for Distributed Optimal Power Flow](https://mlsanity.com/paper/2110.11991/) (2021)
- [LUMINA: A Grid Foundation Model for Benchmarking AC Optimal Power Flow Surrogate Learning](https://mlsanity.com/paper/2605.02133/) (2026)
- [Optimal Power Flow in Highly Renewable Power System Based on Attention Neural Networks](https://mlsanity.com/paper/2311.13949/) (2023)
- [End-to-End Reinforcement Learning of Curative Curtailment with Partial Measurement Availability](https://mlsanity.com/paper/2405.03262/) (2024)
- [Quantum Artificial Intelligence for Mission-Critical Systems: Foundations, Architectural Elements, and Future Directions](https://mlsanity.com/paper/2511.09884/) (2025)
- [Towards Systematic Generalization for Power Grid Optimization Problems](https://mlsanity.com/paper/2605.02026/) (2026)
- [Rebuild AC Power Flow Models with Graph Attention Networks](https://mlsanity.com/paper/2509.22733/) (2025)
- [Robustness of Reinforcement Learning-Based Congestion Management in Low-Voltage Grids](https://mlsanity.com/paper/2607.16004/) (2026)
- [Graph Machine Learning: An Opportunity for Power Systems](https://mlsanity.com/paper/2608.16494/) (2026)
- [Scaling Laws for Physics-Aware ACOPF Surrogate Learning](https://mlsanity.com/paper/2609.16282/) (2026)
- [Learning Samples Importance: Parameterizing Dual Variables in Everywhere Learning](https://mlsanity.com/paper/2609.36310/) (2026)
- [ML-OPF-Bench: Benchmarking Machine Learning for Optimal Power Flow](https://mlsanity.com/paper/2610.04307/) (2026)

## Abstract (arXiv)

We present a rigorous proof of strong NP-hardness of the AC-OPF problem.