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arxiv: 2510.15753 · v2 · submitted 2025-10-17 · 🧮 math.OC

Data-Boosted Optimization for AC Optimal Power Flow: Interior-Point and Spatial Branching Methods

Ignacio Repiso , Salvador Pineda , Juan Miguel Morales This is my paper

Pith reviewed 2026-05-18 06:12 UTC · model grok-4.3

classification 🧮 math.OC
keywords AC Optimal Power FlowInterior-Point MethodsSpatial BranchingData-Driven OptimizationPower System OptimizationGlobal Optimization
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The pith

Historical data boosts convergence for both local and global AC-OPF solvers

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The paper develops data-boosted versions of interior-point and spatial branching solvers for the non-convex AC Optimal Power Flow problem. Historical operating data is used to provide better starting points for interior-point methods and to shrink the feasible region explored by spatial branching. Tests across networks of different sizes, including cases engineered to have multiple local optima, show faster convergence and lower run times for both approaches. Interior-point methods prove especially reliable, frequently reaching the global optimum even when local optima exist, while spatial branching stays slow despite the data assistance.

Core claim

Data-boosted variants of interior-point methods and spatial branching for AC-OPF leverage historical operating data for initialization and region restriction, respectively, yielding consistent gains in convergence speed and computation time. Interior-point methods exhibit robustness by often locating globally optimal solutions in instances with multiple local optima, whereas spatial branching remains computationally demanding even after the enhancements.

What carries the argument

Data-boosted initialization for interior-point methods combined with data-driven restriction of the search region for spatial branching in the AC Optimal Power Flow problem.

Load-bearing premise

Historical operating data is available and representative of the networks, so that using it for initialization or region restriction neither excludes the global optimum nor biases the reported gains.

What would settle it

Running the data-boosted solvers on a new network configuration where the historical data set does not contain the global optimum point or produces no speedup would show whether the performance claims hold without that data match.

Figures

Figures reproduced from arXiv: 2510.15753 by Ignacio Repiso, Juan Miguel Morales, Salvador Pineda.

Figure 1
Figure 1. Figure 1: Voltage bounds reduction for SP-K approach. f n = min i∈IK f ∗ in, f n = max i∈IK f ∗ in, where e ∗ in and f ∗ in denote the real and imaginary components, respectively, of the optimal voltage at bus n for instance i. In addition, the data-driven bounds are rounded up or down to the fifth decimal place to slightly enlarge the feasible region and prevent potential numerical issues related to the solver’s fe… view at source ↗
read the original abstract

The AC Optimal Power Flow (AC-OPF) problem is a non-convex, NP-hard optimization task essential for secure and economic power system operation. While interior-point methods are widely used due to their computational efficiency, spatial branching techniques offer global optimality guarantees at significantly higher computational cost. In this work, we propose data-boosted variants of both approaches that leverage historical operating data to enhance performance. Specifically, data are used to guide initialization in interior-point methods and to restrict the search region in spatial branching. This unified perspective enables a systematic assessment of how learning can accelerate both local and global optimization strategies. We conduct an extensive empirical study across networks of varying sizes under both standard conditions and modified configurations designed to induce local optima. Our results show that data-boosted strategies consistently improve convergence and reduce computation times for both approaches. However, spatial branching remains computationally demanding even with data-driven enhancements, while interior-point methods exhibit remarkable robustness, often converging to globally optimal solutions, even in challenging instances with multiple local optima. These findings highlight the practical effectiveness of modern interior-point solvers and suggest that global optimization methods for AC-OPF still face significant scalability challenges, even when augmented with data-driven guidance.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

1 major / 1 minor

Summary. The manuscript proposes data-boosted variants of interior-point methods (IPM) and spatial branching for the non-convex AC Optimal Power Flow (AC-OPF) problem. Historical operating data are used to guide initialization for IPM and to restrict the feasible region for spatial branching. An extensive empirical study is reported across networks of varying sizes under both standard conditions and modified configurations designed to induce multiple local optima, claiming that the data-boosted strategies consistently improve convergence and reduce computation times for both approaches, with IPM exhibiting robustness in reaching globally optimal solutions while spatial branching remains computationally demanding.

Significance. If the empirical results and the assumption that data-derived restrictions preserve the global optimum hold, the work would provide a useful unified assessment of how learning can accelerate both local and global solvers for AC-OPF. It would highlight the practical robustness of modern IPM implementations and the remaining scalability barriers for global methods, offering guidance for solver choice in power-system applications. The systematic comparison under challenging modified instances adds value beyond standard test cases.

major comments (1)
  1. Abstract and spatial-branching method description: the central claim that data-boosted region restriction improves performance without sacrificing global optimality lacks any explicit verification that the data-derived bounds contain the true global solution. This is load-bearing for the reported improvements and optimality statements, especially in the modified test cases explicitly constructed to induce multiple local optima; historical data from standard conditions may not cover these configurations, and any global optimum lying outside the restricted region would render the comparisons non-equivalent to the unrestricted problem.
minor comments (1)
  1. The abstract would benefit from at least one or two concrete quantitative metrics (e.g., average speed-up factors or success rates) rather than solely qualitative statements such as 'consistently improve' and 'remarkable robustness'.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for the thorough review and valuable feedback. The major comment raises an important point about verifying that data-derived bounds preserve the global optimum. We address this directly below and will incorporate explicit checks in the revision.

read point-by-point responses

  1. Referee: Abstract and spatial-branching method description: the central claim that data-boosted region restriction improves performance without sacrificing global optimality lacks any explicit verification that the data-derived bounds contain the true global solution. This is load-bearing for the reported improvements and optimality statements, especially in the modified test cases explicitly constructed to induce multiple local optima; historical data from standard conditions may not cover these configurations, and any global optimum lying outside the restricted region would render the comparisons non-equivalent to the unrestricted problem.

    Authors: We agree that explicit verification is essential for the claims regarding global optimality preservation. In the original experiments, the data-boosted spatial branching consistently recovered the same objective values as the unrestricted global solver across all instances, including the modified test cases. However, we did not include a dedicated verification step documenting that the known global solutions lie inside the data-derived bounds. In the revised manuscript we will add a new subsection (or appendix) that reports, for each network and configuration, the distance between the unrestricted global solution and the data-derived bounds, confirming containment. For the modified instances we will also clarify the procedure used to generate or select the historical data to ensure relevance to the altered operating conditions. This will make the equivalence of the restricted and unrestricted problems explicit. revision: yes

Circularity Check

0 steps flagged

No significant circularity in empirical data-driven evaluation

full rationale

The paper proposes data-boosted variants of interior-point and spatial branching methods for AC-OPF, using historical operating data for initialization and feasible-region restriction, then reports empirical results on convergence and computation times across test networks. No derivation chain, first-principles prediction, or fitted parameter is presented that reduces by construction to the same inputs or self-citations; performance claims rest on direct experimental measurement rather than algebraic equivalence or load-bearing self-reference. The approach is therefore self-contained against external benchmarks with no circular steps.

Axiom & Free-Parameter Ledger

0 free parameters · 0 axioms · 0 invented entities

Abstract provides no explicit free parameters, axioms, or invented entities; the approach relies on standard assumptions of the two solver families plus the unstated premise that historical data is suitable for guidance.

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Reference graph

Works this paper leans on

25 extracted references · 25 canonical work pages

  1. [1]

    Optimal power flow formulations and their impacts on the performance of solution methods,

    B. Sereeter, C. Vuik, C. Witteveen, and P. Palensky, “Optimal power flow formulations and their impacts on the performance of solution methods,” in2019 IEEE Power & Energy Society General Meeting (PESGM). IEEE, 2019, pp. 1–5

    work page 2019

  2. [2]

    Real-time optimal power flow,

    Y . Tang, K. Dvijotham, and S. Low, “Real-time optimal power flow,” IEEE Transactions on Smart Grid, vol. 8, no. 6, pp. 2963–2973, 2017

    work page 2017

  3. [3]

    Solutions of dc opf are never ac feasible,

    K. Baker, “Solutions of dc opf are never ac feasible,” inProceedings of the Twelfth ACM International Conference on Future Energy Systems, 2021, pp. 264–268

    work page 2021

  4. [4]

    A survey of relaxations and approximations of the power flow equations,

    D. K. Molzahn, I. A. Hiskenset al., “A survey of relaxations and approximations of the power flow equations,”Foundations and Trends® in Electric Energy Systems, vol. 4, no. 1-2, pp. 1–221, 2019

    work page 2019

  5. [5]

    Empirical investigation of non-convexities in optimal power flow problems,

    M. R. Narimani, D. K. Molzahn, D. Wu, and M. L. Crow, “Empirical investigation of non-convexities in optimal power flow problems,” in 2018 Annual American Control Conference (ACC). IEEE, 2018, pp. 3847–3854

    work page 2018

  6. [6]

    Experiments with the interior-point method for solving large scale optimal power flow problems,

    F. Capitanescu and L. Wehenkel, “Experiments with the interior-point method for solving large scale optimal power flow problems,”Electric Power Systems Research, vol. 95, pp. 276–283, 2013

    work page 2013

  7. [7]

    Learning and optimization for efficient and optimal oper- ations in sustainable power systems,

    L. Zhang, “Learning and optimization for efficient and optimal oper- ations in sustainable power systems,” Ph.D. dissertation, University of Washington, 2024

    work page 2024

  8. [8]

    Complete results for a numerical evaluation of interior point solvers for large- scale optimal power flow problems,

    J. Kardos, D. Kourounis, O. Schenk, and R. Zimmerman, “Complete results for a numerical evaluation of interior point solvers for large- scale optimal power flow problems,”arXiv preprint arXiv:1807.03964, 2018

    work page arXiv 2018

  9. [9]

    Lo- cal solutions of the Optimal Power Flow problem,

    W. A. Bukhsh, A. Grothey, K. I. M. McKinnon, and P. A. Trodden, “Lo- cal solutions of the Optimal Power Flow problem,”IEEE Transactions on Power Systems, vol. 28, no. 4, pp. 4780–4788, 2013

    work page 2013

  10. [10]

    Bound tightening for the alternating current optimal power flow problem,

    C. Chen, A. Atamt ¨urk, and S. S. Oren, “Bound tightening for the alternating current optimal power flow problem,”IEEE Transactions on Power Systems, vol. 31, no. 5, pp. 3729–3736, 2015

    work page 2015

  11. [11]

    Scalable global optimization for AC-OPF via quadratic convex relaxation and branch-and-bound,

    M. Iranpour and M. R. Narimani, “Scalable global optimization for AC-OPF via quadratic convex relaxation and branch-and-bound,”arXiv preprint arXiv:2505.18435, 2025

    work page arXiv 2025

  12. [12]

    Data-driven optimal power flow: A physics-informed machine learning approach,

    X. Lei, Z. Yang, J. Yu, J. Zhao, Q. Gao, and H. Yu, “Data-driven optimal power flow: A physics-informed machine learning approach,” IEEE Transactions on Power Systems, vol. 36, no. 1, pp. 346–354, 2020

    work page 2020

  13. [13]

    Inter- pretable machine learning for dc optimal power flow with feasibility guarantees,

    A. Stratigakos, S. Pineda, J. M. Morales, and G. Kariniotakis, “Inter- pretable machine learning for dc optimal power flow with feasibility guarantees,”IEEE Transactions on Power Systems, vol. 39, no. 3, pp. 5126–5137, 2023

    work page 2023

  14. [14]

    Beyond the neural fog: Interpretable learning for ac optimal power flow,

    S. Pineda, J. P ´erez-Ruiz, and J. M. Morales, “Beyond the neural fog: Interpretable learning for ac optimal power flow,”IEEE Transactions on Power Systems, 2025

    work page 2025

  15. [15]

    Review of Machine Learning techniques for Optimal Power Flow,

    H. Khaloie, M. Dolanyi, J.-F. Toubeau, and F. Vall ´ee, “Review of Machine Learning techniques for Optimal Power Flow,”Applied Energy, vol. 388, p. 125637, 2025

    work page 2025

  16. [16]

    Deepopf: A deep neural network approach for security-constrained dc optimal power flow,

    X. Pan, T. Zhao, M. Chen, and S. Zhang, “Deepopf: A deep neural network approach for security-constrained dc optimal power flow,”IEEE Transactions on Power Systems, vol. 36, no. 3, pp. 1725–1735, 2020

    work page 2020

  17. [17]

    Ac power flow feasibility restoration via a state estimation-based post-processing algorithm,

    B. Taheri and D. K. Molzahn, “Ac power flow feasibility restoration via a state estimation-based post-processing algorithm,”Electric Power Systems Research, vol. 235, p. 110642, 2024

    work page 2024

  18. [18]

    Learn- ing to accelerate globally optimal solutions to the ac optimal power flow problem,

    F. Cengil, H. Nagarajan, R. Bent, S. Eksioglu, and B. Eksioglu, “Learn- ing to accelerate globally optimal solutions to the ac optimal power flow problem,”Electric power systems research, vol. 212, p. 108275, 2022

    work page 2022

  19. [19]

    Data-driven probabilistic constraint elimina- tion for accelerated optimal power flow,

    C. Crozier and K. Baker, “Data-driven probabilistic constraint elimina- tion for accelerated optimal power flow,” in2022 IEEE Power & Energy Society General Meeting (PESGM). IEEE, 2022, pp. 1–5

    work page 2022

  20. [20]

    Computational and numerical analysis of ac optimal power flow formulations on large- scale power grids,

    A. S. Nair, S. Abhyankar, S. Peles, and P. Ranganathan, “Computational and numerical analysis of ac optimal power flow formulations on large- scale power grids,”Electric power systems research, vol. 202, p. 107594, 2022

    work page 2022

  21. [21]

    Mathematical programming formulations for the alternating current optimal power flow problem,

    D. Bienstock, M. Escobar, C. Gentile, and L. Liberti, “Mathematical programming formulations for the alternating current optimal power flow problem,”4OR, vol. 18, no. 3, pp. 249–292, 2020

    work page 2020

  22. [22]

    Ye,Interior point algorithms: theory and analysis

    Y . Ye,Interior point algorithms: theory and analysis. John Wiley & Sons, 2011

    work page 2011

  23. [23]

    A simplicial branch-and-bound algorithm for solving quadratically constrained quadratic programs,

    J. Linderoth, “A simplicial branch-and-bound algorithm for solving quadratically constrained quadratic programs,”Mathematical program- ming, vol. 103, no. 2, pp. 251–282, 2005

    work page 2005

  24. [24]

    Mat- power: Steady-state operations, planning, and analysis tools for power systems research and education,

    R. D. Zimmerman, C. E. Murillo-S ´anchez, and R. J. Thomas, “Mat- power: Steady-state operations, planning, and analysis tools for power systems research and education,”IEEE Transactions on power systems, vol. 26, no. 1, pp. 12–19, 2010

    work page 2010

  25. [25]

    Ipvssp4opf,

    OASYS research group, “Ipvssp4opf,” https://github.com/groupoasys/IPvsSP4OPF, 2025, accessed: 2025- 10-10

    work page 2025