用连续变形法训练电力系统优化模型，提升求解可行性与稳定性。
Homotopy-Guided Self-Supervised Learning of Parametric Solutions for AC Optimal Power Flow
- 通过渐变松弛问题引导学习，改善非凸优化的收敛性。
- 在标准测试中可行性率显著高于基线方法，目标值接近完整求解器。
- 无需标注解或外部求解器，适合实时电力调度场景。
学习优化（L2O）参数化交流最优潮流（AC-OPF）解法，有望实现电力系统实时运行中的快速、可复用决策。然而，AC-OPF固有的非凸性导致优化景观复杂，传统学习方法常无法收敛到可行且高质量的解。本文提出一种同伦引导的自监督L2O方法，核心思想是在训练过程中构建目标函数与约束的连续变形：从一个松弛问题开始，其具有宽广的吸引域，再逐步向原始问题转化。该方法提升了收敛稳定性并促进可行性，且无需标注最优解或外部求解器。我们在标准IEEE AC-OPF基准上评估该方法，结果表明，相较于非同伦基线，同伦引导的L2O显著提高了可行性率，同时目标值与完整OPF求解器相当。这些发现证明了同伦启发式在可扩展、约束感知的电力系统优化L2O中的潜力。
原文摘要 · Abstract (English)
Learning to optimize (L2O) parametric approximations of AC optimal power flow (AC-OPF) solutions offers the potential for fast, reusable decision-making in real-time power system operations. However, the inherent nonconvexity of AC-OPF results in challenging optimization landscapes, and standard learning approaches often fail to converge to feasible, high-quality solutions. This work introduces a \textit{homotopy-guided self-supervised L2O method} for parametric AC-OPF problems. The key idea is to construct a continuous deformation of the objective and constraints during training, beginning from a relaxed problem with a broad basin of attraction and gradually transforming it toward the original problem. The resulting learning process improves convergence stability and promotes feasibility without requiring labeled optimal solutions or external solvers. We evaluate the proposed method on standard IEEE AC-OPF benchmarks and show that homotopy-guided L2O significantly increases feasibility rates compared to non-homotopy baselines, while achieving objective values comparable to full OPF solvers. These findings demonstrate the promise of homotopy-based heuristics for scalable, constraint-aware L2O in power system optimization.
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