提出新基准与模型,实现电力优化求解迭代减少76%。
WARP: A Benchmark for Primal-Dual Warm-Starting of Interior-Point Solvers
- 用图神经网络预测完整内点状态,兼顾初值与对偶变量。
- 相比传统方法,迭代次数从23次降至6次,减少76%。
- 专为电力系统优化设计,可适应线路故障场景无需重训。
求解交流最优潮流(AC-OPF)在电力市场运行中至关重要,内点法(IPM)如IPOPT是主流求解器。现有机器学习方法仅预测原始变量初值,宣称可减少30%-46%迭代次数。本文指出,这些结果基于错误的基线:此前对比的是平启动($V_m = 1, V_a = 0$),而实际默认初始点是变量边界中点$(l+u)/2$,该点在对数障碍中心性上已接近最优。以正确基线评估,所有仅预测原始变量的方法均无法减少迭代次数。原因在于内点法的几何特性:原始变量预测精度与收敛速度呈负相关;仅提供最优解$x^*$但无对偶变量会导致求解器发散。通过预言机实验验证,若同时提供完整的原始-对偶-障碍状态$(x^*, λ^*, z^*, μ^*)$,可使IPOPT迭代次数从23次降至3次,减少85%,且此效果无法由仅预测原始变量的方法达成。为此,本文发布包含双标签的AC-OPF数据集、修正的评估协议,以及WARP——一种拓扑条件编码-处理-解码图神经网络,能直接预测异构约束图上的完整内点状态$(\hat{x}, \hat{λ}, \hat{z}, \hat{μ})$。WARP实现76%迭代减少,并天然支持N-1故障拓扑变化,无需重新训练。
原文摘要 · Abstract (English)
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 $V_m = 1, V_a = 0$, 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 $(\hat{x}, \hatλ, \hat{z}, \hatμ)$ 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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