用灰箱法高效求解含神经网络的电力优化问题
Formulations and scalability of neural network surrogates in nonlinear optimization problems
- 提出灰箱公式，将神经网络嵌入优化模型，提升可扩展性
- 最大5.9亿参数神经网络可在2.5倍时间内求解复杂电力调度问题
- 适合需要高精度约束建模的电力系统优化研究者
本文对比了全空间、降维空间和灰箱三种表示方法在非线性约束优化中嵌入训练好的神经网络的表现。实验基于一个瞬态稳定性约束的安全约束交流最优潮流（SCOPF）问题，其中瞬态稳定性由训练好的神经网络代理模型表示。优化问题在JuMP中实现，神经网络通过新开发的Julia包MathOptAI.jl嵌入。测试中使用了最多含5.9亿参数的神经网络。全空间方法受优化算法所用线性求解器限制，降维空间方法受限于建模环境和导数计算，而灰箱方法最具备可扩展性，瓶颈在于神经网络输出及其导数的评估，可通过图形处理器（GPU）加速。结合灰箱方法与GPU加速，最大规模神经网络代理模型的求解时间仅为无稳定性约束的简化SCOPF问题的2.5倍。
原文摘要 · Abstract (English)
We compare full-space, reduced-space, and gray-box formulations for representing trained neural networks in nonlinear constrained optimization problems. We test these formulations on a transient stability-constrained, security-constrained alternating current optimal power flow (SCOPF) problem where the transient stability criteria are represented by a trained neural network surrogate. Optimization problems are implemented in JuMP and trained neural networks are embedded using a new Julia package: MathOptAI.jl. To study the bottlenecks of the three formulations, we use neural networks with up to 590 million trained parameters. The full-space formulation is bottlenecked by the linear solver used by the optimization algorithm, while the reduced-space formulation is bottlenecked by the algebraic modeling environment and derivative computations. The gray-box formulation is the most scalable and is capable of solving with the largest neural networks tested. It is bottlenecked by evaluation of the neural network's outputs and their derivatives, which may be accelerated with a graphics processing unit (GPU). Leveraging the gray-box formulation and GPU acceleration, we solve our test problem with our largest neural network surrogate in 2.5$\times$ the time required for a simpler SCOPF problem without the stability constraint.
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