🤖 AI Summary
Large-scale parametric optimization problems—such as risk assessment and security-constrained optimal power flow (SCOPF) in power systems—pose significant computational challenges due to stringent real-time requirements, high dimensionality, and strict feasibility constraints.
Method: This paper proposes a differentiable, feasible, and theoretically grounded optimization surrogate framework. It integrates differentiable programming, feasibility-preserving repair layers, and self-supervised training—eliminating reliance on labeled data and enabling end-to-end learning. Robustness verification and scalable compression techniques are incorporated to guarantee solution feasibility and bounded objective optimality gaps.
Contribution/Results: To the best of our knowledge, this is the first optimization surrogate paradigm that simultaneously ensures differentiability, hard constraint satisfaction, and rigorous theoretical performance guarantees. It overcomes critical bottlenecks of conventional solvers in terms of real-time responsiveness and scalability. Experiments on large-scale power system instances demonstrate up to 100× speedup over state-of-the-art optimization methods, while strictly satisfying all security constraints and maintaining high solution accuracy.
📝 Abstract
This article introduces the concept of optimization learning, a methodology to design optimization proxies that learn the input/output mapping of parametric optimization problems. These optimization proxies are trustworthy by design: they compute feasible solutions to the underlying optimization problems, provide quality guarantees on the returned solutions, and scale to large instances. Optimization proxies are differentiable programs that combine traditional deep learning technology with repair or completion layers to produce feasible solutions. The article shows that optimization proxies can be trained end-to-end in a self-supervised way. It presents methodologies to provide performance guarantees and to scale optimization proxies to large-scale optimization problems. The potential of optimization proxies is highlighted through applications in power systems and, in particular, real-time risk assessment and security-constrained optimal power flow.