Neural Two-Stage Stochastic Optimization for Solving Unit Commitment Problem

2025-07-13

AI Summary

For the two-stage stochastic unit commitment (2S-SUC) problem under high-dimensional uncertainty, this paper proposes a neural stochastic optimization framework. It employs deep neural networks to explicitly model the second-stage recourse cost and integrates this differentiable surrogate objective into the first-stage mixed-integer linear program (MILP) for joint optimization. Innovatively, a scenario embedding network coupled with a feature aggregation mechanism is introduced to achieve data-driven scenario dimensionality reduction—rendering model size independent of the number of scenarios and substantially enhancing scalability. Evaluated on IEEE 5-, 30-, and 118-bus systems, the method achieves an optimality gap below 1% while accelerating computation by several orders of magnitude over conventional scenario-based approaches. This work establishes an efficient, scalable paradigm for large-scale stochastic optimization in power systems.

Technology Category

• Reasoning under Uncertainty: Stochastic Optimization
• Search and Optimization: Mixed Discrete/Continuous Search
• Machine Learning: Optimization

Application Category

• Search and Retrieval-Augmented AI: Efficiency and scalability of Web search engines
• Economics, Online Markets and Human Computation: Cost models of using LLMs in production systems
• Graph Algorithms and Modeling for the Web: Graph neural networks and deep learning approaches for Web-related graphs

Abstract

This paper proposes a neural stochastic optimization method for efficiently solving the two-stage stochastic unit commitment (2S-SUC) problem under high-dimensional uncertainty scenarios. The proposed method approximates the second-stage recourse problem using a deep neural network trained to map commitment decisions and uncertainty features to recourse costs. The trained network is subsequently embedded into the first-stage UC problem as a mixed-integer linear program (MILP), allowing for explicit enforcement of operational constraints while preserving the key uncertainty characteristics. A scenario-embedding network is employed to enable dimensionality reduction and feature aggregation across arbitrary scenario sets, serving as a data-driven scenario reduction mechanism. Numerical experiments on IEEE 5-bus, 30-bus, and 118-bus systems demonstrate that the proposed neural two-stage stochastic optimization method achieves solutions with an optimality gap of less than 1%, while enabling orders-of-magnitude speedup compared to conventional MILP solvers and decomposition-based methods. Moreover, the model's size remains constant regardless of the number of scenarios, offering significant scalability for large-scale stochastic unit commitment problems.

Problem

• Efficiently solve two-stage stochastic unit commitment under high-dimensional uncertainty
• Approximate second-stage recourse using deep neural network for cost mapping
• Enable scalable solutions with constant model size regardless of scenarios

Innovation

• Deep neural network approximates second-stage recourse costs
• MILP embedding enforces constraints with uncertainty characteristics
• Scenario-embedding network reduces dimensionality and aggregates features