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Structure-Aware Commitment Reduction for Network-Constrained Unit Commitment with Solver-Preserving Guarantees

Guangwen Wang, Jiaqi Wu, Yang Weng, Baosen Zhang

Abstract

The growing number of individual generating units, hybrid resources, and security constraints has significantly increased the computational burden of network-constrained unit commitment (UC), where most solution time is spent exploring branch-and-bound trees over unit-hour binary variables. To reduce this combinatorial burden, recent approaches have explored learning-based guidance to assist commitment decisions. However, directly using tools such as large language models (LLMs) to predict full commitment schedules is unreliable, as infeasible or inconsistent binary decisions can violate inter-temporal constraints and degrade economic optimality. This paper proposes a solver-compatible dimensionality reduction framework for UC that exploits structural regularities in commitment decisions. Instead of generating complete schedules, the framework identifies a sparse subset of structurally stable commitment binaries to fix prior to optimization. One implementation uses an LLM to select these variables. The LLM does not replace the optimization process but provides partial variable restriction, while all constraints and remaining decisions are handled by the original MILP solver, which continues to enforce network, ramping, reserve, and security constraints. We formally show that the masked problem defines a reduced feasible region of the original UC model, thereby preserving feasibility and enabling solver-certified optimality within the restricted space. Experiments on IEEE 57-bus, RTS 73-bus, IEEE 118-bus, and augmented large-scale cases, including security-constrained variants, demonstrate consistent reductions in branch-and-bound nodes and solution time, achieving order-of-magnitude speedups on high-complexity instances while maintaining near-optimal objective values.

Structure-Aware Commitment Reduction for Network-Constrained Unit Commitment with Solver-Preserving Guarantees

Abstract

The growing number of individual generating units, hybrid resources, and security constraints has significantly increased the computational burden of network-constrained unit commitment (UC), where most solution time is spent exploring branch-and-bound trees over unit-hour binary variables. To reduce this combinatorial burden, recent approaches have explored learning-based guidance to assist commitment decisions. However, directly using tools such as large language models (LLMs) to predict full commitment schedules is unreliable, as infeasible or inconsistent binary decisions can violate inter-temporal constraints and degrade economic optimality. This paper proposes a solver-compatible dimensionality reduction framework for UC that exploits structural regularities in commitment decisions. Instead of generating complete schedules, the framework identifies a sparse subset of structurally stable commitment binaries to fix prior to optimization. One implementation uses an LLM to select these variables. The LLM does not replace the optimization process but provides partial variable restriction, while all constraints and remaining decisions are handled by the original MILP solver, which continues to enforce network, ramping, reserve, and security constraints. We formally show that the masked problem defines a reduced feasible region of the original UC model, thereby preserving feasibility and enabling solver-certified optimality within the restricted space. Experiments on IEEE 57-bus, RTS 73-bus, IEEE 118-bus, and augmented large-scale cases, including security-constrained variants, demonstrate consistent reductions in branch-and-bound nodes and solution time, achieving order-of-magnitude speedups on high-complexity instances while maintaining near-optimal objective values.

Paper Structure

This paper contains 18 sections, 2 theorems, 5 equations, 3 figures, 6 tables, 1 algorithm.

Table of Contents

  1. Introduction
  2. Problem Formulation
  3. Commitment-Restricted Unit Commitment Framework
  4. Restricted Unit Commitment Formulation
  5. LLM-Based Restriction Generation
  6. Applying Restrictions and Solving the MILP
  7. Solution Procedure with Feedback
  8. Structural Basis for Commitment Restriction in Unit Commitment
  9. Operating Regimes and Commitment Regularity
  10. Temporal Coupling in Unit Commitment
  11. Feasibility and Optimality Properties
  12. Experimental Validation
  13. Experimental Setup
  14. Comparison with Random Commitment Restriction
  15. Performance Without Historical Commitment Information
  16. ...and 3 more sections

Key Result

Proposition 1

If $\mathcal{F}_M$ is nonempty, then any solution returned by the MILP solver for the restricted problem satisfies all constraints of the original UC formulation. $\blacktriangleleft$$\blacktriangleleft$

Figures (3)

  • Figure 1: Workflow of the proposed solver-preserving commitment variable reduction method. An LLM generates a sparse commitment restriction set, a feasibility screening step removes inconsistent selections, and the resulting reduced UC problem is solved by a MILP solver with full constraint enforcement and certified optimality within the restricted space.
  • Figure 2: Comparison of 24-hour unit commitment schedules from the MILP baseline and the LLM-Assisted method. Rows correspond to generating units and columns to hours; white and black denote on and off states, respectively.
  • Figure 3: Solve-time comparison over 365 consecutive daily unit commitment instances. Each point corresponds to one 24-hour UC problem solved by the MILP baseline and the LLM-Assisted restriction method.

Theorems & Definitions (5)

  • Proposition 1: Feasibility Preservation
  • proof
  • Theorem 1: Reduced Feasible Region
  • proof
  • Remark 1: Optimality in Restricted Space