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Successive Fixing for Large-Scale SCUC Using First-Order Methods

Jinxin Xiong, Yanting Huang, Yingxiao Wang, Linxin Yang, Jianghua Wu, Shunbo Lei, Akang Wang

TL;DR

This work tackles large-scale Security-Constrained Unit Commitment (SCUC) by addressing the LP-relaxation bottleneck with GPU-accelerated first-order methods, which typically yield non-vertex solutions unsuitable for branch-and-cut. It introduces a successive fixing framework that uses a customized HPR-LP solver to generate guided, logic-consistent variable fixings, progressively shrinking the MILP through iterated relaxation, fixing, and presolving. The authors achieve substantial speedups (up to ~20x for LP relaxations and ~10x overall) on benchmarks with more than 13,000 buses without compromising solution quality, and demonstrate robustness across very large instances. The key innovations include instance-aware scaling, low-precision arithmetic on GPUs, and a novel round-and-fix strategy with temporal-consistency checks, enabling scalable, high-quality SCUC solutions in practice.

Abstract

Security-Constrained Unit Commitment is a fundamental optimization problem in power systems operations. The primary computational bottleneck arises from the need to solve large-scale Linear Programming (LP) relaxations within branch-and-cut. Conventional simplex and barrier methods become computationally prohibitive at this scale due to their reliance on expensive matrix factorizations. While matrix-free first-order methods present a promising alternative, their tendency to converge to non-vertex solutions renders them incompatible with standard branch-and-cut procedures. To bridge this gap, we propose a successive fixing framework that leverages a customized GPU-accelerated first-order LP solver to guide a logic-driven variable-fixing strategy. Each iteration produces a reduced Mixed-Integer Linear Programming (MILP) problem, which is subsequently tightened via presolving. This iterative cycle of relaxation, fixing, and presolving progressively reduces problem complexity, producing a highly tractable final MILP model. When evaluated on public benchmarks exceeding 13,000 buses, our approach achieves a tenfold speedup over state-of-the-art methods without compromising solution quality.

Successive Fixing for Large-Scale SCUC Using First-Order Methods

TL;DR

This work tackles large-scale Security-Constrained Unit Commitment (SCUC) by addressing the LP-relaxation bottleneck with GPU-accelerated first-order methods, which typically yield non-vertex solutions unsuitable for branch-and-cut. It introduces a successive fixing framework that uses a customized HPR-LP solver to generate guided, logic-consistent variable fixings, progressively shrinking the MILP through iterated relaxation, fixing, and presolving. The authors achieve substantial speedups (up to ~20x for LP relaxations and ~10x overall) on benchmarks with more than 13,000 buses without compromising solution quality, and demonstrate robustness across very large instances. The key innovations include instance-aware scaling, low-precision arithmetic on GPUs, and a novel round-and-fix strategy with temporal-consistency checks, enabling scalable, high-quality SCUC solutions in practice.

Abstract

Security-Constrained Unit Commitment is a fundamental optimization problem in power systems operations. The primary computational bottleneck arises from the need to solve large-scale Linear Programming (LP) relaxations within branch-and-cut. Conventional simplex and barrier methods become computationally prohibitive at this scale due to their reliance on expensive matrix factorizations. While matrix-free first-order methods present a promising alternative, their tendency to converge to non-vertex solutions renders them incompatible with standard branch-and-cut procedures. To bridge this gap, we propose a successive fixing framework that leverages a customized GPU-accelerated first-order LP solver to guide a logic-driven variable-fixing strategy. Each iteration produces a reduced Mixed-Integer Linear Programming (MILP) problem, which is subsequently tightened via presolving. This iterative cycle of relaxation, fixing, and presolving progressively reduces problem complexity, producing a highly tractable final MILP model. When evaluated on public benchmarks exceeding 13,000 buses, our approach achieves a tenfold speedup over state-of-the-art methods without compromising solution quality.

Paper Structure

This paper contains 12 sections, 1 theorem, 14 equations, 3 figures, 2 tables, 2 algorithms.

Table of Contents

  1. Introduction
  2. Problem Formulation
  3. Enhanced HPR-LP for SCUC Relaxations
  4. Instance-Aware Scaling
  5. Accelerating Computation via Low-Precision Arithmetic
  6. Successive Fixing Framework
  7. Logic-Driven Fixing
  8. Successive Fixing
  9. CASE STUDY
  10. Comparing Against Baselines
  11. Ablation Study
  12. Conclusions

Key Result

Theorem 1

Assume the KKT solution for Problem (eq:lp) exists. Let $\{(\bar{x}^k, \bar{y}^k, \bar{z}^k)\}$ be the sequence generated by (eq:hpr), and $(x^*, y^*, z^*)$ be the corresponding limit point. Then for all $k \geq 0$, where $\mathcal{R}(x,y,z) \coloneqq \left( \right)$ denotes the KKT residual mapping for Problem (eq:lp), $I_m$ is the $m\times m$ identity matrix, and $R_0$ is a constant measuring

Figures (3)

  • Figure 1: A flowchart of our proposed framework, illustrating the transmission filtering outer loop (left panel) and the successive fixing inner loop (right panel). Key algorithmic enhancements are highlighted in red.
  • Figure 2: Time decomposition for the ablation study. Each bar represents the total solution time, containing the time for solving LP relaxations and other procedures (such as presolve, fixing, branching and filtering).
  • Figure 3: $\operatorname{SGM_{10}}$ of the TF and the ablation methods across the 10 largest instances solved by all ablation methods. ("6470rte" is excluded for TF.)

Theorems & Definitions (1)

  • Theorem 1: chen2025hpr