Theory-Driven Modeling and LLM-Guided Evolution for Power System Scheduling

Unit Commitment (UC) and Economic Dispatch (ED) are critical mixed-integer programming (MIP) formulations in modern power systems. The effectiveness of warm-start strategies for large-scale UC/ED MIPs crucially depends on variable selection and hyperparameter configuration. However, existing approaches either rely on expert-designed heuristics or computationally expensive machine learning methods, both of which struggle to adapt effectively across diverse problem structures. To address this, we present a recursive self-improvement framework where an AI system continuously refines its own decision-making strategies through LLM-guided evolutionary learning. The system diagnoses its performance failures, critiques its scoring functions, and autonomously updates all parameters through iterative evolution based on fitness feedback. This recursive loop enables the system to discover interpretable scoring functions (e.g., log-transformed reduced costs) and optimal hyperparameters without manual intervention, demonstrating measurable, reliable, and deployable self-improvement in industrial optimization settings. Experimental results on realistic UC/ED benchmarks demonstrate that our approach significantly outperforms commercial solvers such as Gurobi and baseline methods, achieving substantial speedup while maintaining solution quality. The framework eliminates manual parameter tuning and enables automatic adaptation to diverse problem structure