The transportation sector accounts for approximately 20\% of global CO$_2$ emissions, with road transportation responsible for 71\% in Europe. Electric vehicles (EVs) represent one of the most effective mitigation strategies. According to the IEA, global EV sales reached 17 million units in 2024, with market shares of 40\% in China, 20\% in Europe, and 10\% in the US. This rapid adoption necessitates not only extensive charging infrastructure but also intelligent operational management.

The Electric Vehicle Charging Scheduling Problem (EVCSP) is critical for optimizing the utilization of EV charging infrastructure. It involves scheduling charging requests at stations with limited chargers and constrained grid capacity, aiming to maximize satisfied demands while respecting temporal and energy constraints. This NP-hard problem has motivated the development of exact mathematical programming methods and heuristic techniques such as genetic algorithms, simulated annealing, and tabu search.

Recent advances in artificial intelligence, particularly Large Language Models (LLMs), have demonstrated remarkable reasoning capabilities across various domains. This work investigates whether open-source LLMs can effectively function as evolutionary operators for solving EVCSP. While proprietary LLMs have been explored for optimization, open-source models remain largely unexplored. This gap is significant as open-source models enable local deployment without privacy concerns or API costs. We design a prompt-driven framework where LLMs iteratively evolve populations of candidate solutions, integrating heuristic correction and local search mechanisms to enhance performance.