Representing Search State to a Large Language Model: A Structured Telemetry Interface for Runtime Control of Adaptive Large Neighbourhood Search

Adaptive large neighbourhood search is steered by high-level control decisions, yet its standard adaptation reacts to a narrow reward signal that conveys little about the state of the search. Recent work has strengthened this control with machine-learning and reinforcement-learning policies, but these generally require task-specific training. This paper proposes a framework in which a large language model acts as a bounded, training-free runtime supervisor of the search. The central contribution is a structured telemetry interface that compresses the evolving search into a compact, reproducible state representation over which the model can reason. The supervisor adjusts only search-control parameters and never modifies the solution, so construction, feasibility, and objective evaluation remain inside the metaheuristic. The framework is evaluated on a multi-depot capacitated vehicle routing problem with time windows on real city street networks, against conventional variants and two dedicated solvers. Under an equal iteration budget, the supervised algorithm reduces the mean gap to the best per-instance result from 2.93% to 0.18%, and its difference from the strongest dedicated solver is not statistically significant, although it runs at a higher computational cost. These results indicate that a language model can control metaheuristic search effectively when supported by a structured interface between the algorithm and the model.