Large language model assisted hyper-heuristic evolutionary algorithm for groundwater level prediction.

This paper proposes a novel Large Language Model (LLM)-assisted hyper-heuristic evolutionary algorithm framework (LLMHHEA) to enhance the accuracy of groundwater level (GWL) prediction. Traditional models and artificial neural networks (ANNs) have limitations such as insufficient accuracy, while commonly used metaheuristic optimization methods are often time-consuming and rely on expert experience. LLMHHEA deeply integrates the generative intelligence of LLMs with the hyper-heuristic search paradigm through a co-evolutionary mechanism based on a hybrid encoding scheme. Its core evolutionary mechanisms include: a mutation strategy with dynamically adjusted probabilities (covering metaheuristic, neural network, and LLM-evolved mutations), a mutation-type-constrained directional crossover operation, and an adaptive selection strategy. Experiments on two independent groundwater level (GWL) datasets and one temperature time series dataset demonstrate that LLMHHEA exhibits stable convergence performance and achieves better predictive results compared to traditional metaheuristic-ANN combination methods. Specifically, on Dataset I, the framework identified the best-performing combination of an LLM-improved kepler optimization algorithm (KOA) and adaptive neuro-fuzzy inference system (ANFIS); on Dataset II, it obtained the best combination of an LLM-improved genetic algorithm (GA) and back-propagation network (BP); on the temperature series, it successfully evolved a distinct LLM-improved KOA paired with BP, further validating the framework's generalizability across different variable types and temporal characteristics. The experiments prove that the algorithms improved through LLM-evolved mutation outperform their original versions in both generalization ability and prediction accuracy. This research provides a new intelligent paradigm for complex optimization and prediction problems and offers robust technical support for sustainable water resource management.