Hybridizing evolutionary algorithms and multiple non-linear regression technique for stream temperature modeling

Abstract The present study hybridizes the new-generation evolutionary algorithms and the nonlinear regression technique for stream temperature modeling and compares this approach with conventional gray and black box approaches under natural flow conditions, providing a comprehensive assessment. The nonlinear equation for water temperature modeling was optimized using biogeography-based optimization (BBO) and invasive weed optimization (IWO), simulated annealing algorithm (SA) and particle swarm optimization (PSO). Two black box approaches, a feedforward neural network (FNN) and a long short-term memory (LSTM) network, were also employed for comparison. Additionally, an adaptive neuro-fuzzy inference system (ANFIS) served as a gray box model for river thermal regimes. The models were evaluated based on accuracy, complexity, generality and interpretability. Performance metrics, such as the Nash–Sutcliffe efficiency (NSE), showed that the LSTM model achieved the highest accuracy (NSE = 0.96) but required significant computational resources. In contrast, evolutionary algorithm-based models offered acceptable performance while reducing the computational complexities of LSTM, with all models achieving NSE values above 0.5. Considering interpretability, accuracy and complexity, evolutionary-based nonlinear models are recommended for general applications, such as assessing thermal river habitats. For tasks requiring very high accuracy, the LSTM model is preferred, while ANFIS provides a balanced trade-off between accuracy and interpretability, making it suitable for engineers and ecologists. While all models demonstrate similar generality, this model is developed for a specific location. For other locations, independent models with a similar architecture would need to be developed. Ultimately, the choice of model depends on specific objectives and available resources.