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

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.