RETRACTED: Combination of group method of data handling neural network with multi-objective gray wolf optimizer to predict the viscosity of MWCNT-TiO2 -oil SAE50 nanofluid

Background: Nanofluids are the most widely used materials in various engineering fields. They have different properties under different conditions, and predicting their properties requires several experiments. Artificial intelligence can predict the properties of nanofluids in the shortest time and cost. Methodology: This study aims to predict the viscosity and share rate of MWCNT-TiO2 (40–60)-oil SAE50 nano-lubricant (NL). Machine learning algorithms and neural networks can respond best to this important matter. For this purpose, the Group Method of Data Handling (GMDH) neural network is combined with the meta-heuristic algorithm Multi-Objective Gray Wolf Optimizer (MOGWO). This way, the experimental data is first given to the artificial neural network (ANN). Then, the meta-heuristic algorithm optimizes the hyperparameters of the ANN to bring the predicted results closer to the experimental data and minimize the error. The MOGWO algorithm's regulators are the number of iterations and the number of wolves investigated in this study to better select this algorithm. Then, these modes are measured using two criteria, correlation coefficient (R) and rote mean squared error (RMSE), to choose the best mode. Finally, by using the extracted equations by the GMDH neural network, the best models or the Pareto front can be obtained using the MOGWO meta-heuristic algorithm. Results: The error histogram diagram shows the excellent performance of the combination of the GMDH neural network and the MOGWO meta-heuristic algorithm. The values of R and RMSE for viscosity and shear rate are equal to 0.99217, 15.8749, and 0.99031, 68.7723, respectively. The optimization results showed that the best conditions to meet viscosity and cutting rate are when φ, T, and γ equal 1.21∗e−5, 46.71, and 50.11.