In this research, the proper models are developed to simultaneously predict the energy efficiency, exergy efficiency, and water productivity of a single-slope solar still via an Artificial Neural Network (ANN) and a neural network optimized by Imperialist Competition Algorithm (ICA). The outputs are modeled as a function of the time, ambient temperature, solar radiation, glass temperature, basin temperature, and water temperature. The empirical data are utilized to train both the ANN and ICA-enhanced ANN. The neural network with five hidden neurons demonstrates the best performance. The results reveal that implementing the ICA significantly improves the performance of the ANN in predicting all the three outputs. Thereby, as a result of employing the ICA in the ANN, Mean Absolute Error (MAE) experiences 54.30%, 40.11%, and 53.35% reductions in prediction of the water productivity, energy efficiency, and exergy efficiency, respectively, based on the testing date set. Moreover, based on the test data, the ANN-ICA predicts the water productivity, energy efficiency, and exergy efficiency with root mean square error (RMSE) values of about 15.77, 1.37, and 0.29, respectively. In addition, the developed mathematical correlations are finally presented as a function of the inputs. (C) 2020 Elsevier Ltd. All rights reserved.