Modified Whale Optimization Algorithm based ANN: a novel predictive model for RO desalination plant

In recent decades, nature-inspired optimization methods have played a critical role in helping industrial plant designers to find superior solutions for process parameters. According to the literature, such methods are simple, quick, and indispensable for saving time, money, and energy. In this regard, the Modified Whale Optimization Algorithm (MWOA) hybridized with Artificial Neural Networks (ANN) has been employed in the Reverse Osmosis (RO) desalination plant performance to estimate the permeate flux (0.118‒2.656 L/h m²). The plant’s datasets have been collected from the literature and include four input parameters: feed flow rate (400‒600 L/h), evaporator inlet temperature (60‒80 °C), feed salt concentration (35‒140 g/L) and condenser inlet temperature (20‒30 °C). For this purpose, ten predictive models (MWOA-ANN Model-1 to Model-10) have been proposed, which are capable of predicting more accurate permeate flux (L/h m²) than the existing models (Response Surface Methodology (RSM), ANN and hybrid WOA-ANN models) with minimum errors. Simulation results suggest that the MWOA algorithm demonstrates a stronger optimization capability of finding the correct weights and biases so as to enable superior ANN based modeling without limitation of overfitting. Ten MWOA-ANN models (Model-1 to Model-10) have been proposed to investigate the plant’s performance. Model-6 with a single hidden layer (H = 1), eleven hidden layer nodes (n = 11) and the thirteen search agents (SA = 13) produced most outstanding regression results (R² = 99.1%) with minimal errors (MSE = 0.005). The residual errors for Model-6 are also found to be within limits (span of − 0.1 to 0.2). Finally, the findings show that the screened MWOA-ANN models are promising for identifying the best process parameters in order to assist industrial plant designers.