Integration of an artificial neural network and a simulated annealing algorithm for the optimization of the river water pollution index

The Shatt Al-Arab River is the primary source of the water supply in the Al-Basrah province. Therefore, this study aimed to assess the water pollution index (WPI) of the Shatt Al-Arab River at 15 water treatment plants (WTPs) from 2011 to 2020 (except for WTP No. 11, which was sampled from 2012 to 2020). The WPI included 12 physicochemical parameters: turbidity (Tur), pH, electrical conductivity (EC), total dissolved solids (TDS), total hardness (TH), potassium (K+), sodium (Na+), magnesium (Mg+2), calcium (Ca+2), alkalinity (Alk), chloride (Cl−), and sulfate (SO4−2). Two modeling methods, multiple linear regression (MLR) and an artificial neural network (ANN), were utilized to forecast the minimum value of the WPI. The simulated annealing (SA) technique and an integrated ANN-SA technique were used to estimate the best independent variable values that minimized the value of the WPI. A multilayer feed-forward neural network with a backpropagation algorithm was chosen for this study. A regression technique was employed to generate the WPI predicted equation which was also chosen as an objective function of the SA and combined ANN-SA. For the MLR method, the correlation coefficient (R) and mean squared error (MSE) values for the WPI were 4.746 × 10−7 and 1, respectively. The best ANN structure (10-17-1) predicted a WPI with MSE and R values of 8.851 × 10−11 and 1, respectively, for the training, 1.220 × 10−7 and 1 for the validation, and 1.354 × 10−9 and 1 for the testing. In contrast to the results obtained from the measured data, MLR analysis, and ANN technique, the combined ANN-SA method demonstrated the lowest WPI value at optimal parameters. The minimum WPI value for the integrated ANN-SA was 0.373.