## 1 Introduction  
Water quality explains the descriptions of biological, chemical, and physical characteristics of water bodies [1; 2]. The assessment of water quality parameters, such as dissolved oxygen (DO), algae, nitrogen (N), total nitrogen (TN), phosphorus (P), total phosphorus (TP), biochemical oxygen demand (BOD), and chemical oxygen demand (COD), is necessary to improve the operational performance and develop water resource management effectively [3]. DO, as one of the water quality parameters, refers to the free-level non-compound oxygen dissolved in water or other liquids [4; 5; 6; 7; 8]. Too high or low levels of DO concentration can affect the maintenance of water quality [9]. Therefore, DO is a key parameter to assess water quality in rivers, reservoirs, and lakes, and as one of the indicators for the healthy functioning of aquatic ecosystems [10]. Water quality modeling includes contaminant transport, biochemical transformation, and forecasting/prediction of water pollution [3; 11]. Accurate forecasting/prediction of water quality can provide the basic data to control water quality and deal with water quality incidents [12]. In traditional water quality modeling, water quality models can be calibrated using the trial and error method. However, since the traditional calibration processes require a large number of iterations, they cannot be effective [11]. Therefore, the inverse methods (e.g., fuzzy logic, Bayesian inference, and maximum entropy technique, etc. ), which are more robust, objective, and sound approaches, are recommended. One of the widely used inverse methods is the indirect inverse method, which is developed using forging nonlinear optimization problems [11; 13]. The diverse researches on water quality modeling using heuristic approaches (e.g., artificial neural network (ANN), adaptive neuro-fuzzy inference systems (ANFIS), and support vector machines (SVM), etc.) have been investigated and reported in the literature during the past two decades [14; 15; 16; 17; 18; 19; 20]. [PERSON] et al. [21] suggested the cascade correlation neural network (CCNN) to predict the missing monthly data of water quality parameters. [PERSON] et al. [22] suggested the backpropagation neural network (BPNN) to quantify the cause-and-effect relationship in reservoir eutrophication. [PERSON] et al. [23] developed the BPNN to forecast water quality in reservoirs. [PERSON] et al. [11] developed the genetic algorithm-based neural network (GA-NN) to solve inverse water quality problems. [PERSON] et al. [24] predicted the BOD concentration using the feedforward neural network (FFNN) in the Melen River, Turkey. [PERSON] et al. [3] used ANNs to predict three water quality parameters (i.e., total dissolved solids, electrical conductivity, and turbidity) in the Johor River, Malaysia. [PERSON] et al. [25] employed SVM (i.e., support vector classification (SVC) and regression (SVR)) to optimize a monitoring program using water quality data. [PERSON] et al. [26] used a radial basis function neural network (RBFNN) for water quality prediction in the wastewater treatment process. [PERSON] et al. [9] proposed the FFNN to predict water quality indexes in the Kinta River, Malaysia. [PERSON] and [PERSON] [12] provided a hybrid approach combining the BPNN and wavelet transform (WT) to develop a water quality model. [PERSON] and [PERSON] [27] developed the k-means clustering-based multilayer perceptron (k-means MLP) for modeling the COD concentration in Adapazari, Turkey. [PERSON] et al. [28] implemented a hybrid model based on integrated SVR with the firefly algorithm (FFA) for prediction of the water quality indicator (WQI) over a period of 10 years in the Euphrates River, Iraq. Among the various heuristic techniques, ANNs (e.g., BPNN, MLP, and FFNN) have been accomplished for prediction, forecasting, modelling, and estimation of DO [29; 30]; BOD and DO [31]; TN, TP, and DO [32] using different input data in the river stream.