## 1 Introduction  
Dams are among the superstructures that require very precise studies to explore every part of them from many aspects of safety, performance, and environment. The main part of these structures is their spillway, which enables operators to dispose of excess inflows to reservoirs in a controlled or uncontrolled manner. When water with high velocity is passing through the spillway, it should be designed with energy dissipaters downstream. Ski jumps taking away water from the bucket and into the air in the form of a water jet are among widely used energy dissipaters in spillways. At the outlet of these spillways where water jets to the riverbed, a plunge pool is formed due to the energy of the high-velocity water, which is often capable of excavating holes into even hard rocks and soil. In order to prevent any possible erosion and to control the stability of the dam body and other structures accurately, and to have a safe design facing the dynamic process of this phenomena, precise prediction of this scouring is critical. Physical hydraulic models and mathematical simulation are among practices employed in studying hydraulic related phenomena including erosion and scour. Being time and cost-inefficient, physical hydraulic models are merely employed in the final phases of studies. In addition, the reliability of these models is still questionable [1]. With advances in computer science, computational fluid dynamics (CFD) methods have been broadly used in these studies [2]. However, complexities and computational limitations are still drawbacks of these methods. Therefore, researchers are still investigating an easy and immediate technique for initial estimates of scour in the feasibility study phase. In this regard, due to the growing interest in using soft computing practices recently in several disciplines [3], researchers used these techniques to estimate scour depth for different hydraulic structures [1; 4; 5; 6; 7; 8; 9; 10; 11; 12; 13]. Artificial neural networks (ANN) is a branch of artificial intelligence (AI), which are capable of perceiving complex nonlinear behavior of phenomena [6]. This approach, which is inspired by human brains' functions, is employed in prediction studies of several hydraulic parameters [14; 15; 16; 17; 18; 19; 20]. Moreover, it has been used in the estimation of equilibrium bridge pier scour effectively [21; 22]. Recently, [PERSON] et al. [23] predicted scour depth downstream of weirs by employing the adaptive neuro-fuzzy inference system (ANFIS) coupled with biogeography based optimization (ANFIS-BBO), invasive weed optimization (ANFIS-IWO) and teaching-learning based optimization (ANFIS-TLBO) algorithms. They found better performance with the ANFIS-IWO model (RMSE = 0.148) over the other models. Table 1 summarizes a brief review of the application of soft computing techniques in hydraulic structures studies. Due to uncertainties in soft computing modeling techniques, including the topology of the network and training algorithms, scientists have employed a broad range of techniques to improve the performance of these approaches. Applying different optimization tools has been among these solutions. To this end, ANNs and then other standalone intelligent models were combined with evolutionary algorithms such as genetic algorithms (GA) or particle swarm optimization (PSO) as optimization tools by numerous researchers to estimate scour depth at bridge piers [24]. [PERSON] et al. [25] evaluated the ability of a hybrid intelligent model (ANFIS-GA) in the estimation of scour depth around inclined bridge piers. [PERSON] et al. [26] developed two hybrid models, namely, ANN-APSO and ANN-GA, to predict scour depth at bridge piers and concluded that the models were more reliable in terms of precision and time consumption. [PERSON] and [PERSON] [27] developed a hybrid swarm intelligence-based support vector machine (PSO-SVM) method for the prediction of scour depth around bridge pier with different kernel functions.