# Scouring Depth Assessment Downstream of Weirs Using Hybrid Intelligence Models
## 2 Materials and Methods
### Description of the Optimization Methods  
To obtain the optimistic value of the ANFIS parameters, several optimization methods, including biogeography based optimization (BBO), cultural, invasive weeds optimization (IWO), and teaching learning-based optimization (TLBO) algorithms are used. A brief description of the optimization methods used in the present study is demonstrated as follows:  
* _Biogeography based optimization_  
[PERSON] [51] proposed the mathematical expression of migration behavior between species in different habitats for solving optimization problems. He employed two indices named Habitat-Suitability Index (HSI) and Suitability Index Variables (SIV). The HSI denotes the quality of living conditions in a suitable habitat. The living condition is related to many factors such as climate conditions, natural sources and richness of food sources. The SIV measures the suitability of living in a specific habitat utilizing several stated factors. The roulette wheel selection concept is used to enhance the quality of habitats with low living conditions. The basis of procedure in Biogeography based optimization (BBO) model is iterative computation. In each iteration, the fitness function is measured until the best solution with appropriate convergence is achieved, and then the computation procedure is terminated. * _Cultural algorithm_  
[PERSON] and [PERSON] [52] proposed the cultural algorithm for solving non-linear problems. This algorithm includes two main search spaces as (i) population space, and (ii) belief space. The population space is similar to genetic algorithm procedure, while belief space depends on the culture of a specific population. The belief space simulates the knowledge about the culture of the population. In this space, the overall experiences from successful members are saved and will be transferred to the next generations. The belief space includes two types of knowledge as: (i) situational knowledge and (ii) normative knowledge. The belief and population spaces interact with each other through a pre-defined protocol. In this way, a mechanism is adopted to regenerate the population space based on cultures governed in belief space. For selecting a group to make belief space, the acceptance function is defined to choose the qualified members for new generations. Then, the influence function makes the belief of a total population similar to the one for solving the problem. * _Invasive weeds optimization_  
Invasive weeds optimization (IWO) method was introduced by [PERSON] and [PERSON] [53] for solving engineering problems. This method employs the mechanism of generating weeds colonies and exploring appropriate position for growth. This method contains four main functions as follows:  
* Generating primary population function: the seeds which are also named as prime solutions are dispersed randomly in search space for finding a fitting solution to tackle problems. * Reproduction function: the IWO employs the minimum and maximum quantity of weeds colony objective functions. * Spatial dispersal function: the primary duty of this function is to provide randomness in the model. This function helps to spread the seed around parental plants. In each iteration, this function measures the standard deviation of new produced results. Competitive exclusion function: the main task of this function is to increase the chance of surviving for weak plants which contain a low level of fitness function. In this regard, after reaching to maximum number of population, the members of colonies are sorted, and colonies with the highest number of the population are selected for further calculations in the next iteration. _Teaching Learning Based Optimization_  
[PERSON] et al., [54] proposed teaching learning based optimization (TLBO) algorithm based on the interaction among learners and teachers in a classroom. This method contains two significant stages: \"teacher stage\" and \"learner stage\". In the first stage, the teacher attempts to enhance learner grades. In the next stage.