# Novel Nature-Inspired Hybrids of Neural Computing for Estimating Soil Shear Strength
## 4 Results and Discussion
### Optimizing the ANN Using DA, WOA, and IWO  
An MLP neural network is selected to represent the basic network of this study. Although the literature review shows the high capability of the ANN for estimating various scientific phenomena, utilizing these models has been associated with some computational drawbacks such as getting trapped in local minima. Hence, the aforementioned optimization techniques are employed to overcome these shortcomings.  
To this end, a trial and error process was first carried out in MATLAB 2014 environment to determine the most efficient architecture of the ANN. Although an MLP could contain several hidden layers, many previous studies have shown the adequacy of one of it for predicting any complex problem [33; 34]. The results showed that the MLP with five hidden nodes presents the lowest error of performance. Note that based on the input and output parameters, the proposed ANN had 12 and 1 nodes in the first and last layer, respectively. Next, the ANN was mathematically introduced to each one of the DA, WOA, and IWO to achieve the most appropriate computational weights and biases. Each model was performed within 1000 repetitions to optimize the ANN. Note that the _RMSE_ criterion was considered as the objective function to measure the error at each iteration. Based on the population size, nine different complexities (i.e., population sizes of 10, 25, 50, 75, 100, 200, 300, 400, and 500) were tested for each ensemble. Note that the populations size is a common variable in metaheuristic algorithms that denotes the size of the involved individuals (e.g., the whale population in the WOA technique). Figure 7a-c depicts the convergence curves for each structure of the used models. Besides populations size, there are other influential parameters for some of the optimization algorithms [35; 36; 37; 38; 39]. In this work, after determining the best complexity, a trial-and-error process was executed to optimize these parameters. Based on the results, the WOA with an intensification factor = 1, and the IWO with a variance reduction exponent = 2, initial value of standard deviation = 0.5, and final value of standard deviation = 0.001 build the most powerful networks.  
As is seen, each ensemble shows different convergence behavior. All of the DA-ANN networks, for example, needed 500 repetitions at maximum to minimize the error. This is while the majority of the objective function was reduced during the first 200 repetitions and has remained more or less steady after that for the WOA-ANN. In addition, the IWO-ANN kept minimizing the error until the last moment as the curves have a downward trend. Eventually, all three models presented the best performance by the population size = 400. The obtained _RMSE_ for the DA-ANN, WOA-ANN, and IWO-ANN were 0.02725, 0.02382, and 0.02225, respectively. It denotes that the IWO performed more efficiently than two other algorithms in optimizing the ANN.  
Moreover, the required time for implementing the models is examined. Since the computation time of the typical ANN is considerably shorter than its improved versions, this parameter is discussed only for the ensemble models, due to the higher accuracy of them. Figure 8 illustrates the obtained _RMSE_  
Figure 7: Executed sensitivity analysis for the (**a**) DA-ANN, (**b**) WOA-ANN, and (**c**) IWO-ANN. ANN: artificial neural network, IWO: invasive weed optimization, WOA: whale optimization algorithm.  
versus the taken computation time. According to this diagram, on the operating system at 2.5 GHz and six gigs of RAM, the implementation of the models required 13,859.2, 5884.9, and 5043.6 s, respectively.