## 1 Introduction  
Soil bearing capacity is one of the most crucial engineering parameters which needs to be meticulously investigated before any construction action [1, 2]. Thus, having an accurate approximation of the bearing capacity is a very important prerequisite of many geotechnical engineering projects as it is a function of various soil characteristics [3]. The ultimate applicable stress (\(F_{\mathit{tilt}}\)) is obtained based on the maximum settlement ratio, which is 0.1 of the footing width [4, 5]. In this regard, many scholars investigated or introduced relationships to give the \(F_{\mathit{tilt}}\)[6, 7]. [PERSON] and [PERSON] [8] used the stress characteristic lines method for forecasting the static bearing capacity of strip footing installed on two-layered soils. Up to now, different numerical and analytical approaches were utilized to analyze the bearing capacity [9, 10, 11]. However, as a matter of fact, traditional methods and laboratory approaches are not applicable without spending a huge amount of time and money. On the other hand, due to the high competency of artificial intelligence techniques in different engineering applications, they can be used as inexpensive yet accurate models for estimating geotechnical parameters like bearing capacity. The advent of soft computing approaches provided proper accurate models such as artificial neural network (ANN), adaptive neuro-fuzzy inference system (ANFIS), etc. for numerous engineering calculations with a focus on estimation tasks. These models were also successfully used for bearing capacity analysis [12; 13; 14]. In this sense, [PERSON] et al. [15] employed three models of neuro-fuzzy, ANN, and fuzzy for predicting the ultimate bearing capacity of shallow foundations (on cohesionless soil). Their results showed the superiority of intelligent models to popular bearing capacity theories. Also, [PERSON] and [PERSON] [16] employed linear genetic programming to estimate the ultimate bearing capacity of shallow foundations resting on rock masses. Metaheuristic algorithms suggest potent solutions for several optimization problems. They are also used for optimizing the performance of well-known predictive models like the support vector machine (SVM), ANN, and ANFIS [17; 18; 19]. As for the application of metaheuristic algorithms in bearing capacity analysis, different algorithms were applied to enhance the accuracy of the mentioned models [2; 20; 21]. [PERSON] et al. [22] applied the biogeography-based optimization (BBO) algorithm to ANN and ANFIS for estimating the failure likelihood of shallow footings. The results showed that the used algorithm can increase the classification accuracy of the ANN (from 98.2% to 98.4%) and, more considerably, the ANFIS (from 97.6% to 98.5%). Likewise, [PERSON] et al. [23] compared the optimization capability of the dragonfly algorithm (DA) and Harris hawks optimization (HHO) in adjusting the computational parameters of the ANN. Their study revealed that both these algorithms can effectively handle the mentioned task. However, referring to the calculated values of area under the curve (AUC), the DA (AUC = 0.942 and error = 0.1171) performed more accurately than the HHO (AUC = 0.915 and error = 0.1350). According to the literature review, despite the broad application of popular metaheuristics (e.g., imperialist competition algorithm (ICA) and particle swarm optimization (PSO)) for bearing capacity analysis [2; 24; 25], there are still many unused techniques which might be more capable. Hence, the main focus of the present paper was to investigate the applicability of several metaheuristic algorithms, namely, whale optimization algorithm (WOA), league champion optimization (LCA), moth-flame optimization (MFO), and ant colony optimization (ACO), for optimizing the performance of the ANN to discover powerful models. The necessity of coupling these algorithms lies in some computational drawbacks [26; 27] of the ANN which can be prevailed through proper adjustment of the weights and biases.