Determination of the friction capacity of driven piles using three sophisticated search schemes

Proper approximation of friction capacity (FC) of driven piles is a noticeable issue in geotechnical engineering. Hence, the pivotal focus of the current research is on proposing reliable predictors for evaluating this parameter. Three artificial neural networks (ANNs) improved by firefly algorithm (FA), multi-tracker optimization algorithm (MTOA), and black hole algorithm (BHA) are used to estimate the FC when it is affected by four key factors, namely pile length, pile diameter, vertical effective stress, and undrained shear strength. Checking the optimization process of different population sizes revealed that the MTOA and BHA need the population twice as many as the FA does (400 vs. 200). The results showed that all three models can properly comprehend the association of FC to the mentioned parameters. According to the values of root mean square error (RMSE) as well as the coefficient of determination (R2) obtained in the prediction phase (6.9606 and 0.8827, 8.5411 and 0.8370, 6.0454 and 0.9194, respectively, for the FA-ANN, MTOA-ANN, and BHA-ANN), the BHA-ANN is more accurate than two other algorithms, however, the MTOA-ANN gained the largest accuracy of training. The suggested models proved the high efficiency of hybrid predictors and can be potential alternatives to experimental and traditional approaches.