The main focus in designing pile foundations is the pile bearing capacity (PBC), influenced by various soil characteristics and foundation parameters. Piles play a crucial role in transferring structural loads to the ground. Accurate prediction of PBC is essential in geotechnical structure design. While, artificial neural networks have been used for this purpose, they have limitations, such as difficulties in finding global minima and slow convergence. Machine learning methods, promising for creating new models and algorithms, are favored over empirical approaches. This study utilizes Gaussian process regression (GPR) and employs meta heuristic optimizations, the Honey Badger algorithm, and the improved gray wolf optimizer (IGWO), for optimal results. A dataset of 231 samples from prior studies was compiled for a PBC predictive model employing soft computing techniques. Variables, including friction angle, cohesion, pile-soil friction angle, flap number, pile length, soil-specific weight, and pile area, were carefully chosen for comprehensive modeling. The GPIG model, amalgamating the GPR model with IGWO, emerged as the optimal predictor for PBC values based on the results. Notable R2 and RMSE\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\text{RMSE}}$$\end{document} values manifested this superiority during both the training and testing phases. Specifically, in the training phase, the GPIG model demonstrated exceptional performance with R2 and RMSE\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\text{RMSE}}$$\end{document} values of 0.996\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$0.996$$\end{document} and 118.7 KN, respectively. In the testing phase, the model continued to exhibit robust predictive capabilities, with R2 and RMSE\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\text{RMSE}}$$\end{document} values of 0.981\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$0.981$$\end{document} and 276.1 KN, respectively.
