Optimum loading paths for successful tube hydroforming processes have been studied by several researchers. In this paper, an adaptive, heuristic, nonlinear mathematical model (AHNM) was proposed to optimize the loading path of a hydroforming process through adaptive minimization of the internal pressure and axial load of the process. Firstly, Finite Element Analysis (FEA) was used to analyze the hydroforming process where several features of the process were extracted from the FEA for further analyses of the relations among them. To capture these relations and include them in the AHNM, the paper examined several Machine Learning algorithms including Multiple Linear Regression, Multiple Ridge Regression, Decision Tree, and Random Forest. The Multiple Ridge Regression was found to give the highest accuracy to efficiently linear modelling the inputs and outputs of the FEA of the hydroforming process. The AHNM model was implemented, solved, and optimized using several steps of tee protrusion height that create several loading paths. It was found that increasing the number of steps and starting with small increment leads to minimizing the system requirements.