<p>The primary objectives of this study are to propose a modified approach to monitor the strength of weld joints in the pulsed metal inert gas welding (P-MIG) process and give a novel contribution to available literature on model selection criteria. The focus is on achieving high ultimate tensile strength (UTS) by considering various welding parameters such as pulse voltage, background voltage, pulse duration, pulse frequency, wire feed rate, welding speed, and root mean square values of welding current and voltage. The study also examines the effects of these parameters on UTS by developing a mathematical model using a hybrid approach that combines artificial neural networks and regression, referred to as the multiple nonlinear neuro-regression method. Forty-seven different models, including linear, trigonometric, logarithmic, quadratic, and rational forms, are proposed to mathematically define the UTS behavior of mild steel plate. A stability analysis assessed the model’s ability to account for the welding process parameters during the modeling phase. This approach has not previously been employed as a criterion for model selection in prior modeling studies. Furthermore, the study includes modified versions of different optimization methods; differential evaluation, random search, simulated annealing, and the Nelder-Mead algorithm simultaneously. The results indicated that the different algorithms converged on the same design, which corresponds to the UTS of 499&#xa0;MPa. This represents a 7% increment compared to the value reported in the referenced study. Besides, four algorithms presented seven distinct alternative designs. The proposed neuro-regression methodology is expected to be highly effective in accurately defining complex engineering phenomena.</p>