This research addresses, from a perspective of metaheuristic optimization, the problem regarding parametric estimation in single-phase transformers while considering voltage and current measures at the transformer terminals and weighing linear loads. Transformer parametric estimation is modeled as a nonlinear problem in order to minimize the mean square error between the calculated voltage and current variables and the measurements taken. The nonlinearities are associated with Kirchhoff’s first and second laws applied to the equivalent electrical circuit of the single-phase transformer. The nonlinear optimiza tion problem is solved by applying a metaheuristic optimization algorithm known as the generalized normal distribution optimizer (GNDO), which uses evolution rules that allow exploring and exploiting the solution space via the classical probability function based on normal distributions. Numerical results in three test transfomers of 20, 45, and 112,5 kVA demonstrate the effectiveness and robustness of the proposed GNDO approach when com pared to other optimizers reported in the literature, such as the crow search algorithm, the coyote optimization algorithm, and the exact solution of the nonlinear optimization model using the fmincon solver of the MATLAB software. All numerical simulations con firm the potential of the GNDO approach to deal with complex optimization problems in engineering and science with promising results and low computational effort.