This paper presents a multi-objective design optimization of a power transformer to find the optimal geometry of its core and the low- and high-voltage windings, representing the minimum power losses and the minimum core and copper weights. The optimal design is important because it allows manufacturers to build more efficient and economical transformers. The approach employs a manufacturer’s design methodology, which is based on the usage of the laws of physics and leads to an analytical transformer model with the advantage of requiring a low amount of computing time. Afterward, the multi-objective design optimization is defined along with its constraints, and they are solved using the Non-Sorting Genetic Algorithm III (NSGA-III), which finds a set of optimal solutions. Once an optimal solution is selected from the Pareto front, it is necessary to fine-tune it with the 3D Finite Element Analysis (FEA). To avoid the large computing times needed to carry out the 3D Finite Element (FE) model simulations used in multi-objective design optimization, Response Surface Methodology (RSM) polynomial models are developed using 3D FE model transformer simulations. Finally, a second multi-objective design optimization is carried out using the developed RSM empirical models that represent the cost functions and is solved using the NSGA-III. The numerical results of the optimal core and windings geometries demonstrate the validity of the proposed design methodology based on the NSGA-III. The used global optimizer has the feature of solving optimization problems with many cost functions, but it has not been applied to the design of transformers. The results obtained in this paper demonstrate better performance and accuracy with respect to the commonly used NSGA-II.