High step-up converters have been widely used in renewable energy systems and, recently, in automotive applications, due to their high voltage gain capability. In these applications, efficiency and high-power density are usually required, although these characteristics are commonly opposite objectives. Therefore, a multi-objective optimization is quite useful in order to comply with both requirements of high efficiency and small size. In that sense, the Finite Element Method can be effective to complement optimization methods. This paper presents a procedure to optimize the efficiency and the volume of a high step-up converter that utilizes a coupled inductor with three windings installed in only one core. This optimization procedure is carried out using 3D and 2D Finite Element Method simulations. In this procedure, a complete modeling of power losses, size, and flux density is evaluated by comparing different materials and dimensions. The results of this modeling stage are introduced into a multi-objective optimization algorithm to obtain a Pareto front. Finally, the optimization methodology is validated by experimental tests.