Purpose The purpose of this paper is to focus on the implementation and management of multi‐objective optimizations, with the help of heuristic algorithms such as space mapping methods. Design/methodology/approach The authors consider the design of electromechanical actuators by the use of mathematical and computer means. Experiments are then virtual, because they correspond to numerical simulations. Dimensioning is then ensured by an optimization procedure of the space mapping type, whose main characteristic consists in using two models of the same size actuator (instead of a single one for classical optimization methods). Moreover, one considers here that multiple outputs are defined: this defines a multi‐objective optimization. This paper proposes several techniques making it possible to include the definition of multiple objectives to be fulfilled as part of an output space mapping optimization process. Findings The proposed approaches make it possible to stabilize and accelerate the convergence of multi‐objective optimizations performed by space mapping. This is illustrated by the example of the dimensioning of a resonant linear electromagnetic actuator. Originality/value The approach presented in the paper is original because it allows finding of a solution to the multi‐objective problem, without building any Pareto front, and most effectively by improving the convergent behavior of the optimization algorithm.