This thesis focuses on the simultaneous optimization of expensive-to-evaluate functions that depend on a high number of parameters. This situation is frequently encountered in fields such as design engineering through numerical simulation. Bayesian optimization relying on surrogate models (Gaussian Processes) is particularly adapted to this context.The first part of this thesis is devoted to the development of new surrogate-assisted multi-objective optimization methods. To improve the attainment of Pareto optimal solutions, an infill criterion is tailored to direct the search towards a user-desired region of the objective space or, in its absence, towards the Pareto front center introduced in our work. Besides targeting a well-chosen part of the Pareto front, the method also considers the optimization budget in order to provide an as wide as possible range of optimal solutions in the limit of the available resources.Next, inspired by shape optimization problems, an optimization method with dimension reduction is proposed to tackle the curse of dimensionality. The approach hinges on the construction of hierarchized problem-related auxiliary variables that can describe all candidates globally, through a principal component analysis of potential solutions. Few of these variables suffice to approach any solution, and the most influential ones are selected and prioritized inside an additive Gaussian Process. This variable categorization is then further exploited in the Bayesian optimization algorithm which operates in reduced dimension.