  Multi-objective optimization aims at finding trade-off solutions to
conflicting objectives. These constitute the Pareto optimal set. In the context
of expensive-to-evaluate functions, it is impossible and often non-informative
to look for the entire set. As an end-user would typically prefer a certain
part of the objective space, we modify the Bayesian multi-objective
optimization algorithm which uses Gaussian Processes to maximize the Expected
Hypervolume Improvement, to focus the search in the preferred region. The
cumulated effects of the Gaussian Processes and the targeting strategy lead to
a particularly efficient convergence to the desired part of the Pareto set. To
take advantage of parallel computing, a multi-point extension of the targeting
criterion is proposed and analyzed.
