This talk addresses the problem of derivative-free global optimization of a real-valued function under multiple inequality constraints. Both the objective function and the constraint functions are assumed to be smooth, nonlinear, expensive-to-evaluate black-box functions. As a consequence, the number of evaluations that can be used to carry out the optimization is very limited. We focus in this work on the case of strongly constrained problems, where finding a feasible design, using such a limited budget of simulations, is a challenge in itself. The method that we propose to overcome this difficulty has its roots in the recent literature on Gaussian process-based methods for reliability analysis—in particular, the Bayesian Subset Simulation (BSS) algorithm of Li, Bect and Vazquez—and multi-objective optimization. More specifically, we consider a decreasing sequence of nested subsets of the design space, which is defined and explored sequentially using a combination of Sequential Monte Carlo (SMC) techniques and sequential Bayesian design of experiments. The proposed method obtains promising result on challenging test cases from the literature.