  This work proposes the integration of two new constraint-handling approaches
into the blackbox constrained multiobjective optimization algorithm
DMulti-MADS, an extension of the Mesh Adaptive Direct Search (MADS) algorithm
for single-objective constrained optimization. The constraints are aggregated
into a single constraint violation function which is used either in a two-phase
approach, where research of a feasible point is prioritized if not available
before improving the current solution set, or in a progressive barrier
approach, where any trial point whose constraint violation function values are
above a threshold are rejected. This threshold is progressively decreased along
the iterations. As in the single-objective case, it is proved that these two
variants generate feasible and/or infeasible sequences which converge either in
the feasible case to a set of local Pareto optimal points or in the infeasible
case to Clarke stationary points according to the constraint violation
function. Computational experiments show that these two approaches are
competitive with other state-of-the-art algorithms.
