The class of Mesh Adaptive Direct Search (MADS) algorithms is designed for the optimization of constrained black-box problems. The purpose of this paper is to compare instantiations of MADS under different strategies to handle constraints. Intensive numerical tests are conducted from feasible and/or infeasible starting points on three real engineering applications.

The three instantiations are GPS, LTMADS, and ORTHOMADS. Constraints are handled by the extreme barrier, the progressive barrier, or by a mixture of both. The applications are the optimization of a styrene production process, a MDO mechanical engineering problem, and a well positioning problem, and the codes are publicly available.