Constrained blackbox optimization with the NOMAD solver on the COCO constrained test suite.

The context of this work is constrained blackbox optimization. It describes the mesh adaptive direct search (MADS) derivative-free optimization algorithm using the progressive barrier strategy to handle quantifiable and relaxable constraints. Through its implementation in the NOMAD solver, MADS is tested on the new bbob-constrained suite of analytical constrained problems from the COCO platform, and compared with the CMA-ES heuristic. Computational tests are illustrated with the postprocessing graphs from the COCO platform, as well as with data profiles, an established tool in the derivative-free optimization community, adapted here for the constrained case. The results illustrate that researchers must be very careful with the use of these tools, which are complementary and should ideally be used together. Their many variations may show different outcomes, and hence many graphs are necessary in order to provide the best overall view.