We consider the solution of derivative-free optimization problems with continuous, integer, discrete and categorical variables in the context of costly black-box mixed-variable industrial problems. Our approach is based on NOMAD, an implementation of the mesh-adaptive direct-search method (MADS), supplemented with surrogate models and strategies in the local poll and global search steps. The surrogate models are radial basis function interpolations managed by the surrogate-assisted evolutionary software MINAMO developed at Cenaero. The proposed approach is validated on a collection of problems from the literature and we compare several surrogate-based strategies. In the general mixed-variable case, the results show that employing MINAMO as a surrogate-based strategy within NOMAD in the poll and search steps increases both robustness and efficiency when compared to MINAMO's surrogate-based evolutionary algorithm alone or to NOMAD. On problems with mixed-integer variables only, we also experiment with the specialized mixed-integer solver BONMIN instead of MINAMO's evolutionary algorithm in the search step. It turns out to be slightly more efficient and substantially more robust when high accuracy is required.
Published September 2017 , 29 pages