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Complex engineering design problems, such as those involved in aerospace,civil, or energy engineering, require the use of numerically costly simulationcodes in order to predict the behavior and performance of the system to bedesigned. To perform the design of the systems, these codes are often embeddedinto an optimization process to provide the best design while satisfying thedesign constraints. Recently, new approaches, called Quality-Diversity, havebeen proposed in order to enhance the exploration of the design space and toprovide a set of optimal diversified solutions with respect to some featurefunctions. These functions are interesting to assess trade-offs. Furthermore,complex engineering design problems often involve mixed continuous, discrete,and categorical design variables allowing to take into account technologicalchoices in the optimization problem. In this paper, a new Quality-Diversitymethodology based on mixed continuous, discrete and categorical Bayesianoptimization strategy is proposed. This approach allows to reduce thecomputational cost with respect to classical Quality - Diversity approacheswhile dealing with discrete choices and constraints. The performance of theproposed method is assessed on a benchmark of analytical problems as well as onan industrial design optimization problem dealing with aerospace systems.

Bayesian Quality-Diversity approaches for constrained optimization problems with mixed continuous, discrete and categorical variables