Bayesian optimization for mixed variables using an adaptive dimension reduction process: applications to aircraft design

Multidisciplinary design optimization methods aim at adapting numerical optimization
techniques to the design of engineering systems involving multiple disciplines. In this context,
a large number of mixed continuous, integer and categorical variables might arise during the
optimization process and practical applications involve a large number of design variables. Recently, there has been a growing interest in mixed variables constrained Bayesian optimization
but most existing approaches severely increase the number of the hyperparameters related
to the surrogate model. In this paper, we address this issue by constructing surrogate mod-
els using less hyperparameters. The reduction process is based on the partial least squares
method. An adaptive procedure for choosing the number of hyperparameters is proposed.
The performance of the proposed approach is confirmed on analytical tests as well as two real
applications related to aircraft design. A significant improvement is obtained compared to
genetic algorithms.