Multidisciplinary Design Optimization (MDO) methods aim at adapting numerical optimization techniques to the design of engineering systems involving multiple disciplines or components. Among MDO architectures, various ones are considering the resolution of the Multidisciplinary Design Analysis (MDA). In our study, the system of interest being an aircraft, the resolution of the MDA will be provided by the Future Aircraft Sizing Tool with Overall Aircraft Design (FAST-OAD), a point mass approach that estimates the required fuel and energy consumption for a given set of top-level aircraft requirements. In this context, a large number of mixed continuous, integer and categorical variables that arise from aircraft design has to be tackled by the optimization process. Recently, there has been a growing interest in mixed variables constrained Bayesian optimization based on Gaussian process surrogate models. In this setting, most existing approaches severely increase the dimension of the covariance matrix related to the surrogate. In fact, the construction of the Gaussian process model may not be scalable to practical applications involving a large number of mixed variables. In this paper, we address this issue by constructing a covariance kernel for the surrogate model that depends on only a few hyperparameters. The new kernel is constructed based on the information obtained from the partial least squares method. The obtained numerical results lead to interesting results for the optimization of a baseline aircraft and to reduce the fuel consumption of "DRAGON", a new hybrid electric propulsion aircraft, with a high number of mixed variables and for a small budget of time-consuming evaluations.