  Due to the increasing demand for high performance and cost reduction within
the framework of complex system design, numerical optimization of
computationally costly problems is an increasingly popular topic in most
engineering fields. In this paper, several variants of the Efficient Global
Optimization algorithm for costly constrained problems depending simultaneously
on continuous decision variables as well as on quantitative and/or qualitative
discrete design parameters are proposed. The adaptation that is considered is
based on a redefinition of the Gaussian Process kernel as a product between the
standard continuous kernel and a second kernel representing the covariance
between the discrete variable values. Several parameterizations of this
discrete kernel, with their respective strengths and weaknesses, are discussed
in this paper. The novel algorithms are tested on a number of analytical
test-cases and an aerospace related design problem, and it is shown that they
require fewer function evaluations in order to converge towards the
neighborhoods of the problem optima when compared to more commonly used
optimization algorithms.
