  Recently, there has been a growing interest for mixed-categorical meta-models
based on Gaussian process (GP) surrogates. In this setting, several existing
approaches use different strategies either by using continuous kernels (e.g.,
continuous relaxation and Gower distance based GP) or by using a direct
estimation of the correlation matrix. In this paper, we present a kernel-based
approach that extends continuous exponential kernels to handle
mixed-categorical variables. The proposed kernel leads to a new GP surrogate
that generalizes both the continuous relaxation and the Gower distance based GP
models. We demonstrate, on both analytical and engineering problems, that our
proposed GP model gives a higher likelihood and a smaller residual error than
the other kernel-based state-of-the-art models. Our method is available in the
open-source software SMT.
