On the implementation of a global optimization method for mixed-variable problems

An optimization problem without any structural information on the objective function or the constraints, but for which we have the ability to evaluate them at given points, is called a black-box problem. The area of derivativefree optimization is dedicated to the study of optimization algorithms that do not rely on computing the partial derivatives of the objective function, and it is naturally applied to black-box problems. Many optimization problems in engineering are solved by treating them as a black box, for two main reasons: first, the objective function may not be known in an explicit form, e.g., when it is the output of a complex computer simulation; second, even if derivatives may exist and be computable, the effort required may make it impractical, or the low accuracy of their computation may make them unreliable. This paper discusses the implementation of a global derivative-free optimization algorithm that is specifically aimed at black-box problems with expensive objective function evaluations.