Black-box Mixed-Variable Optimisation using a Surrogate Model that Satisfies Integer Constraints

A challenging problem in both engineering and computer science is that of minimising a function for which we have no mathematical formulation available, that is expensive to evaluate, and that contains continuous and integer variables, for example in automatic algorithm configuration. Surrogate modelling techniques are very suitable for this type of problem, but most existing techniques are designed with only continuous or only discrete variables in mind. Mixed-Variable ReLU-based Surrogate Modelling (MVRSM) is a surrogate modelling algorithm that uses a linear combination of rectified linear units, defined in such a way that (local) optima satisfy the integer constraints. This method is both more accurate and more efficient than the state of the art on several benchmarks with up to 238 continuous and integer variables.