Towards single- and multiobjective Bayesian global optimization for mixed integer problems

Bayesian Global Optimization (BGO) is a very efficient technique to optimize expensive evaluation problems. However, the application domain is limited to continuous search spaces when using a BGO algorithm. To solve mixed integer problems with a BGO algorithm, this paper adapts the heterogeneous distance function to construct the Kriging models and applies these new Kriging models in Multi-objective Bayesian Global Optimization (MOBGO). The proposed mixed integer MOBGO algorithm and the traditional MOBGO algorithm are compared on three mixed integer multi-objective optimization problems (MOP), w.r.t. the mean value of the hypervolume (HV) and the related standard deviation.