Surrogate-based optimization of distillation columns using an iterative Kriging approach is investigated. Focus is on deterministic global optimization to avoid suboptimal local minima. The determination of optimal setups and operating conditions for ideal and non-ideal distillation columns, leading to mixed-integer nonlinear programming (MINLP) problems, serve as case studies. It is found that the optimization using the adapted Kriging approach yields similar results compared to the direct global optimization of the original problem in the ideal case, while it leads to a huge improvement compared to a multistart local optimization approach in the non-ideal case.