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Real-world optimization problems may require time consuming and expensive measurements or simulations. Recently, the application of surrogate model-based approaches was extended from continuous to combinatorial spaces. This extension is based on the utilization of suitable distance measures such as Hamming or Swap Distance. In this work, such an extension is implemented for Kriging (Gaussian Process) models. Kriging provides a measure of uncertainty when determining predictions. This can be harnessed to calculate the Expected Improvement (EI) of a candidate solution. In continuous optimization, EI is used in the Efficient Global Optimization (EGO) approach to balance exploitation and exploration for expensive optimization problems. Employing the extended Kriging model, we show for the first time that EGO can successfully be applied to combinatorial optimization problems. We describe …