A Gaussian-process surrogate model based on already acquired data is employed to approximate an unknown target surface. In order to optimally locate the next function evaluations in parameter space a whole variety of utility functions are at one's disposal. However, good choice of a specific utility or a certain combination of them prepares the fastest way to determine a best surrogate surface or its extremum for lowest amount of additional data possible. In this paper, we propose to consider

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... e global (integrated) variance as an utility function, i.e., to integrate the variance of the surrogate over a finite volume in parameter space. It turns out that this utility not only complements the tool set for fine tuning investigations in a region of interest but expedites the optimization procedure in toto.