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Bi-objective decision making in global optimization based on statistical models. (English) Zbl 1432.90128

The minimization of an objective function on a given subset of a finite-dimensional space is considered. The objective function is characterized as “expensive” and “black box”, which means that its values are unknown and modelled as random variables. Statistical models applied in the literature to such situations introduce a utility function depending of previous interations expressing in some way the utility of a current iteration and the obtained information is used to compute the next iteration. The authors propose to use directly mean values and standard deviations for establishing the iteration process. They use a bi-criterial problem based on an appropriate trade off between the mean values and standard deviations on each iteration. Both theoretical and numerical examples are presented to illustrate the general theory proposed in the paper.

MSC:

90C26 Nonconvex programming, global optimization

Software:

ParEGO
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References:

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