Fractional universal kriging metamodel and simulation optimization

Although the kriging metamodels have been developed specifically as geological interpolation methods, they have been used successfully for deterministic simulation optimization (SO) problems since 1990s. Recently, kriging metamodels have been used in some studies for SO in stochastic systems. In this thesis, a fractional universal kriging (FUK) meta-model is proposed to model higher-order drift functions that the relation between input and output variables cannot always be defined by linear or quadratic drift functions meta-model. Based on modelling analysis and the comparison of results, the proposed "FUK metamodel" gives a better quality estimation than the ordinary kriging (OK) and universal kriging (UK) metamodels according to the mean squared error and maximum squared error for the most of the considered test problems. On the basis of these results, it is proposed to use FUK metamodels instead of simulation models of complex system. In addition, the proposed FUK metamodel was applied to the message routing problem and produced a better estimate than the OK metamodel.