Time complexity reduction in efficient global optimization using cluster kriging

Hao Wang, Bas van Stein, Michael T. M. Emmerich, Thomas Bäck

Abstract: Efficient Global Optimization (EGO) is an effective method to optimize expensive black-box functions and utilizes Kriging models (or Gaussian process regression) trained on a relatively small design data set. In real-world applications, such as experimental optimization, where a large data set is available, the EGO algorithm becomes computationally infeasible due to the time and space complexity of Kriging. Recently, the so-called Cluster Kriging methods have been proposed to reduce such complexities for the big data, where data sets are clustered and Kriging models are built on each cluster. Furthermore, Kriging models are combined in an optimal way for the prediction. In addition, we analyze the Cluster Kriging landscape to adopt the existing infill-criteria, e.g., the expected improvement. The approach is tested on selected global optimization problems. It is shown by the empirical studies that this approach significantly reduces the CPU time of the EGO algorithm while maintaining the convergence rate of the algorithm.