Expected improvement in efficient experimental design supported by a global optimizer

• We developed a new surrogate-based optimization algorithm for experimental design.
• The algorithm consists of a conventional infill-criterion and a global optimizer.
• Fewer experiments are required if using the newly developed experimental design.

To develop an efficient experimental design method for real process applications, the well-known expected improvement infill criterion, which is usually adopted in achieving the surrogate-based optimization, and the global optimizer DIRECT are combined as the core of the developed experimental method. The method iterates through initial experimental design, empirical modeling and model-based optimization to allocate informative experiments for the next iteration. Specifically, the Kriging regression is adopted as the surrogate model due to its demonstrated prediction accuracy and reliable prediction uncertainty. Adopting a suitable threshold value of the initial expected improvement during the optimization process, the experiments located by the global optimizer could accelerate the optimization process to reach the defined target. Three termination criterions for stopping the iterating process are proposed to meet the requirements of both the simulation optimization problems and the experimental systems. Three simulation test problems demonstrate the efficiency of the developed experimental design method.