From Expected Improvement to Investment Portfolio Improvement: Spreading the Risk in Kriging-Based Optimization

The increasing use of time-consuming simulations in the industry has spawned a growing interest in coupling optimization algorithms with fast-to-compute surrogate models. A major challenge in this approach is to select the approximated solutions to evaluate on the real problem. To address this, the Kriging meta-model offers both an estimate of the mean value and the standard error in an unknown point. This feature has been exploited in a number of so-called prescreening utility functions that seek to maximize the outcome of an expensive evaluation. The most widely used are the Probability of Improvement (PoI) and Expected Improvement (ExI) functions. This paper studies this challenge from an investment portfolio point-of-view. In short, the PoI favors low risk investments whereas the ExI promotes high risk investments. The paper introduces the investment portfolio improvement (IPI) approach as a strategy mixing the two extremes. The novel approach is applied to seven benchmark problems and two real world examples from the pump industry.