Simulation optimization using stochastic kriging with robust statistics

Abstract

Metamodels are widely used as fast surrogates to facilitate the optimization of simulation models. Stochastic kriging (SK) is an effective metamodeling tool for a mean response surface implied by stochastic simulation. In SK, it is usually assumed that the experimental data are normally distributed and uncontaminated. However, these assumptions can be easily violated in many practical applications. This paper proposes a new type of SK for simulation models that may have non-Gaussian responses; this new SK uses robust estimators of location (or central tendency) and scale (or variability) that are well-known in the literature on robust statistics. Statistical properties of the robust estimators used in this paper are briefly analyzed and the performances of the proposed methods are compared through numerical examples of different features. The comparison results show that the proposed robust SK with the robust estimators is quite efficient, no matter whether the standard assumptions hold or not.

Keywords:

• Simulation
• stochastic kriging
• contamination
• model departure
• outlier-resistance

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

This work of Professor Ma was supported by the National Natural Science Foundation of China under grant NSFC–71931006. The work of Professor Ouyang was supported by the National Natural Science Foundation of China under grants NSFC–72072089, 71702072, 11901299 and the Qing Lan Project, the China Postdoctoral Science Foundation under grant 2019T120429. The work of Professor Han was supported by the National Natural Science Foundation of China under grant NSFC–71902089. The work of Professor Park was supported under the framework of the international cooperation program managed by the National Research Foundation of Korea (2018K2A9A2A06019662).