Assessing the value of another cycle in Gaussian process surrogate-based optimization

Surrogate-based optimization (SBO) for engineering design, popular in the optimization of complex engineering systems (e.g., aerospace, automotive, oil industries), proceeds in design cycles. Each cycle consists of the analysis of a number designs, the fitting of a surrogate, optimization based on the surrogate, and exact analysis at the design obtained by the optimization. However, due to time and cost constraints, the design optimization is usually limited to a small number of cycles each with substantial number of simulations (short cycle SBO) and rarely allowed to proceed to convergence. This paper takes a first step towards establishing a statistically rigorous procedure for assessing the merit of investing in another cycle of analysis versus accepting the present best solution. The proposed approach assumes that the set of locations for the next cycle is given, and it relies on: (1) a covariance model obtained from available input/output data, (2) a Gaussian process-based surrogate model, and (3) the fact that the predictions in the next cycle are a realization of a Gaussian process with a covariance matrix and mean specified using (1) and (2). Its effectiveness was established using descriptive and inference statistical elements in the context of a well-known test function and the optimization of an alkali-surfactant-polymer flooding of petroleum reservoirs.