Statistica Sinica 28 (2018), 671-692

SEQUENTIAL PARETO MINIMIZATION OF

PHYSICAL SYSTEMS USING CALIBRATED

COMPUTER SIMULATORS

Po-Hsu Allen Chen, Thomas J. Santner and Angela M. Dean

The Ohio State University

Abstract: This paper proposes a sequential design methodology for a combined physical system and computer simulator experiment having multiple outputs, in the setting where the goal is to find the Pareto Front and Set of the *means of the physical system outputs.* The methodology is based on a statistically-calibrated simulator. In this paper, the simulator is a computer implementation of a deterministic mathematical model of the physical system; it contains the same set of control(able) inputs as those used to represent the physical system, plus additional calibration inputs for adjusting the simulator output to better mimic the mean of the physical system. A minimax fitness function is proposed for guiding the sequential search for new vectors of control input settings when additional observations on the *physical system* are to be taken. Based on a Bayesian calibrated model, the update step maximizes the posterior expected minimax fitness function over untried control inputs. When additional runs of the *simulator* are to be taken, the control input settings are chosen as above; then calibration input settings are selected to minimize the sum, over the set of predicted output means, of the posterior mean squared prediction errors. Using the Hypervolume Indicator function to assess Pareto Front accuracy, the performance of the sequential procedure is evaluated using analytic test functions from the multiple-objective optimization literature.

Key words and phrases: Combined physical and simulator experiment, computer experiment, multiobjective optimization.