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Abstract:
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This research is concerned with using calibrated simulators to optimize multiobjective functions in the sense of Pareto; conflicting multiobjective functions need not have a common optimizer. A sequential design methodology, based on a calibrated simulator, is proposed for determining the Pareto Front and Set of a multiple-output physical system. When additional physical observations can be taken sequentially, we propose a minimax improvement function to guide the search for the next vector of control input settings. Based on a Bayesian calibrated model, this method maximizes the posterior expected improvement function over untried control inputs. Alternatively, if the additional runs can only be made by using a computer simulator, the control input is chosen as above, and calibration parameters are selected to minimize the sum of the posterior mean square prediction errors. Using the Hypervolume Indicator function to assess Pareto Front accuracy, the sequential procedure is shown to perform well through examples from the multiobjective optimization literature.
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