Multiobjective optimization of expensive-to-evaluate deterministic computer simulator models

Many engineering design optimization problems contain multiple objective functions all of which are desired to be minimized, say. This paper proposes a method for identifying the Pareto Front and the Pareto Set of the objective functions when these functions are evaluated by expensive-to-evaluate deterministic computer simulators. The method replaces the expensive function evaluations by a rapidly computable approximator based on a Gaussian process (GP) interpolator. It sequentially selects new input sites guided by values of an “improvement function” given the current data. The method introduced in this paper provides two advances in the interpolator/improvement framework. First, it proposes an improvement function based on the “modified maximin fitness function” which is known to identify well-spaced non-dominated outputs when used in multiobjective evolutionary algorithms. Second, it uses a family of GP models that allows for dependence among output function values but which permits zero covariance should the data be consistent with this model. A closed-form expression is derived for the improvement function when there are two objective functions; simulation is used to evaluate it when there are three or more objectives. Examples from the multiobjective optimization literature are presented to show that the proposed procedure can improve substantially previously proposed statistical improvement criteria for the computationally intensive multiobjective optimization setting.