Optimization of expensive black-box problems with penalized expected improvement

This paper proposes a new infill criterion for the optimization of expensive black-box design problems. The method complements the classical Efficient Global Optimization algorithm by considering the distribution of improvement instead of merely the expectation. During the optimization process, we maximize a penalized expected improvement acquisition function from a specially collected infill candidate set. Specifically, the acquisition function is formulated by penalizing the expected improvement with the variation of improvement, and the infill candidate set is composed of some global and local maxima of the expected improvement function which are identified to be “mutually non-dominated”. Some conditions necessary for setting the penalty coefficient of the acquisition function are investigated, and the definition of “mutually non-dominated infill candidates” is presented. The proposed method is demonstrated with a 1-D analytical function and benchmarked using six 10-D analytical functions and an underwater vehicle structural optimization problem. The results show that the proposed method is efficient for the optimization of expensive black-box design problems.