Simple Intuitive Multi-objective ParalLElization of Efficient Global Optimization: SIMPLE-EGO

Abstract

This paper describes how to parallelize the Efficient Global Optimization (EGO) algorithm, by making use of a simple multi-objective formulation. EGO constructs a Kriging approximation of the cost function, and then improves this approximation by adding additional designs to the initial designs. These aditional designs are added sequentially, one by one. In a specific iteration, the design is added where the Expected Improvement (EI) acquisition function is maximized. The EI function is typically maximized in the vicinity of the current best sampled point, or in a region that has large uncertainty. We demonstrate that instead of using the EI function, a multi-objective formulation can be used to decide where to add points. The two objectives that dictate where new designs should be sampled are function value, and uncertainty. The resulting Pareto front contains multiple designs that can be analyzed in parallel in the next iteration. Our study concludes with numerical examples.