A multi-objective batch infill strategy for efficient global optimization

High-fidelity simulations and/or physical experiments are often required to evaluate performance of products and processes. Although accurate, they are often time consuming and/or costly, which makes it prohibitive to use them within a global optimization framework. To deal with this issue, Surrogate Assisted Optimization (SAO) approaches have been commonly used in literature. Efficient Global Optimization (EGO) is one such approach which relies on Kriging model and maximizes the expected improvement to identify the best location for sampling. Most EGO approaches studied in the literature sample one point at a time. However, this approach is inefficient for the cases when it is possible to evaluate a batch of solutions at the same cost as a single solution. This might happen for example, when a number of physical samples could be tested in an experimental setup simultaneously, or a number of simulations could be run in parallel on a cluster. This study presents an approach to sample multiple locations at each iteration. To achieve this, a multi-objective (MO) formulation is proposed and solved which considers maximization of expected improvement and maximization of distance from existing truly evaluated solutions. A decomposition based approach is then used to sample the infill solutions from the resulting non-dominated front. Numerical experiments are presented on ten well known benchmarks and a comparison is done with existing methods to demonstrate the efficacy of the proposed approach. The results obtained for constrained optimization problems are particularly encouraging.