A batch infill strategy for computationally expensive optimization problems

Abstract

Efficient Global Optimization (EGO) is a well established iterative scheme for solving computationally expensive optimization problems. EGO relies on an underlying Kriging model and maximizes the expected improvement (EI) function to obtain an infill (sampling) location. The Kriging model is in turn updated with this new truly eval- uated solution and the process continues until the termination condition is met. The serial nature of the process limits its efficiency for applica- tions where a batch of solutions can be evaluated at the same cost as a single solution. Examples of such cases include physical experiments conducted in batches for drug design and material synthesis, and com- putational analyses executed on parallel infrastructure. In this paper we present a multi-objective formulation to deal with such classes of prob- lems, wherein instead of a single solution, a batch of solutions are iden- tified for concurrent evaluation. The strategies use different objectives depending on the archive of the evaluated solutions. The performance the proposed approach is studied on a number of unconstrained and con- strained benchmarks and compared with contemporary MO formulation based approaches to demonstrate its competence.