Generating optimal designs with user‐specified pure replication structure

Abstract

Over recent decades, optimal experimental design has surged in popularity due to affordable computing and efficient algorithms. However, some researchers highlight that this focus has often side‐lined the importance of including pure experimental replication in designs, as many optimality criteria do not inherently suggest designs with replicates. In this study, we introduce an approach that allows the designer to input a desired replication structure into the optimal design search. We list all potential replication structures, indicate the corresponding budget for pure‐error (PE) and lack‐of‐fit (LOF) degrees‐of‐freedom, and use particle swarm optimization to search for the optimal design in each scenario. We demonstrate our approach on various unexplored ‐optimal design scenarios and several scenarios recently discussed in literature. Our findings reveal the existence of highly‐efficient ‐optimal designs with unique replication structures, offering designers informed choices on allocating a limited budget for PE and LOF degrees‐of‐freedom. This method is versatile and compatible with other optimizers, such as the coordinate exchange.