Generating designs for comparative experiments with two blocking factors

Often, comparative experiments involve a single treatment factor and two blocking factors, for example, augmented row–column, two-phase, and incomplete row–column experiments. These experiments are widely used in agriculture. Finding good designs for these experiments is a major challenge when the number of treatments is large and the blocking structure is complex. In this paper, we first propose a new search algorithm that is combined with efficient update formulae, so that optimal designs with two blocking factors can be found within a reasonable time. Second, we compare augmented row–column designs generated with our new method to those obtained from CycDesigN, DiGGer, and the OPTEX procedure of SAS in terms of computing times as well as the quality of solutions. Third, we illustrate our proposed approach with four applications. We show an example where our efficient update formulae work while existing update formulae cannot be applied, and we use our search framework to generate augmented row–column, two-phase, and incomplete row–column designs. We end the paper with a conclusion along with suggestions for potential applications.