Balancing Multiple Criteria Incorporating Cost using Pareto Front Optimization for Split-Plot Designed Experiments

Finding a D‐optimal design for a split‐plot experiment requires knowledge of the relative size of the whole plot (WP) and sub‐plot error variances. Since this information is typically not known a priori, we propose an optimization strategy based on balancing performance across a range of plausible variance ratios. This approach provides protection against selecting a design which could be sub‐optimal if a single initial guess is incorrect. In addition, options for incorporating experimental cost into design selection are explored. The method uses Pareto front multiple criteria optimization to balance these objectives and allows the experimenter to understand the trade‐offs between several design choices and select one that best suits the goals of the experiment. We present new algorithms for populating the Pareto front for the split‐plot situation when the number of WPs is either fixed or flexible. We illustrate the method with a case study and demonstrate how considering robustness across variance ratios offers improved performance. The Pareto approach identifies multiple promising designs, and allows the experimenter to understand trade‐offs between alternatives and examining their robustness to different ways of combining the objectives. New graphical summaries for up to four criteria are developed to help guide improved decision‐making.