Optimal designed experiments using a Pareto front search for focused preference of multiple objectives

Finding a best designed experiment based on balancing several competing goodness measures of the design is becoming more important in many applications. The Pareto front approach allows the practitioner to understand trade-offs between alternatives and make more informed decisions. Efficient search for the front is a key to successful use and broad adoption of the method. A substantial computational improvement that conducts a more focused search when the experimenter has a focused a priori preference for the prioritizations of the multiple criteria is described. By utilizing a user-specified desirability function weight distribution for quantifying the preferences on different criteria, an algorithm to efficiently populate the desired portion of the front for two-criterion optimization is developed. Improvements over the full Pareto front search for completeness of the front in the region of interest, computational efficiency, and variation of the search are demonstrated with a screening design example where the objectives are precise model estimation and capability to protect against model mis-specification. Much of the existing literature focuses exclusively on finding the Pareto front, but does not offer strategies for making a choice of a best solution from the rich set of options identified on the front. A streamlined decision-making process with a set of tailored graphical tools to facilitate an informed and justifiable decision is described. The graphics incorporate a priori focused prioritization of the criteria, and hence are helpful to match decisions to design goals.