Optimization of Designed Experiments Based on Multiple Criteria Utilizing a Pareto Frontier

Balancing competing objectives to select an optimal design of experiments involves flexibly combining measures to select a winner. The Pareto front approach for simultaneously considering multiple responses is adapted to design of experiments. The Pareto approach identifies a suite of potential best designs based on different emphases of the objectives. We propose a new algorithm, the Pareto Aggregating Point Exchange (PAPE) algorithm, to more efficiently explore candidate designs by populating the Pareto frontier with all possible contending designs identified during the search. The connection between the Pareto and the Derringer-Suich (1980) desirability function approaches is established and graphical methods are given which enable the user to easily explore design robustness to different weightings of the competing objectives as well as trade-offs between criteria among competing designs. The method is illustrated with two examples: a screening design setting in which it is of interest to simultaneously consider D-efficiency and protect against model misspecification, and a robust parameter design example where simultaneous consideration of D-S-mean, D-S-variance, and design size is of interest. This article has supplementary material online.