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 Ds-mean, Ds-variance, and design size is of interest. This article has supplementary material online.

[1]  Charles G. Pfeifer.  Experiments with Mixtures: Design, Models, and the Analysis of Mixture Data , 1983 .

[2]  Lothar Thiele,et al.  An evolutionary algorithm for multiobjective optimization: the strength Pareto approach , 1998 .

[3]  G. Derringer,et al.  Simultaneous Optimization of Several Response Variables , 1980 .

[4]  M H Nathanson,et al.  Multiple-objective criteria for optimal experimental design: application to ferrokinetics. , 1985, The American journal of physiology.

[5]  Peter J. Fleming,et al.  Genetic Algorithms for Multiobjective Optimization: FormulationDiscussion and Generalization , 1993, ICGA.

[6]  Connie M. Borror,et al.  Robust Parameter Design: A Review , 2004 .

[7]  Douglas C. Montgomery,et al.  A Nonlinear Programming Solution to the Dual Response Problem , 1993 .

[8]  M.A. El-Sharkawi,et al.  Pareto Multi Objective Optimization , 2005, Proceedings of the 13th International Conference on, Intelligent Systems Application to Power Systems.

[9]  Alan J. Miller,et al.  A review of some exchange algorithms for constructing discrete D-optimal designs , 1992 .

[10]  Wolfram Gronwald,et al.  Evolutionary Pareto-optimization of stably folding peptides , 2008, BMC Bioinformatics.

[11]  David M. Steinberg,et al.  Comparison of designs for computer experiments , 2006 .

[12]  W. DuMouchel,et al.  A simple Bayesian modification of D-optimal designs to reduce dependence on an assumed model , 1994 .

[13]  Connie M. Borror,et al.  Model-Robust Optimal Designs: A Genetic Algorithm Approach , 2004 .

[14]  Douglas C. Montgomery,et al.  Modified Desirability Functions for Multiple Response Optimization , 1996 .

[15]  Hiroaki Ishii,et al.  Simultaneous optimization of several response variables in experimental design , 2009 .

[16]  H. Trautmann,et al.  Preference-based Pareto optimization in certain and noisy environments , 2009 .

[17]  Connie M. Borror,et al.  Graphical Tools for Assessing the Sensitivity of Response Surface Designs to Model Misspecification , 2009, Technometrics.

[18]  R. D. Cook,et al.  A Comparison of Algorithms for Constructing Exact D-Optimal Designs , 1980 .

[19]  R. Romero-Villafranca,et al.  Ds-optimal experimental plans for robust parameter design , 2007 .

[20]  Jasbir S. Arora,et al.  Survey of multi-objective optimization methods for engineering , 2004 .

[21]  C. D. Gelatt,et al.  Optimization by Simulated Annealing , 1983, Science.

[22]  Christine M. Anderson-Cook,et al.  A Closer Look at D-Optimality for Screening Designs , 2010 .

[23]  Theodore T. Allen,et al.  An experimental design criterion for minimizing meta‐model prediction errors applied to die casting process design , 2003 .

[24]  John H. Holland,et al.  Adaptation in Natural and Artificial Systems: An Introductory Analysis with Applications to Biology, Control, and Artificial Intelligence , 1992 .

[25]  David E. Goldberg,et al.  A niched Pareto genetic algorithm for multiobjective optimization , 1994, Proceedings of the First IEEE Conference on Evolutionary Computation. IEEE World Congress on Computational Intelligence.

[26]  Kalyanmoy Deb,et al.  MULTI-OBJECTIVE FUNCTION OPTIMIZATION USING NON-DOMINATED SORTING GENETIC ALGORITHMS , 1994 .

[27]  Kalyanmoy Deb,et al.  Muiltiobjective Optimization Using Nondominated Sorting in Genetic Algorithms , 1994, Evolutionary Computation.

[28]  V. Torczon,et al.  Direct search methods: then and now , 2000 .

[29]  K. Lewis,et al.  Pareto analysis in multiobjective optimization using the collinearity theorem and scaling method , 2001 .

[30]  N. Draper,et al.  Treating bias as variance for experimental design purposes , 1992 .

[31]  G. Box,et al.  A Basis for the Selection of a Response Surface Design , 1959 .

[32]  Christopher J. Nachtsheim,et al.  A Class of Three-Level Designs for Definitive Screening in the Presence of Second-Order Effects , 2011 .