Response surface optimization for a nonlinearly constrained irregular experimental design space

References

• Aspenberg, D., J. Jergeus, and L. Nilsson. 2013. “Robust Optimization of Front Members in a Full Frontal Car Impact.” Engineering Optimization 45 (3): 245–264.
   Web of Science ®Google Scholar
• Bandaru, S., and K. Deb. 2011. “Towards Automating the Discovery of Certain Innovative Design Principles Through a Clustering-Based Optimization Technique.” Engineering Optimization 43 (9): 911–941.
   Web of Science ®Google Scholar
• Bruggi, M., and S. Mariani. 2013. “Optimization of Sensor Placement to Detect Damage in Flexible Plates.” Engineering Optimization 45 (6): 659–676.
   Web of Science ®Google Scholar
• Cook, D., and V. Fedorov. 1995. “Invited Discussion Paper Constrained Optimization of Experimental Design.” Statistics 26 (2): 129–148.
   Web of Science ®Google Scholar
• Cook, R. D., and C. J. Nachtsheim. 1980. “A Comparison of Algorithms for Constructing Exact D-Optimal Designs.” Technometrics 22 (3): 315–324.
   Web of Science ®Google Scholar
• de Aguiar, P. F., B. Bourguignon, M. S. Khots, D. L. Massart, and R. Phan-Than-Luu. 1995. “D-Optimal Designs.” Chemometrics and Intelligent Laboratory Systems 30 (2): 199–210.
   Web of Science ®Google Scholar
• DuMouchel, W., and B. Jones. 1994. “A Simple Bayesian Modification of D-Optimal Designs to Reduce Dependence on an Assumed Model.” Technometrics 36 (1): 37–47.
   Web of Science ®Google Scholar
• Dykstra, O. 1971. “The Augmentation of Experimental Data to Maximize [X′X].” Technometrics 13 (1): 682–688.
   Google Scholar
• Fedorov, V. V. 1972. Theory of Optimal Experiments. New York: Academic Press.
   Google Scholar
• Fedorov, V. V., R. C. Gagnon, and S. L. Leonov. 2002. “Design of Experiments with Unknown Parameters in Variance.” Applied Stochastic Models in Business and Industry 18 (3): 207–218.
   Web of Science ®Google Scholar
• Harman, R., and L. Pronzato. 2007. “Improvements on Removing Nonoptimal Support Points in D-Optimum Design Algorithms.” Statistics & Probability Letters 77 (1): 90–94.
   Web of Science ®Google Scholar
• Jin, R., W. Chen, and A. Sudjianto. 2005. “An Efficient Algorithm for Constructing Optimal Design of Computer Experiments.” Journal of Statistical Planning and Inference 134 (1): 268–287.
   Web of Science ®Google Scholar
• John, R. C. S., and N. R. Draper. 1975. “D-Optimality for Regression Designs: A Review.” Technometrics 17 (1): 15–23.
   Web of Science ®Google Scholar
• Khuri, A. I., and S. Mukhopadhyay. 2010. “Response Surface Methodology.” Wiley Interdisciplinary Reviews: Computational Statistics 2 (2): 128–149.
   Google Scholar
• Kiefer, J. 1959. “Optimum Experimental Designs.” Journal of the Royal Statistical Society: Series B (Methodological) 21: 272–304.
   Web of Science ®Google Scholar
• Kiefer, J., and J. Wolfowitz. 1959. “Optimum Designs in Regression Problems.” The Annals of Mathematical Statistics 30 (2): 271–294.
   Google Scholar
• Lin, D. K. J., and W. Tu. 1995. “Dual Response Surface Optimization.” Journal of Quality Technology 27 (1): 34–39.
   Web of Science ®Google Scholar
• Lucas, J. M. 1976. “Which Response Surface Design is Best: A Performance Comparison of Several Types of Quadratic Response Surface Designs in Symmetric Regions.” Technometrics 18 (4): 411–417.
   Web of Science ®Google Scholar
• Mathai, A. M., and H. J. Haubold. 2017. Fractional and Multivariate Calculus. New York, NY: Springer.
   Google Scholar
• MathWorks. 2016. MATLAB. Natick, MA: MathWorks.
   Google Scholar
• Miller, A. J., and N. K. Nguyen. 1994. “Algorithm AS 295: A Fedorov Exchange Algorithm for D-Optimal Design.” Journal of the Royal Statistical Society. Series C (Applied Statistics) 43 (4): 669–677.
   Web of Science ®Google Scholar
• Minitab. 2016. Minitab Software (Version 17). State College, PA: Minitab.
   Google Scholar
• Mitchell, T. J. 1974. “An Algorithm for the Construction of ‘D-Optimal’ Experimental Designs.” Technometrics 16 (2): 203–210.
   Web of Science ®Google Scholar
• Mitchell, T. J., and F. L. Miller Jr. 1970. “Use of Design Repair to Construct Designs for Special Linear Models.” Mathematics Division Annual Progress Report (ORNL-4661), 13.
   Google Scholar
• Montgomery, D. C. 2013. Introduction to Statistical Quality Control. 7th ed. Hoboken, NJ: John Wiley & Sons.
   Google Scholar
• Montgomery, D. C. 2017. Design and Analysis of Experiments. 9th ed. Hoboken, NJ: John Wiley & Sons.
   Google Scholar
• Muller, W. G. 2007. Fundamentals of Experimental Design in Collecting Spatial Data. Berlin: Springer.
   Google Scholar
• Myers, R. H., D. C. Montgomery, and C. M. Anderson-Cook. 2009. Response Surface Methodology: Process and Product Optimization Using Designed Experiments. Hoboken, NJ: Wiley.
   Google Scholar
• Nguyen, N. K., and A. J. Miller. 1992. “A Review of Some Exchange Algorithms for Constructing Discrete D-Optimal Designs.” Computational Statistics & Data Analysis 14 (4): 489–498.
   Web of Science ®Google Scholar
• Ozdemir, A. 2017. “Development of the D-Optimality-Based Coordinate-Exchange Algorithm for an Irregular Design Space and the Mixed-Integer Nonlinear Robust Parameter Design Optimization.” PhD dissertation, Clemson University.
   Google Scholar
• Ozdemir, A., and B. R. Cho. 2016. “A Nonlinear Integer Programming Approach to Solving the Robust Parameter Design Optimization Problem.” Quality and Reliability Engineering International 32 (8): 2859–2870.
   Web of Science ®Google Scholar
• Ozdemir, A., and B. R. Cho. 2017. “Response Surface-Based Robust Parameter Design Optimization with Both Qualitative and Quantitative Variables.” Engineering Optimization 49 (10): 1796–1812.
   Web of Science ®Google Scholar
• Poston, W. L., E. J. Wegman, and J. L. Solka. 1998. “D-Optimal Design Methods for Robust Estimation of Multivariate Location and Scatter.” Journal of Statistical Planning and Inference 73 (1): 205–213.
   Web of Science ®Google Scholar
• Pronzato, L. 2003. “Removing Non-Optimal Support Points in D-Optimum Design Algorithms.” Statistics & Probability Letters 63 (3): 223–228.
   Web of Science ®Google Scholar
• Sahraian, M., and S. Kodiyalam. 2000. “Tuning PID Controllers Using Error-Integral Criteria and Response Surfaces Based Optimization.” Engineering Optimization 33 (2): 135–152.
   Web of Science ®Google Scholar
• SAS Institute. 2013. Using JMP 11. Cary, NC: SAS Institute.
   Google Scholar
• SAS Institute. 2016. SAS/STAT 14.2 User’s Guide. Cary, NC: SAS Institute.
   Google Scholar
• Smith, K. 1918. “On the Standard Deviations of Adjusted and Interpolated Values of an Observed Polynomial Function and Its Constants and the Guidance They Give Towards a Proper Choice of the Distribution of Observations.” Biometrika 12 (1-2): 1–85.
   Google Scholar
• Stat-Ease. 2016. Design-Expert Software 10. Minneapolis, MN: Stat-Ease, Inc.
   Google Scholar
• Vining, G. G., and R. H. Myers. 1990. “Combining Taguchi and Response Surface Philosophies: A Dual Response Approach.” Journal of Quality Technology 22 (1): 38–45.
   Web of Science ®Google Scholar
• Wald, A. 1943. “On the Efficient Design of Statistical Investigations.” The Annals of Mathematical Statistics 14 (2): 134–140.
   Google Scholar
• Wang, G. G., Z. Dong, and P. Aitchison. 2001. “Adaptive Response Surface Method—A Global Optimization Scheme for Approximation-Based Design Problems.” Engineering Optimization 33 (6): 707–733.
   Web of Science ®Google Scholar