Abstract
We use the simulated annealing algorithm to construct mixed multilevel balanced orthogonal arrays. We demonstrate how this algorithm can be used to find the multilevel balanced experimental design matrix with the minimal number of runs. These orthogonal arrays are widely used in the quality improvement projects. By formulating the problem as an optimization problem, we show that simulated annealing can find the global optimum, while avoiding being trapped in local extrema. An important application of our results is in experimental designs where variables are discrete in nature. A well balanced design not only saves experimental cost but also arrives at conclusions robust to environmental changes.
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References
E. Aarts and J. Korst, Simulated Annealing and Boltzmann Machines, Wiley (1989)
Bohachevsky, I. O., M. E. Johnson, and M. L. Stein, “Generalized Simulated Annealing for Function Optimization”, Technometrics, 28, 209–217 (1986).
Bose, R. C, “Mathematical Theory of the Symmetrical Factorial Design”, Sankhya, 8, 107–166 (1947).
Bose, R. C. and Bush, K. A., “Orthogonal Arrays of Strength Two and Three”, Ann. Math. Stat., 23, 508–524 (1952).
Bose, R. C. and Kishen, K., “On the Problem of Confounding in General Symmetrical Factorial Design”, Sankhya, 5, 21–36 (1940).
Cheng, C. S., “Some Orthogonal Main-effect Plans for Asymmetrical Factorials”, Technometrics, 31, 475–477 (1989).
Dey, A., Orthogonal Fractional Factorial Design, NewYork, Halsted (1985).
Fisher, R. A., “The Arrangement of Field Experiments”, Jour. Min. Agri., 33, 503–513 (1926).
Kirkpatrick, S., C. D. Gelat, and M. P. Vecchi, “Optimization by Simulated Annealing,” Sci., 220, 671 (1983).
Metropolis, N., A. Roselbluth, M. Roselbluth, A. Teller, and E. Teller, “Equation of State Calculations by Fast Computing Machines,” J. Chem. Phys., 21, 1087 (1953).
Taguchi, G., System of Experimental Design, Volumes 1 and 2, White Plains, UNIPUB (1987).
Wang, J. C, Orthogonal Arrays and Nearly Orthogonal Arrays with Mixed Levels: Construction and Applications, Ph.D. Dissertation, University of Wisconsin — Madison (1989).
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© 1992 Springer-Verlag New York, Inc.
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Wang, R.H., Safadi, R.B. (1992). Generating Mixed Multilevel Orthogonal Arrays By Simulated Annealing. In: Page, C., LePage, R. (eds) Computing Science and Statistics. Springer, New York, NY. https://doi.org/10.1007/978-1-4612-2856-1_100
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DOI: https://doi.org/10.1007/978-1-4612-2856-1_100
Publisher Name: Springer, New York, NY
Print ISBN: 978-0-387-97719-5
Online ISBN: 978-1-4612-2856-1
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