Abstract
This chapter first summarizes Response Surface Methodology (RSM), which started with Box and Wilson’s 1951 article on RSM for real, non-simulated systems. RSM is a stepwise heuristic that uses first-order polynomials to approximate the response surface locally. An estimated polynomial metamodel gives an estimated local gradient, which RSM uses in steepest ascent (or descent) to decide on the next local experiment. When RSM approaches the optimum, the latest first-order polynomial is replaced by a second-order polynomial. The fitted second-order polynomial enables the estimation of the optimum. This chapter then focuses on simulated systems, which may violate the assumptions of constant variance and independence. A variant of RSM that provably converges to the true optimum under specific conditions is summarized, and an adapted steepest ascent that is scale-independent is presented. Next, the chapter generalizes RSM to multiple random responses, selecting one response as the goal variable and the other responses as the constrained variables. This generalized RSM is combined with mathematical programming to estimate a better search direction than the steepest ascent direction. To test whether the estimated solution is indeed optimal, bootstrapping may be used. Finally, the chapter discusses robust optimization of the decision variables, while accounting for uncertainties in the environmental variables.
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References
M. E. AngĂĽn. Black Box Simulation Optimization: Generalized Response Surface Methodology. CentER Dissertation Series, Tilburg University, Tilburg, the Netherlands, 2004.
E. Angün, D. den Hertog, G. Gürkan, and J. P. C. Kleijnen. Response surface methodology with stochastic constraints for expensive simulation. Journal of the Operational Research Society, 60(6):735–746, 2009.
E. R. Barnes. A variation on Karmarkar’s algorithm for solving linear programming problems. Mathematical Programming, 36:174–182, 1986.
R. R. Barton. Response surface methodology. In S. I. Gass and M. C. Fu, editors, Encyclopedia of Operations Research and Management Science, pages 1307–1313. Springer, New York, 3rd edition, 2013.
R. R. Barton and M. Meckesheimer. Metamodel-based simulation optimization. In Handbooks in Operations Research and Management Science, Elsevier/North Holland, 13:535–574, 2006.
T. Bartz-Beielstein. Experimental Research in Evolutionary Computation: The New Experimentalism. Springer, Berlin, 2006.
S. Bashyam and M. C. Fu. Optimization of (s, S) inventory systems with random lead times and a service level constraint. Management Science, 44:243–256, 1998.
A. Ben-Tal and A. Nemirovski. Robust convex optimization. Mathematics of Operations Research, 23(4):769–805, 1998.
A. Ben-Tal and A. Nemirovski. Selected topics in robust convex optimization. Mathematical Programming, 112(1):125–158, 2008.
B. W. M. Bettonvil, E. del Castillo, and J. P. C. Kleijnen. Statistical testing of optimality conditions in multiresponse simulation-based optimization.European Journal of Operational Research, 199(2):448–458, 2009.
H. Beyer and B. Sendhoff. Robust optimization—a comprehensive survey. Computer Methods in Applied Mechanics and Engineering, 196:33–34, pp. 3190–3218, 2007.
G. E. P. Box and K. B. Wilson. On the experimental attainment of optimum conditions.Journal of the Royal Statistical Society, Series B, 13(1):1–38, 1951.
K. H. Chang, L. J. Hong, and H. Wan. Stochastic trust-region response-surface method (STRONG) – a new response-surface framework for simulation optimization, INFORMS Journal on Computing, 25(2):230–243, 2013.
K. H. Chang, M. K. Li, and H. Wan. Combining STRONG with screening designs for large-scale simulation optimization, IIE Transactions, 46:357–373, 2014.
M. Chih. A more accurate second-order polynomial metamodel using a pseudo-random number assignment strategy. Journal of the Operational Research Society, 64:198–207, 2013.
A. R. Conn, N. L. M. Gould, and P. L. Toint. Trust-Region Methods. SIAM, 2000.
G. Dellino, J. P. C. Kleijnen, and C. Meloni. Robust optimization in simulation: Taguchi and Response Surface Methodology. International Journal of Production Economics, 125(1):52–59, 2010.
G. Dellino, J. P. C. Kleijnen, and C. Meloni. Robust optimization in simulation: Taguchi and Krige combined.INFORMS Journal on Computing, 24(3):471–484, 2012.
R. L. Dykstra. Establishing the positive definiteness of the sample covariance matrix. The Annals of Mathematical Statistics, 41(6):2153–2154, 1970.
B. Efron and R. J. Tibshirani. An Introduction to the Bootstrap. Chapman & Hall, New York, 1993.
M. C. Fu and H. Qu. Regression models augmented with direct stochastic gradient estimators. INFORMS Journal on Computing, 26(3):484–499, 2014.
P. E. Gill, W. Murray, and M. H. Wright. Practical Optimization. Academic Press, London, 12th edition, 2000.
W. D. Kelton, R. P. Sadowski, and D. T. Sturrock. Simulation with Arena. McGraw-Hill, Boston, MA, 4th edition, 2007.
A. I. Khuri. Multiresponse surface methodology. In Handbook of Statistics, volume 13, edited by S. Ghosh and C. R. Rao, Elsevier, Amsterdam, 1996.
J. P. C. Kleijnen. Statistical Techniques in Simulation, Part II. Dekker, New York, 1975.
J. P. C. Kleijnen. Simulation and optimization in production planning: a case study. Decision Support Systems, 9:269–280, 1993.
J. P. C. Kleijnen. Response surface methodology for constrained simulation optimization: an overview. Simulation Modelling Practice and Theory, 16:50–64, 2008.
J. P. C. Kleijnen. Design and Analysis of Simulation Experiments. Springer, 2nd edition, 2015.
J. P. C. Kleijnen, D. den Hertog, and E. Angün. Response surface methodology’s steepest ascent and step size revisited. European Journal of Operational Research, 159:121–131, 2004.
J. P. C. Kleijnen, D. den Hertog and E. Angün. Response surface methodology’s steepest ascent and step size revisited: correction. European Journal of Operational Research, 170:664–666, 2006.
A. M. Law. Simulation Modeling and Analysis. McGraw-Hill, Boston, MA, 5th edition, 2014.
R. H. Myers, A. I. Khuri, and W. H. Carter. Response surface methodology: 1966–1988. Technometrics, 31(2):137–157, 1989.
R. H. Myers, D. C. Montgomery, and C. M. Anderson-Cook. Response Surface Methodology: Process and Product Optimization using Designed Experiments. Wiley, New York, 3rd edition, 2009.
V. N. Nair, editor. Taguchi’s parameter design: a panel discussion. Technometrics, 34(2):127–161, 1992.
S. H. Ng, K. Xu, and W. K. Wong. Optimization of multiple response surfaces with secondary constraints for improving a radiography inspection process. Quality Engineering, 19(1):53–65, 2007.
G. J. Park, T. H. Lee, K. H. Lee, and K. H. Hwang. Robust design: an overview. AIAA Journal, 44(1):181–191, 2006.
H. Qu and M. C. Fu. On direct gradient enhanced simulation metamodels. In C. Laroque, J. Himmelspach, R. Pasupathy, O. Rose, and A. M. Uhrmacher, editors, Proceedings of the 2012 Winter Simulation Conference, pages 478–489, 2012.
R. Rikards and J. Auzins. Response surface method for solution of structural identification problems. Fourth International Conference on Inverse Problems in Engineering, Rio de Janeiro, Brazil, 2002.
S. C. Rosen, C. M. Harmonosky, and M. T. Traband. Optimization of systems with multiple performance measures via simulation: survey and recommendations. Computers & Industrial Engineering, 54(2):327–339, 2008.
W. Shi, J. P. C. Kleijnen, and Z. Liu. Factor screening for simulation with multiple responses: sequential bifurcation. European Journal of Operational Research, 237(1):136–147, 2014.
G. Taguchi. System of Experimental Designs, Volumes 1 and 2. UNIPUB/ Krauss International, White Plains, New York, 1987.
W. Van den Bogaard and J. P. C. Kleijnen. Minimizing waiting times using priority classes: A case study in response surface methodology. Discussion Paper FEW 77.056, (http://arno.uvt.nl/show.cgi?fid=105001 accessed 12 March 2014), 1977.
I. Yanikoglu, D. den Hertog, and J. P. C. Kleijnen. Adjustable robust parameter design with unknown distributions. CentER Discussion Paper (http://arno.uvt.nl/show.cgi?fid=129316 accessed 12 March 2014), 2013.
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Kleijnen, J.P.C. (2015). Response Surface Methodology. In: Fu, M. (eds) Handbook of Simulation Optimization. International Series in Operations Research & Management Science, vol 216. Springer, New York, NY. https://doi.org/10.1007/978-1-4939-1384-8_4
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