Nelder-Mead Simplex Modifications for Simulation Optimization

Russell R. Barton and John S. Ivey, Jr.
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Russell R. Barton: Department of Industrial and Systems Engineering, The Pennsylvania State University, University Park, Pennsylvania 16802
John S. Ivey, Jr.: The Eastman Kodak Company, Rochester, New York 14650

Management Science, 1996, vol. 42, issue 7, 954-973

Abstract: When the Nelder-Mead method is used to optimize the expected response of a stochastic system (e.g., an output of a discrete-event simulation model), the simplex-resizing steps of the method introduce risks of inappropriate termination. We give analytical and empirical results describing the performance of Nelder-Mead when it is applied to a response function that incorporates an additive white-noise error, and we use these results to develop new modifications of Nelder-Mead that yield improved estimates of the optimal expected response. Compared to Nelder-Mead, the best performance was obtained by a modified method, RS + S9, in which (a) the best point in the simplex is reevaluated at each shrink, step and (b) the simplex is reduced by 10% (rather than 50%) at each shrink step. In a suite of 18 test problems that were adapted from the MINPACK collection of NETLIB, the expected response at the estimated optimal point obtained by RS + S9 had errors that averaged 15% less than at the original method's estimated optimal point, at an average cost of three times as many function evaluations. Two well-known existing modifications for stochastic responses, the (n + 3)-rule and the next-to-worst rule, were found to be inferior to the new modification RS + S9.

Keywords: experimental designs; stochastic optimization; direct-search techniques; discrete-event simulation (search for similar items in EconPapers)
Date: 1996
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Citations: View citations in EconPapers (21)

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