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INFORMS Journal on Computing Vol. 12, No. 4, Fall 2000 0899-1499 100 1204-0272 $05.00 © 2000 INFORMS

A Revised Simplex Search Procedure for Stochastic Simulation Response Surface Optimization
DAVID G. HUMPHREY JAMES R. WILSON Nortel Networks, Operations Research Department, Research Triangle Park, NC 27713, Email: humphre@nortelnetworks.com Department of Industrial Engineering, North Carolina State University, Raleigh, NC 27695, Email: jwilson@eos.ncsu.edu, Web: http://www.ie.ncsu.edu/jwilson
(Received: September 1997; revised: April 2000; accepted: May 2000)

We develop a variant of the Nelder-Mead (NM) simplex search procedure for stochastic simulation optimization that is designed to avoid many of the weaknesses encumbering similar direct-search methods—in particular, excessive sensitivity to starting values, premature termination at a local optimum, lack of robustness against noisy responses, and computational inefficiency. The Revised Simplex Search (RSS) procedure consists of a three-phase application of the NM method in which: (a) the ending values for one phase become the starting values for the next phase; (b) the step size for the initial simplex (respectively, the shrink coefficient) decreases geometrically (respectively, increases linearly) over successive phases; and (c) the final estimated optimum is the best of the ending values for the three phases. To compare RSS versus NM and procedure RS S9 due to Barton and Ivey, we summarize a simulation study based on four selected performance measures computed for six test problems that include additive white-noise error, with three levels of problem dimensionality and noise variability used in each problem. In the selected test problems, RSS yielded significantly more accurate estimates of the optimum than NM or RS S9, and both RSS and RS S9 required roughly four times as many function evaluations as NM.

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