A revised simplex search procedure for stochastic simulation response surface optimization

A revised simplex search procedure for stochastic simulation response surface optimization

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Article ID: iaor20013097
Country: United States
Volume: 12
Issue: 4
Start Page Number: 272
End Page Number: 283
Publication Date: Sep 2000
Journal: INFORMS Journal On Computing
Authors: ,
Keywords: optimization, programming: probabilistic
Abstract:

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 RSS9 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 RSS9, and both RSS and RSS9 required roughly four times as many function evaluations as NM.

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