A revised simplex search procedure for stochastic simulation response-surface optimization

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 such direct-search methods-in particular, excessive sensitivity to starting values, premature termination at a local optimum, lack of robustness against noisy responses, and lack of computational efficiency. 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 size of 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 the NM procedure and RS9 (a simplex search procedure recently proposed by Barton and Ivey (1996)), we summarize a simulation study based on separate factorial experiments and follow-up multiple comparisons tests for four selected performance measures computed on each of six test problems, with three levels of problem dimensionality and noise variability used in each problem. The experimental results provide substantial evidence of RSS's improved performance with only marginally higher computational effort.