A Comparison of Evolution Strategies with Other Direct Search Methods in the Presence of Noise
Computational Optimization and Applications
Global Optimization of Stochastic Black-Box Systems via Sequential Kriging Meta-Models
Journal of Global Optimization
Retrospective-approximation algorithms for the multidimensional stochastic root-finding problem
ACM Transactions on Modeling and Computer Simulation (TOMACS)
IEICE Transactions on Fundamentals of Electronics, Communications and Computer Sciences
A restarted and modified simplex search for unconstrained optimization
Computers and Operations Research
Querying simplexes in quasi-triangulation
Computer-Aided Design
A benchmark of kriging-based infill criteria for noisy optimization
Structural and Multidisciplinary Optimization
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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.