Abstract
We demonstrate the use of multiple surrogates and kriging believer for parallelizing surrogate-based contour estimation. For the demonstration example, we reduce wall clock time with minimal penalty in number of simulations.
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Notes
That is \(E_G[F(\mathbf{x})] = \int_{\bar{g} - \epsilon(\mathbf{x})}^{{\bar{g}} + \epsilon(\mathbf{x})}{\left[ \epsilon(\mathbf{x}) - | \bar{g} - G (\mathbf{x}) | \right]f_{G}({g})d{g}}\). Further discussion and derivation can be found in Bichon (2010).
Here, we used differential evolution as implemented in the companion software of Price et al. (2005) to solve this optimization problem.
This version runs EGRA with surrogates that might not furnish uncertainty estimates. These estimates can certainly be provided by sophisticated schemes, e.g. the Bayesian approach (Seok et al. 2002). Here, we use the kriging uncertainty estimates with all other surrogates (Viana and Haftka 2009). Although theoretically less attractive, this heuristic avoids the overhead of estimating the uncertainty for each surrogate.
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Acknowledgments
We thank Mr. David Easterling and Mr. Nick Radcliffe for help in coding the linear Shepard.
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This work was supported in part by U.S. Air Force Office of Scientific Research grant FA9550-09-1-0153 and National Science Foundation grant CMMI-0856431.
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Viana, F.A.C., Haftka, R.T. & Watson, L.T. Sequential sampling for contour estimation with concurrent function evaluations. Struct Multidisc Optim 45, 615–618 (2012). https://doi.org/10.1007/s00158-011-0733-9
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DOI: https://doi.org/10.1007/s00158-011-0733-9