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Problem Formulations for Simulation-based Design Optimization using Statistical Surrogates and Direct Search

Bastien Talgorn(bastientalgorn***at***yahoo.fr)
S├ębastien Le Digabel(sebastien.le.digabel***at***gerad.ca)
Michael Kokkolaras(michael.kokkolaras***at***mcgill.ca)

Abstract: Typical challenges of simulation-based design optimization include unavailable gradients and unreliable approximations thereof, expensive function evaluations, numerical noise, multiple local optima and the failure of the analysis to return a value to the optimizer. One possible remedy to alleviate these issues is to use surrogate models in lieu of the computational models or simulations and derivative-free optimization algorithms. In this work, we use the R dynaTree package to build statistical surrogates of the blackboxes and the direct search method for derivative-free optimization. We present different formulations for the surrogate problem considered at each search step of the Mesh Adaptive Direct Search (MADS) algorithm using a surrogate management framework. The proposed formulations are tested on twenty analytical benchmark problems and two simulation-based multidisciplinary design optimization problems. Numerical results confirm that the use of statistical surrogates in MADS improves the efficiency of the optimization algorithm.

Keywords: Simulation-based design optimization; mesh adaptive direct search (MADS); surrogate management framework; statistical surrogates.

Category 1: Convex and Nonsmooth Optimization (Nonsmooth Optimization )

Category 2: Nonlinear Optimization (Constrained Nonlinear Optimization )

Category 3: Applications -- Science and Engineering

Citation: Technical report, Les Cahiers du GERAD G-2014-04, 2014.

Download: [PDF]

Entry Submitted: 02/19/2014
Entry Accepted: 02/19/2014
Entry Last Modified: 02/19/2014

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