Optimal Aeroacoustic Shape Design Using the Surrogate Management Framework

Marsden, Alison; Wang, Meng; Dennis, John E.; Moin, Parviz

doi:10.1023/b:opte.0000033376.89159.65

Cited by 126 publications

(77 citation statements)

References 32 publications

(19 reference statements)

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“…The search strategy may, for example, be based on a heuristic exploration of the domain, or it may employ surrogate functions based on response surfaces, interpolatory models, or simplified physics models. Surrogates are most often tailored for specific applications; see, e.g., [6,9,11,25,26,28]. Let us simply denote by S k the finite set of mesh points used in the search step at iteration k.…”

Section: Description Of An Iterationmentioning

confidence: 99%

A Progressive Barrier for Derivative-Free Nonlinear Programming

Audet¹,

Dennis²

2009

SIAM J. Optim.

171

146

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Abstract. We propose a new constraint-handling approach for general constraints that is applicable to a widely used class of constrained derivative-free optimization methods. As in many methods that allow infeasible iterates, constraint violations are aggregated into a single constraint violation function. As in filter methods, a threshold, or barrier, is imposed on the constraint violation function, and any trial point whose constraint violation function value exceeds this threshold is discarded from consideration. In the new algorithm, unlike the filter method, the amount of constraint violation subject to the barrier is progressively decreased adaptively as the iteration evolves. We test this progressive barrier (PB) approach versus the extreme barrier (EB) with the generalized pattern search (Gps) and the lower triangular mesh adaptive direct search (LTMads) methods for nonlinear derivative-free optimization. Tests are also conducted using the Gps-filter, which uses a version of the Fletcher-Leyffer filter approach. We know that Gps cannot be shown to yield kkt points with this strategy or the filter, but we use the Clarke nonsmooth calculus to prove Clarke stationarity of the sequences of feasible and infeasible trial points for LTMads-PB. Numerical experiments are conducted on three academic test problems with up to 50 variables and on a chemical engineering problem. The new LTMads-PB method generally outperforms our LTMads-EB in the case where no feasible initial points are known, and it does as well when feasible points are known. which leads us to recommend LTMads-PB. Thus the LTMads-PB is a useful practical extension of our earlier LTMads-EB algorithm, particularly in the common case for real problems where no feasible point is known. The same conclusions hold for Gps-PB versus Gps-EB.Key words. mesh adaptive direct search algorithm, filter algorithm, barrier approach, constrained optimization, nonlinear programming AMS subject classifications. 90C30, 90C56, 65K05, 49J52

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Section: Description Of An Iterationmentioning

confidence: 99%

A Progressive Barrier for Derivative-Free Nonlinear Programming

Audet¹,

Dennis²

2009

SIAM J. Optim.

171

146

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“…While the search step contributes nothing to the convergence theory of GPS (and in fact, an unsuitable search may impede performance), the use of surrogates enables the user to potentially gain significant improvement early on in the iteration process at much lower cost. See [28] for evidence to support this assertion.…”

Section: Local Optimality For Mixed Variablesmentioning

confidence: 98%

Filter Pattern Search Algorithms for Mixed Variable Constrained Optimization Problems

Abramson¹,

Audet²,

Dennis³

2004

126

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A new class of algorithms for solving nonlinearly constrained mixed variable optimization problems is presented. This class combines and extends the Audet-Dennis generalized pattern search (GPS) algorithms for bound constrained mixed variable optimization, and their GPS-filter algorithms for general nonlinear constraints. In generalizing existing algorithms, new theoretical convergence results are presented that reduce seamlessly to existing results for more specific classes of problems. While no local continuity or smoothness assumptions are required to apply the algorithm, a hierarchy of theoretical convergence results based on the Clarke calculus is given, in which local smoothness dictates what can be proved about certain limit points generated by the algorithm. We believe this is the first algorithm with provable convergence results to directly target this class of problems.

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“…The SMF has been used successfully in a variety of complex problems, including unsteady fluid mechanics [30][31][32], helicopter rotor blade design [33,34], quantifying uncertainity in bypass graft models [35] and identifying arterial G&R parameters [36]. The SMF method was originally developed for computationally expensive simulations and can be applied to discontinuous functions and problems with nonlinear constraints [37].…”

Section: Surrogate Management Framework (Smf)mentioning

confidence: 99%

Computational Simulation of the Adaptive Capacity of Vein Grafts in Response to Increased Pressure

Ramachandra

Sankaran

Humphrey

et al. 2015

Journal of Biomechanical Engineering

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Vein maladaptation, leading to poor long-term patency, is a serious clinical problem in patients receiving coronary artery bypass grafts (CABGs) or undergoing related clinical procedures that subject veins to elevated blood flow and pressure. We propose a computational model of venous adaptation to altered pressure based on a constrained mixture theory of growth and remodeling (G&R). We identify constitutive parameters that optimally match biaxial data from a mouse vena cava, then numerically subject the vein to altered pressure conditions and quantify the extent of adaptation for a biologically reasonable set of bounds for G&R parameters. We identify conditions under which a vein graft can adapt optimally and explore physiological constraints that lead to maladaptation. Finally, we test the hypothesis that a gradual, rather than a step, change in pressure will reduce maladaptation. Optimization is used to accelerate parameter identification and numerically evaluate hypotheses of vein remodeling.

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Optimal Aeroacoustic Shape Design Using the Surrogate Management Framework

Cited by 126 publications

References 32 publications

A Progressive Barrier for Derivative-Free Nonlinear Programming

A Progressive Barrier for Derivative-Free Nonlinear Programming

Filter Pattern Search Algorithms for Mixed Variable Constrained Optimization Problems

Computational Simulation of the Adaptive Capacity of Vein Grafts in Response to Increased Pressure

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