Managing surrogate objectives to optimize a helicopter rotor design - Further experiments

Booker, Andrew J.; Frank, Paul D.; Dennis, J. E.; Moore, Douglas; Serafini, David B.

doi:10.2514/6.1998-4717

Cited by 34 publications

(42 citation statements)

References 8 publications

(4 reference statements)

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“…Note that if = 0, then d (g) is identical to d (1) in equation (9), and if = g ∞ , then then d (g) is identical to d (∞) in equation (11). The following result implicitly provides a sufficiency condition on the quality of the approximation.…”

Section: Pruning With An Approximation Of the Gradientmentioning

confidence: 95%

“…It can be as simple as doing nothing (i.e., the finite set of mesh points is empty), or it can make use of heuristics, such as genetic algorithms, or surrogate functions based on interpolation or on simplified models. See [10] and [11] for examples of how this can be done effectively.…”

Section: The Search Stepmentioning

confidence: 99%

“…GPS algorithms can be applied to these problems, particularly when f is quite expensive to evaluate, and GPS can also be used in the surrogate management framework [10,11]. We can not justify further global assumptions about the class of problems [10] we target, but fortunately, the Clarke [13] calculus enables a simple unified convergence analysis by allowing for f X to be extended valued (see [8]).…”

Section: Introductionmentioning

confidence: 99%

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Generalized pattern searches with derivative information

Abramson¹,

Audet

Dennis

2003

Math. Program., Ser. B

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Abstract.A common question asked by users of direct search algorithms is how to use derivative information at iterates where it is available. This paper addresses that question with respect to Generalized Pattern Search (GPS) methods for unconstrained and linearly constrained optimization. Specifically this paper concentrates on the GPS POLL step. Polling is done to certify the need to refine the current mesh, and it requires O(n) function evaluations in the worst case. We show that the use of derivative information significantly reduces the maximum number of function evaluations necessary for POLL steps, even to a worst case of a single function evaluation with certain algorithmic choices given here. Furthermore, we show that rather rough approximations to the gradient are sufficient to reduce the POLL step to a single function evaluation. We prove that using these less expensive POLL steps does not weaken the known convergence properties of the method, all of which depend only on the POLL step.

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Section: Pruning With An Approximation Of the Gradientmentioning

confidence: 95%

Section: The Search Stepmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Generalized pattern searches with derivative information

Abramson¹,

Audet

Dennis

2003

Math. Program., Ser. B

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“…From the standpoint of convergence, the MADS poll step overcomes poor correlation, but at a higher cost. In fact, the class of MADS algorithms has been shown to be robust in solving problems, even when the surrogate predicts poorly [11].…”

Section: New Surrogate Strategiesmentioning

confidence: 99%

An efficient class of direct search surrogate methods for solving expensive optimization problems with CPU-time-related functions

Abramson

Asaki

Dennis

et al. 2011

Struct Multidisc Optim

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In this paper, we characterize a new class of computationally expensive optimization problems and introduce an approach for solving them. In this class of problems, objective function values may be directly related to the computational time required to obtain them, so that, as the optimal solution is approached, the computational time required to evaluate the objective is significantly less than at points farther away from the solution. This is motivated by an application in which each objective function evaluation requires both a numerical fluid dynamics simulation and an image registration process, and the goal is to find the parameter values of a predetermined reference image by comparing the flow dynamics from the numerical simulation and the reference image through the image comparison process. In designing an approach to numerically solve the more general class of problems in an efficient way, we make use of surrogates based on CPU times of previously evaluated points, rather than their function values, all within the search step framework of mesh adaptive direct search algorithms. Because of the expected positive correlation between function values and their CPU times, a time cutoff parameter is added to the objective function evaluation to allow its termination during the comparison process if the computational time exceeds a specified threshold. The approach was tested using the NOMADm and DACE MATLAB software packages, and results are presented. *

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Section: The Search Stepmentioning

confidence: 99%

Generalized Pattern Searches With Derivative Information

Audet¹,

Dennis²,

Abramson³

2003

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Public reporting burden for the collection of information is estimated to average 1 hour per response, including the time for reviewing instructions, searching existing data sources, gathering and maintaining the data needed, and completing and reviewing the collection of information. Abstract: A common question asked by users of direct search algorithms is how to use derivative information at iterates where it is available. This paper addresses that question with respect to Generalized Pattern Search (GPS) methods for unconstrained and linearly constrained optimization. Specifically this paper concentrates on the GPS poll step. Polling is done to certify the need to refine the current mesh, and it requires O(n) function evaluations in the worst case. We show that the use of derivative information significantly reduces the maximum number of function evaluations necessary for poll steps, even to a worst case of a single function evaluation with certain algorithmic choices given here. Furthermore, we show that rather rough approximations to the gradient are sufficient to reduce the poll step to a single function evaluation. We prove that using these less expensive poll steps does not weaken the known convergence properties of the method, all of which depend only on the poll step.

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Managing surrogate objectives to optimize a helicopter rotor design - Further experiments

Cited by 34 publications

References 8 publications

Generalized pattern searches with derivative information

Generalized pattern searches with derivative information

An efficient class of direct search surrogate methods for solving expensive optimization problems with CPU-time-related functions

Generalized Pattern Searches With Derivative Information

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