A constrained, globalized, and bounded Nelder?Mead method for engineering optimization

Luersen, Marco Antônio; Riche, Rodolphe Le; Guyon, Frédéric

doi:10.1007/s00158-003-0320-9

Cited by 84 publications

(50 citation statements)

References 9 publications

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“…(11), when these are chosen as variables in a gradient-based optimization method, there could be difficulties in computing the gradient and issues with the stability and convergence of the optimizer [21]. For this reason, three non-gradient optimization algorithms are employed and compared: a Nelder-Mead simplex scheme [24], a genetic algorithm [25] and simulated annealing [26].…”

Section: Extended Rational Function Approximation Approachmentioning

confidence: 99%

Parametric reduced order model approach for rapid dynamic loads prediction

Castellani¹,

Lemmens

Cooper³

2016

Aerospace Science and Technology

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A parametric reduced order methodology for loads estimation is described that produces a fast and accurate prediction of gust and manoeuvre loads for different flight conditions and structural parameter variations. The approach enables efficient prediction of the peak loads whilst maintaining the correlated time histories for different loads. It is then possible to determine correlated loads plots with reduced computation without losing accuracy. The effectiveness of the methodology is demonstrated by considering loads arising from families of gusts and pitching manoeuvres acting upon a numerical transport aircraft aeroservoelastic model with varying flight conditions and structural properties.

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Section: Extended Rational Function Approximation Approachmentioning

confidence: 99%

Parametric reduced order model approach for rapid dynamic loads prediction

Castellani¹,

Lemmens

Cooper³

2016

Aerospace Science and Technology

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“…The RFA is performed employing and comparing three non-gradient optimization algorithms: a Nelder-Mead simplex scheme, both in its unconstrained and constrained bounded version [13], a genetic algorithm [14] and simulated annealing [15]. As indicators of the goodness of the fit, the total root mean square error and the Frequency Response Assurance Criterion (FRAC) are calculated as…”

Section: Optimized Rational Function Approximationmentioning

confidence: 99%

Reduced Order Model Approach for Efficient Aircraft Loads Prediction

Castellani¹,

Lemmens²,

Cooper³

2015

SAE Int. J. Aerosp.

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General rightsThis document is made available in accordance with publisher policies. Please cite only the published version using the reference above. Full terms of use are available: http://www.bristol.ac.uk/pure/about/ebr-terms Page 1 of 9 2015-01-0066 Reduced Order Model Approach for Efficient Aircraft Loads PredictionAuthor, co-author (Do NOT enter this information. It will be pulled from participant tab in MyTechZone)Affiliation (Do NOT enter this information. It will be pulled from participant tab in MyTechZone) AbstractFlight loads calculations play a fundamental role in the development and certification of an aircraft and have an impact on the structural sizing and weight. The number of load cases required by the airworthiness regulations is in the order of tens of thousands and the analysis must be repeated for each design iteration. On large aircraft, CS-25 explicitly requires taking into account for loads prediction, airframe flexibility, unsteady aerodynamics and interaction of systems and structure, leading to computationally expensive numerical models. Thus there is a clear benefit in speeding-up this calculation process. This paper presents a methodology aiming to significantly reduce the computational time to predict loads due to gust and maneuvers. The procedure is based on Model Order Reduction, whose goal is the generation of a Reduced Order Model (ROM) able to limit the computational cost compared to a full analysis whilst retaining accuracy. The method is applied to a commercial transport aircraft modeled with beam elements, unsteady aerodynamics based on Doublet Lattice Method and servo-hydraulic actuators for the control surfaces. The aeroelastic equations of motion are formulated in the time-domain, through the Rational Function Approximation and application of the Balanced Truncation method. The results obtained with the reduced model shows a very good accuracy with respect to the full model and a significant saving in computational time. The impact of flexibility on the gust load factor is also highlighted, comparing it with the quasi-static analysis by Pratt's formula, current standard for Part 23 aircraft.

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“…In order to handle boundary constraints due to the DL/ML model, we used the extended version of the PRO algorithm introduced in the Active Harmony framework [32]. The same extension to handle boundaries was employed in our implementation of the Simplex method, and its stopping criteria are based on the work by Luersen [21]. Regarding initial simplex selection for our Simplex search implementation, we used a modeldriven approach based on the DL model for square tiling.…”

Section: Search Space Reduction By Dl/ml Modelmentioning

confidence: 99%

Analytical Bounds for Optimal Tile Size Selection

Shirako

Sharma

Fauzia

et al. 2012

Lecture Notes in Computer Science

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Abstract. In this paper, we introduce a novel approach to guide tile size selection by employing analytical models to limit empirical search within a subspace of the full search space. Two analytical models are used together: 1) an existing conservative model, based on the data footprint of a tile, which ignores intra-tile cache block replacement, and 2) an aggressive new model that assumes optimal cache block replacement within a tile. Experimental results on multiple platforms demonstrate the practical effectiveness of the approach by reducing the search space for the optimal tile size by 1,307× to 11,879× for an Intel Core-2-Quad system; 358× to 1,978× for an Intel Nehalem system; and 45× to 1,142× for an IBM Power7 system. The execution of rectangularly tiled code tuned by a search of the subspace identified by our model achieves speed-ups of up to 1.40× (Intel Core-2 Quad), 1.28× (Nehalem) and 1.19× (Power 7) relative to the best possible square tile sizes on these different processor architectures. We also demonstrate the integration of the analytical bounds with existing search optimization algorithms. Our approach not only reduces the total search time from Nelder-Mead Simplex and Parallel Rank Ordering methods by factors of up to 4.95× and 4.33×, respectively, but also finds better tile sizes that yield higher performance in tuned tiled code.

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A constrained, globalized, and bounded Nelder?Mead method for engineering optimization

Cited by 84 publications

References 9 publications

Parametric reduced order model approach for rapid dynamic loads prediction

Parametric reduced order model approach for rapid dynamic loads prediction

Reduced Order Model Approach for Efficient Aircraft Loads Prediction

Analytical Bounds for Optimal Tile Size Selection

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