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Cox, Steven; Haftka, Raphael T.; Baker, Chuck A.; Grossman, Bernard; Mason, William H.; Watson, Layne T.

doi:10.1023/a:1012782825166

Cited by 63 publications

(11 citation statements)

References 8 publications

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“…By identifying the potentially optimal intervals, the algorithm balances its effort between global and local searches of the objective function to guarantee a global optimum. The successful application of DIRECT algorithm in aerodynamic optimization has been reported by many authors [28,29,30]. This algorithm is found suitable for global optimization problems with bound constraints and a real-valued objective function when the objective function is a "black box" function or evaluation.…”

Section: Global Optimization By Direct Algorithmmentioning

confidence: 96%

Numerical Investigation of Configurations with Optimum Swirl Recovery for Propeller Propulsion Systems

Liu

Eitelberg

et al. 2019

AIAA Journal

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This paper addresses the design of swirl recovery vanes (SRVs) for propeller propulsion in tractor configuration at cruise conditions using numerical tools. A multi-fidelity optimization framework is formulated for the design purpose, which exploits low-fidelity potential flow-based analysis results as input for high-fidelity Euler equationbased simulations. Furthermore, a model alignment procedure between low-and high-fidelity models is established based on a shape-preserving response prediction algorithm. Two cases of swirl recovery are examined. The first is the swirl recovery by the trailing wing which leads to a reduction of the lift-induced drag. This is achieved by the optimization of the wing twist distribution. The second case is swirl recovery by a set of stationary vanes, which leads to production of additional thrust. In the latter case, four configurations are evaluated by locating the vanes at different azimuthal and axial positions relative to the wing. An optimum configuration is identified where the vanes are positioned on the blade-downgoing side downstream of the wing. For the configuration and conditions examined, the wing twist optimization reduces the induced drag by 3.9 counts (5.9% of wing induced drag), while the optimized 4-bladed SRVs lead to an induced-drag reduction of 6.1 counts (9.2% of wing induced drag).

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Section: Global Optimization By Direct Algorithmmentioning

confidence: 96%

Numerical Investigation of Configurations with Optimum Swirl Recovery for Propeller Propulsion Systems

Liu

Eitelberg

et al. 2019

AIAA Journal

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“…In order to end up with a small region where the global minimum is located, many subdivisions are necessary, thus requiring many function evaluations. For this reason, it has been observed that although the DIRECT algorithm rapidly finds the region where the global minimum is located, its local convergence properties are rather poor (see, e.g., Cox et al 2001;Bartholomew-Biggs et al 2002;Ljungberg et al 2004, for applications in the extremely hard problems of the design of high-speed civil transport, aircrafts and bioinformatics). In summary, the DIRECT method is an ideal candidate for its application as an estimator of the region where the global minimum is located, but not for determining it.…”

Section: Convergencementioning

confidence: 99%

Advanced Forward Modeling and Inversion of Stokes Profiles Resulting from the Joint Action of the Hanle and Zeeman Effects

Ramos

Bueno

Degl’Innocenti

2008

Astrophysical Journal

144

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A big challenge in solar and stellar physics in the coming years will be to decipher the magnetism of the solar outer atmosphere (chromosphere and corona) along with its dynamic coupling with the magnetic fields of the underlying photosphere. To this end, it is important to develop rigorous diagnostic tools for the physical interpretation of spectropolarimetric observations in suitably chosen spectral lines. Here we present a computer program for the synthesis and inversion of Stokes profiles caused by the joint action of atomic level polarization and the Hanle and Zeeman effects in some spectral lines of diagnostic interest, such as those of the He i 10830Å and 5876Å (or D 3 ) multiplets. It is based on the quantum theory of spectral line polarization, which takes into account in a rigorous way all the relevant physical mechanisms and ingredients (optical pumping, atomic level polarization, level crossings and repulsions, Zeeman, Paschen-Back and Hanle effects). The influence of radiative transfer on the emergent spectral line radiation is taken into account through a suitable slab model. The user can either calculate the emergent intensity and polarization for any given magnetic field vector or infer the dynamical and magnetic properties from the observed Stokes profiles via an efficient inversion algorithm based on global optimization methods. The reliability of the forward modeling and inversion code presented 1 Consejo Superior de Investigaciones Científicas (Spain)-2 -here is demonstrated through several applications, which range from the inference of the magnetic field vector in solar active regions to determining whether or not it is canopy-like in quiet chromospheric regions. This user-friendly diagnostic tool called "HAZEL" (from HAnle and ZEeman Light) is offered to the astrophysical community, with the hope that it will facilitate new advances in solar and stellar physics.

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“…DIRECT has also proven effective on low-dimensional, real-world problems from a wide range of fields, including genetics [42], surgery [76], air transport [8], power generation [2,13,34], astronomy [4], hydrogen fuel cell management [74], photovoltaic systems [49], hard disk design [77], aircraft routing [1], and many others [3,6,20,24,35,44,58,71]. However, DIRECT has been found to be less competitive on higher-dimensional problems [47].…”

Section: Introductionmentioning

confidence: 99%

The DIRECT algorithm: 25 years Later

Jones

Martins

2020

J Glob Optim

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Introduced in 1993, the DIRECT global optimization algorithm provided a fresh approach to minimizing a black-box function subject to lower and upper bounds on the variables. In contrast to the plethora of nature-inspired heuristics, DIRECT was deterministic and had only one hyperparameter (the desired accuracy). Moreover, the algorithm was simple, easy to implement, and usually performed well on low-dimensional problems (up to six variables). Most importantly, DIRECT balanced local and global search (exploitation vs. exploration) in a unique way: in each iteration, several points were sampled, some for global and some for local search. This approach eliminated the need for “tuning parameters” that set the balance between local and global search. However, the very same features that made DIRECT simple and conceptually attractive also created weaknesses. For example, it was commonly observed that, while DIRECT is often fast to find the basin of the global optimum, it can be slow to fine-tune the solution to high accuracy. In this paper, we identify several such weaknesses and survey the work of various researchers to extend DIRECT so that it performs better. All of the extensions show substantial improvement over DIRECT on various test functions. An outstanding challenge is to improve performance robustly across problems of different degrees of difficulty, ranging from simple (unimodal, few variables) to very hard (multimodal, sharply peaked, many variables). Opportunities for further improvement may lie in combining the best features of the different extensions.

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Cited by 63 publications

References 8 publications

Numerical Investigation of Configurations with Optimum Swirl Recovery for Propeller Propulsion Systems

Numerical Investigation of Configurations with Optimum Swirl Recovery for Propeller Propulsion Systems

Advanced Forward Modeling and Inversion of Stokes Profiles Resulting from the Joint Action of the Hanle and Zeeman Effects

The DIRECT algorithm: 25 years Later

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