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Carter, R. G.; Gablonsky, J. M.; Patrick, A.; Kelley, C. T.; Eslinger, Owen

doi:10.1023/a:1013123110266

Cited by 72 publications

(14 citation statements)

References 27 publications

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“…The algorithm is available as part of the TOMLAB suite of optimization tools for MATLAB, and a description of the method is available on the TOMLAB website. 5 According to this description, glcCluster is a hybrid algorithm, combining DIRECT, a clustering algorithm, and local search. It takes advantage of the previously mentioned tendency for the sampled points from DIRECT to cluster (be more dense) in high-performing regions of the space, as shown in Fig.…”

Section: Glcclustermentioning

confidence: 99%

“…Problems with noise in the objective function present a special challenge (e.g., the value of f min is only known approximately due to noise) and have been considered by Deng and Ferris [9]. Extensions to handle the case when the objective function is evaluated by a simulation that can fail (and thus no value is provided) have been proposed by Carter et al [5] as well as Na et al [48]. Adaptations of DIRECT for symmetric problems-problems in which the objective is the same for any permutation of the inputs-have been proposed by Grbić et al [21] and by Paulavičius and Žilinskas [50].…”

Section: Other Extensions Of Directmentioning

confidence: 99%

See 1 more Smart Citation

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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Section: Glcclustermentioning

confidence: 99%

Section: Other Extensions Of Directmentioning

confidence: 99%

The DIRECT algorithm: 25 years Later

Jones

Martins

2020

J Glob Optim

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“…Since during the search it uses a set of possible estimates of L and does not use its single overestimate, only the so-called everywhere dense convergence (i.e., convergence of the sequence of trial points to any point of the search interval) can be established for this method; it is also difficult to apply for the DIRECT some meaningful stopping criterion, such as, for example, stopping on achieving a desired accuracy in solution. Nevertheless, due to its relative simplicity and a satisfactory performance on several test functions and applied problems, the DIRECT has been widely adopted in practical applications (see, e.g., [10,15,17,23,39,49,66,75,120]) and has attracted the attention of the researchers (for its theoretical and experimental analysis and several modifications see, e.g., [22,23,34,40,49,56,65,95]).…”

Section: Geometricmentioning

confidence: 99%

Univariate geometric Lipschitz global optimization algorithms

Kvasov¹,

Sergeyev²

2012

Numerical Algebra, Control &Amp; Optimization

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In this survey, univariate global optimization problems are considered where the objective function or its first derivative can be multiextremal black-box costly functions satisfying the Lipschitz condition over an interval. Such problems are frequently encountered in practice. A number of geometric methods based on constructing auxiliary functions with the usage of different estimates of the Lipschitz constants are described in the paper.

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“…[43][44][45][46][47][48][49] The algorithm optimizes functions using a decreasing sequence of finite difference steps to approximate the gradient. We have applied this method in the analysis of MEIS and CAICISS experiments through combination with ion scattering simulation codes.…”

Section: Structural Optimization Using Iffcomentioning

confidence: 99%

Structural analysis of the Cu(100)-p(2×2)-Sn surface using low and medium energy ion scattering spectroscopies

et al. 2011

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The atomic structure of the Cu(100)-p(2 × 2)-Sn surface has been studied using medium energy ion scattering (MEIS), co-axial impact collision ion scattering spectroscopy (CAICISS), low energy electron diffraction (LEED), and Auger electron spectroscopy (AES). The complex p(2 × 2)-based LEED pattern with antiphase domains was observed at an estimated Sn coverage of 0.21 ML, confirmed with AES. The existence of subsurface Sn atoms was immediately ruled out by the lack of blocking dips in the MEIS Sn scattered yield, whereas the initial analysis of the CAICISS data ruled out the three overlayer models, allowing quantitative fitting to focus on the Cu-Sn substitutional surface alloy model. The fitted model showed that the surface relaxed outward following Sn deposition and also demonstrated an out-of-plane shift of Sn atoms in the outermost layer.

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Untitled

Cited by 72 publications

References 27 publications

The DIRECT algorithm: 25 years Later

The DIRECT algorithm: 25 years Later

Univariate geometric Lipschitz global optimization algorithms

Structural analysis of the Cu(100)-p(2×2)-Sn surface using low and medium energy ion scattering spectroscopies

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