MrDIRECT: a multilevel robust DIRECT algorithm for global optimization problems

Liu, Qunfeng; Zeng, Jinshan; Yang, Gang

doi:10.1007/s10898-014-0241-8

Cited by 20 publications

(21 citation statements)

References 21 publications

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“…To improve the inefficient behavior of the PBA, the authors in [32] combine the PBA with a multigrid algorithm. The work in [33] applies a multigrid approach to the robust version of DIRECT algorithm [31], obtaining a multilevel robust DIRECT (MrDIRECT) algorithm. Although additional parameters are required by this new version, the authors show that the MrDIRECT is insensitive to the parameters.…”

Section: Direct-type Methodsmentioning

confidence: 99%

“…The local optimizer aims to reduce the value of f min which, by affecting the selection of hyperrectangles, improves the global search capability. At the same time, choosing a larger value of ε will directly improve the global search [33].…”

Section: Direct-type Methodsmentioning

confidence: 99%

“…In this paper, we aim to integrate the filter methodology into a DIRECT-type method algorithm for solving CGO problems. The derivative-free and deterministic global optimizer DIRECT [27] is a partition-based algorithm [34] that identifies potential optimal hyperrectangles and divides them further to produce finer and finer partitions of the hyperrectangles [17,18,21,26,30,33]. It has been shown that the set of points sampled by the DIRECT algorithm is dense in the search space [27].…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Filter-based DIRECT method for constrained global optimization

Costa

Rocha

Fernandes³

2017

J Glob Optim

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This paper presents a DIRECT-type method that uses a filter methodology to assure convergence to a feasible and optimal solution of nonsmooth and nonconvex constrained global optimization problems. The filter methodology aims to give priority to the selection of hyperrectangles with feasible center points, followed by those with infeasible and non-dominated center points and finally by those that have infeasible and dominated center points. The convergence properties of the algorithm are analyzed. Preliminary numerical experiments show that the proposed filter-based DIRECT algorithm gives competitive results when compared with other DIRECT-type methods.

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Section: Direct-type Methodsmentioning

confidence: 99%

Section: Direct-type Methodsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Filter-based DIRECT method for constrained global optimization

Costa

Rocha

Fernandes³

2017

J Glob Optim

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“…Liu et al [38,39] address the weakness of global drag and slow refinement of local optima with an idea that, in spirit, is the same as the revised DIRECT by Jones discussed in the previous section. Namely, they use a local optimizer to fine tune solutions.…”

Section: Multilevel Direct (Mrdirect and Mrdirect 075 )mentioning

confidence: 99%

“…However, DIRECT has been found to be less competitive on higher-dimensional problems [47]. Moreover, many authors have noticed the tendency for DIRECT to get close to the global optimum quickly, but take a long time to refine the solution to high accuracy [38,39,51,63].…”

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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