Investigation of selection strategies in branch and bound algorithm with simplicial partitions and combination of Lipschitz bounds

Paulavičius, Remigijus; Žilinskas, Julius; Grothey, Andreas

doi:10.1007/s11590-009-0156-3

Cited by 58 publications

(22 citation statements)

References 18 publications

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“…It is easy to see that the expression (18) is a special case of (17). The criterion (17) can be used as a selection strategy in simplicial Lipschitz branch and bound algorithm improving its performance over usual selection strategies (Paulavičius et al 2010). By means of the same substitutions, (13) can be reduced to the following formula for the point of unconstrained minimum…”

Section: Theorem 1 the Unconditional Maximum Of U(x) Is Equal Tomentioning

confidence: 99%

P-algorithm based on a simplicial statistical model of multimodal functions

Žilinskas

2010

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Section: Theorem 1 the Unconditional Maximum Of U(x) Is Equal Tomentioning

confidence: 99%

P-algorithm based on a simplicial statistical model of multimodal functions

Žilinskas

2010

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“…The number of elements and the structure of the working set usually depend on the selection method used by the algorithm [28]. A stack or LIFO (Last In First Out) data structure is suitable for depth-first search.…”

Section: Introductionmentioning

confidence: 99%

On parallel Branch and Bound frameworks for Global Optimization

et al. 2017

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Branch and Bound (B&B) algorithms are known to exhibit an irregularity of the search tree. Therefore, developing a parallel approach for this kind of algorithms is a challenge. The efficiency of a B&B algorithm depends on the chosen Branching, Bounding, Selection, Rejection, and Termination rules. The question we investigate is how the chosen platform consisting of programming language, used libraries, or skeletons influences programming effort and algorithm performance. Selection rule and data management structures are usually hidden to programmers for frameworks with a high level of abstraction, as well as the load balancing strategy, when the algorithm is run in parallel. We investigate the question by implementing a multidimensional Global Optimization B&B algorithm with the help of three frameworks with a different level of abstraction (from more to less): Bobpp, Threading Building Blocks (TBB), and a customized Pthread implementation. The following has been found. The Bobpp implementation is easy to code, but exhibits the poorest scalability. On the contrast, the TBB and Pthread implementations scale almost linearly on the used platform. The TBB approach shows a slightly better productivity.

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“…Traditionally, such problems were solved by Lipschitz optimization methods [1], [2], [3], [4], [5], [6]. The Lipschitz global optimization method requires only a few parameters and this is the major reason why they are ideal for "blackbox" optimization problems.…”

Section: Introductionmentioning

confidence: 99%

A Parallel DISIMPL for Pile Placement Optimization in Grillage-Type Foundations

Paulavičius

Ilinskas

Herrera

et al. 2013

2013 Eighth International Conference on P2P, Parallel, Grid, Cloud and Internet Computing

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Recently it was shown, that proposed simplicial partition based DISIMPL algorithm gives very competitive results to well known DIRECT algorithm for standard test functions and performs particularly well when the search space and the numbers of local and global optimizers may be reduced by avoiding symmetries. However, the simplicial partition has a cost (except for the case where the original feasible region is a simplex): in order to use simplicial partitions hyper-rectangular feasible region should be covered by simplices. After initial covering 2 n objective function evaluations is performed for DISIMPL-V and n! for DISIMPL-C. This limits DISIMPL method to rather small dimensional problems. To increase the applicability of the DISIMPL algorithm to higher dimensional problems a parallel DISIMPL for multicore computers was created and investigated in this paper. The efficiency of the developed parallel algorithm is investigated solving up to 55 dimensional optimal design of grillage-type foundations "blackbox" optimization problem.

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Investigation of selection strategies in branch and bound algorithm with simplicial partitions and combination of Lipschitz bounds

Cited by 58 publications

References 18 publications

P-algorithm based on a simplicial statistical model of multimodal functions

P-algorithm based on a simplicial statistical model of multimodal functions

On parallel Branch and Bound frameworks for Global Optimization

A Parallel DISIMPL for Pile Placement Optimization in Grillage-Type Foundations

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