DO INHERENTLY SEQUENTIAL BRANCH-AND-BOUND ALGORITHMS EXIST?

In the construction of algorithms for [Formula: see text] optimization problems the Branch-and-Bound paradigm is an essential tool. Furthermore, Branch-and-Bound algorithms are traditionally regarded as well suited for parallel implementation due to the subdivision of the problem considered into essentially independent subproblems. In this paper we present experimental results for a Branch-and-Bound algorithm for the Graph Partitioning Problem showing that the traditional parallelization of a Branch-and-Bound algorithm does not always lead to an efficient parallel algorithm. The main reason seems to be lack of meaningful work, i.e. concurrent existence of subproblems which have to be solved to ensure optimality of the solution. We support this claim with experimental results.

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Implementation of parallel branch-and-bound algorithms – experiences with the graph partitioning problem

Annals of Operations Research ◽

10.1007/bf02073939 ◽

1991 ◽

Vol 33 (5) ◽

pp. 329-349 ◽

Cited By ~ 16

Author(s):

Jens Clausen ◽

Jesper Larsson Träff

Keyword(s):

Branch And Bound ◽

Graph Partitioning ◽

Branch And Bound Algorithms ◽

Graph Partitioning Problem ◽

Parallel Branch And Bound ◽

Partitioning Problem

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GLOBAL OPTIMIZATION USING THE BRANCH‐AND‐BOUND ALGORITHM WITH A COMBINATION OF LIPSCHITZ BOUNDS OVER SIMPLICES

Technological and Economic Development of Economy ◽

10.3846/1392-8619.2009.15.310-325 ◽

2009 ◽

Vol 15 (2) ◽

pp. 310-325 ◽

Cited By ~ 11

Author(s):

Remigijus Paulavičius ◽

Julius Žilinskas

Keyword(s):

Global Optimization ◽

Branch And Bound ◽

Optimization Problems ◽

The Other ◽

Branch And Bound Algorithm ◽

Global Optimization Algorithm ◽

Lipschitz Optimization ◽

Branch And Bound Algorithms ◽

Simple Bounds ◽

Branch And Bound Techniques

Many problems in economy may be formulated as global optimization problems. Most numerically promising methods for solution of multivariate unconstrained Lipschitz optimization problems of dimension greater than 2 use rectangular or simplicial branch‐and‐bound techniques with computationally cheap, but rather crude lower bounds. The proposed branch‐and‐bound algorithm with simplicial partitions for global optimization uses a combination of 2 types of Lipschitz bounds. One is an improved Lipschitz bound with the first norm. The other is a combination of simple bounds with different norms. The efficiency of the proposed global optimization algorithm is evaluated experimentally and compared with the results of other well‐known algorithms. The proposed algorithm often outperforms the comparable branch‐and‐bound algorithms. Santrauka Daug įvairių ekonomikos uždavinių yra formuluojami kaip globaliojo optimizavimo uždaviniai. Didžioji dalis Lipšico globaliojo optimizavimo metodų, tinkamų spręsti didesnės dimensijos, t. y. n > 2, uždavinius, naudoja stačiakampį arba simpleksinį šakų ir rėžių metodus bei paprastesnius rėžius. Šiame darbe pasiūlytas simpleksinis šakų ir rėžių algoritmas, naudojantis dviejų tipų viršutinių rėžių junginį. Pirmasis yra pagerintas rėžis su pirmąja norma, kitas – trijų paprastesnių rėžių su skirtingomis normomis junginys. Gautieji eksperimentiniai pasiūlyto algoritmo rezultatai yra palyginti su kitų gerai žinomų Lipšico optimizavimo algoritmų rezultatais.

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A New Coarsening Strategy for Multilevel Graph Partitioning

Advanced Materials Research ◽

10.4028/www.scientific.net/amr.490-495.504 ◽

2012 ◽

Vol 490-495 ◽

pp. 504-508

Author(s):

Lu Yao ◽

Zheng Hua Wang ◽

Wei Cao ◽

Zong Zhe Li

Keyword(s):

Theoretical Analysis ◽

Graph Partitioning ◽

State Of The Art ◽

Poor Quality ◽

The State ◽

Experimental Results ◽

Multilevel Algorithms ◽

Graph Partitioning Problem ◽

Partitioning Problem ◽

Multilevel Graph Partitioning

When applying multilevel scheme to solve the graph partitioning problem, shortcomings and limitations exist in the state-of-the-art coarsening schemes depend mainly on finding maximal matchings to obtain the coarse graphs, which can cause the multilevel algorithms to produce poor-quality solutions. This paper proposes an improved coarsening scheme by improving vertex combining strategy and edge ordering criteria. The new coarsening scheme is more effective in quality, which is proved by both theoretical analysis and experimental results.

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