An Out-of-Core Branch and Bound Method for Solving the 0-1 Knapsack Problem on a GPU

2017 ◽  
pp. 254-267 ◽  
Author(s):  
Jingcheng Shen ◽  
Kentaro Shigeoka ◽  
Fumihiko Ino ◽  
Kenichi Hagihara
Keyword(s):  
Branch And Bound ◽  
Knapsack Problem ◽  
Branch And Bound Method

scholarly journals Computational Enhancement in the Application of the Branch and Bound Method for Linear Integer Programs and Related Models

2019 ◽  
Vol 4 (5) ◽  
pp. 1140-1153
Author(s):  
Masar Al-Rabeeah ◽  
Elias Munapo ◽  
Ali Al-Hasani ◽  
Santosh Kumar ◽  
Andrew Eberhard
Keyword(s):  
Branch And Bound ◽  
Knapsack Problem ◽  
Upper Bound ◽  
Computational Experiments ◽  
Branch And Bound Method ◽  
Integer Programs ◽  
Before And After

In this paper, a reformulation that was proposed for a knapsack problem has been extended to single and bi-objective linear integer programs. A further reformulation by adding an upper bound constraint for a knapsack problem is also proposed and extended to the bi-objective case. These reformulations significantly reduce the number of branch and bound iterations with respect to these models. Numerical illustrations have been presented and computational experiments have been carried out to compare the behaviour before and after the reformulation. For this purpose, Tora software was used.

scholarly journals PARALLEL IMPLEMENTATION OF THE COMBINED ALGORITHM OF THE BRANCH AND BOUND METHOD

2020 ◽  
pp. 437-439
Author(s):  
Valeriy Ivaschenko ◽  
Gennady Shvachych ◽  
Vladimir Konovalenkov ◽  
Vladimir Khristyan
Keyword(s):  
Distributed Computing ◽  
Branch And Bound ◽  
Knapsack Problem ◽  
Heuristic Search ◽  
Parallel Implementation ◽  
Branch And Bound Algorithm ◽  
Specific Class ◽  
Branch And Bound Method ◽  
Common Solution ◽  
Combined Algorithm

Parallel implementation of a combined branch-and-bound algorithm for the knapsack problem are considered. An approach combining parallel implementations of the branch-and-bound method and the heuristic search is proposed and implemented. Basic attention is focused on the questions of research of efficiency and acceleration for calculations due to the increase of the cluster system knots. As a result of the proposed approach, a organization scheme of the combined algorithm of distributed computing was obtained. The approach proposed in this paper saves the developers’ efforts by reapplying common parts of the algorithm to solve various problems of optimization. In fact, one can implement a common solution scheme for different platforms once, and later use only problem-dependent modules for a specific class of problems.

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