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Open AccessArticle

A Multi-Branch-and-Bound Binary Parallel Algorithm to Solve the Knapsack Problem 0–1 in a Multicore Cluster

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Faculty of Accounting, Administration & Informatics, UAEM, Avenida Universidad 1001 Colonia Chamilpa, C.P. 62209 Cuernavaca, Mexico
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Research Center in Engineering and Applied Sciences, Autonomous University of Morelos State (UAEM), Avenida Universidad 1001 Colonia Chamilpa, C.P. 62209 Cuernavaca, Mexico
3
Department of Research and Technological Development (IDT), Emiliano Zapata Technological University of Morelos State, C. P. 62760 Emiliano Zapata, Mexico
*
Author to whom correspondence should be addressed.
Appl. Sci. 2019, 9(24), 5368; https://doi.org/10.3390/app9245368
Received: 8 October 2019 / Revised: 2 December 2019 / Accepted: 3 December 2019 / Published: 9 December 2019
(This article belongs to the Section Computing and Artificial Intelligence)
This paper presents a process that is based on sets of parts, where elements are fixed and removed to form different binary branch-and-bound (BB) trees, which in turn are used to build a parallel algorithm called “multi-BB”. These sequential and parallel algorithms calculate the exact solution for the 0–1 knapsack problem. The sequential algorithm solves the instances published by other researchers (and the proposals by Pisinger) to solve the not-so-complex (uncorrelated) class and some problems of the medium-complex (weakly correlated) class. The parallel algorithm solves the problems that cannot be solved with the sequential algorithm of the weakly correlated class in a cluster of multicore processors. The multi-branch-and-bound algorithms obtained parallel efficiencies of approximately 75%, but in some cases, it was possible to obtain a superlinear speedup. View Full-Text
Keywords: uncorrelated; weakly correlated; superlinear speedup uncorrelated; weakly correlated; superlinear speedup
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Zavala-Díaz, J.C.; Cruz-Chávez, M.A.; López-Calderón, J.; Hernández-Aguilar, J.A.; Luna-Ortíz, M.E. A Multi-Branch-and-Bound Binary Parallel Algorithm to Solve the Knapsack Problem 0–1 in a Multicore Cluster. Appl. Sci. 2019, 9, 5368.

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