Parallelization of a Branch and Bound Algorithm on Multicore Systems

Abstract

The general m-machine permutation flowshop problem with the total flow-time objective is known to be NP-hard for m ≥ 2. The only practical method for finding optimal solutions has been branch-and-bound algorithms. In this paper, we present an improved sequential algorithm which is based on a strict alternation of Generation and Exploration execution modes as well as Depth-First/Best-First hybrid strategies. The experimental results show that the proposed scheme exhibits improved performance compared with the algorithm in [1]. More importantly, our method can be easily extended and implemented with lightweight threads to speed up the execution times. Good speedups can be obtained on shared-memory multicore systems.

Scalable Distributed Branch and Bound for the Permutation Flow Shop Problem

“…Some other works were interested on solving the PFSP by using different distributed environments, such as, C. Chung et al, who implemented a parallel B&B Algorithm on Multicore Systems [4] and conducted several experiments using random problems to test the effectiveness of their algorithm. Unlike the algorithm presented in [4], M. Ancau in his paper [11], used benchmarks of Taillard to test his algorithm. However, he did not give optimal solutions for all tested instances since he used approximate methods of resolution.…”

A parallel graph edit distance algorithm

“…A master-slave hybrid Depth-First/Best-First was proposed in (Chung et al, 2012). The master thread keeps generating the tree nodes at a predetermined level (i.e., level i) and saves them to a work pool.…”

“…The approaches in (Rao and Kumar, 1987), (Chung et al, 2012) and (Neary and Cappello, 2005) are interesting since the communication is asynchronous 2 and thus there is no need to stop a thread if it did not finish its tasks, unless another thread ran out of tasks. In (Chung et al, 2012), however, load balancing is not integrated. Thus, when there are no more problems to be generated by the master thread, some threads might become idle for a certain amount of time while waiting the other threads to finish their associated tasks.…”