arXivDaily arXiv每日学术速递 周一至周五更新
arXiv 2006.08327cs.AImath.OC
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离散并行机器调度选址问题的精确与启发式方法

Exact and heuristic methods for the discrete parallel machine scheduling location problem

Universidade Federal de Pernambuco(伯南布哥联邦大学);Universidade Federal do Rio Grande do Norte(北里奥格兰德联邦大学)

Raphael Kramer, Arthur Kramer

AI总结:

研究离散并行机器调度选址问题,提出弧流公式、列生成算法及三种启发式方法,通过框架算法求解,在基准实例中找到最优解,并在新实例中取得较小差距。

摘要:

离散并行机器最大完工时间调度选址(ScheLoc)问题是一个结合了设施选址与作业调度的集成组合优化问题。该问题在于从有限候选集中选择 $p$ 台机器的位置,并在这些机器上调度一组作业,旨在最小化最大完工时间。根据机器位置的不同,作业可能具有不同的释放时间,因此选址决策直接影响调度决策。为求解该问题,提出了一种新的弧流公式、一种列生成算法和三种启发式过程,并通过广泛的计算实验进行评估。通过将所提过程嵌入框架算法中,我们能够为相关文献中的所有基准实例找到已证明的最优解,并为新的挑战性实例集获得较小的百分比差距。

英文摘要:

The discrete parallel machine makespan scheduling location (ScheLoc) problem is an integrated combinatorial optimization problem that combines facility location and job scheduling. The problem consists in choosing the locations of $p$ machines among a finite set of candidates and scheduling a set of jobs on these machines, aiming to minimize the makespan. Depending on the machine location, the jobs may have different release dates, and thus the location decisions have a direct impact on the scheduling decisions. To solve the problem, it is proposed a new arc-flow formulation, a column generation and three heuristic procedures that are evaluated through extensive computational experiments. By embedding the proposed procedures into a framework algorithm, we are able to find proven optimal solutions for all benchmark instances from the related literature and to obtain small percentage gaps for a new set of challenging instances.

机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。

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