解决具有连续性约束的并行处理器调度和垃圾箱打包问题:数学模型和计算研究

IF 6 2区 管理学 Q1 OPERATIONS RESEARCH & MANAGEMENT SCIENCE
Fatih Burak Akçay, Maxence Delorme
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引用次数: 0

摘要

具有连续性约束的并行处理器调度问题和垃圾箱打包问题在组合优化领域非常重要,因为这两个问题都可以作为若干二维打包问题的有效精确分解方法的组成部分。在本研究中,我们广泛回顾了这两个问题的现有数学公式,以及一些模型增强和下限技术,并使用最先进的求解器在大量文献实例集上对每个元素的计算行为进行了实证评估。我们还评估了中间相遇模式和反射表述等最新发展是否可用于更有效地解决这两个问题。我们的实验表明,某些特征(如所使用的数学模型)对一种方法能否解决实例有重大影响,而其他特征(如对称性约束的使用)尽管在理论上有用,但并没有带来任何经验上的优势。总之,我们的目标是帮助研究界设计出更有效、更简单的算法,以解决带有连续性约束的并行处理器调度和垃圾箱打包问题以及与之密切相关的扩展问题,从而最终将这些算法集成到更多的二维打包问题精确方法中。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Solving the parallel processor scheduling and bin packing problems with contiguity constraints: Mathematical models and computational studies
The parallel processor scheduling and bin packing problems with contiguity constraints are important in the field of combinatorial optimization because both problems can be used as components of effective exact decomposition approaches for several two-dimensional packing problems. In this study, we provide an extensive review of existing mathematical formulations for the two problems, together with some model enhancements and lower bounding techniques, and we empirically evaluate the computational behavior of each of these elements using a state-of-the-art solver on a large set of literature instances. We also assess whether recent developments such as meet-in-the middle patterns and the reflect formulation can be used to solve the two problems more effectively. Our experiments demonstrate that some features, such as the mathematical model used, have a major impact on whether an approach is able to solve an instance, whereas other features, such as the use of symmetry-breaking constraints, do not bring any empirical advantage despite being useful in theory. Overall, our goal is to help the research community design more effective yet simpler algorithms to solve the parallel processor scheduling and bin packing problems with contiguity constraints and closely related extensions so that, eventually, those can be integrated into a larger number of exact methods for two-dimensional packing problems.
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来源期刊
European Journal of Operational Research
European Journal of Operational Research 管理科学-运筹学与管理科学
CiteScore
11.90
自引率
9.40%
发文量
786
审稿时长
8.2 months
期刊介绍: The European Journal of Operational Research (EJOR) publishes high quality, original papers that contribute to the methodology of operational research (OR) and to the practice of decision making.
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