发表机构
University of Fribourg; Université de Haute-Alsace（弗里堡大学; 上阿尔萨斯大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文研究带冲突图约束的作业车间调度问题，明确其计算复杂性，开发混合整数线性模型与下界，提出遗传算法，通过基准及随机实例验证了所提方法的性能。
AI 中文摘要
我们研究带冲突图的作业车间调度问题（JSC），其中冲突图中相邻的作业不能在不同机器上同时加工，目标是最小化最大完成时间（makespan）。该问题对作业共享额外资源同时保留各自机器工艺路线的场景进行建模。我们首先研究其计算复杂性，建立JSC与带单位容量资源的资源受限作业车间问题变体之间的多项式等价关系。尽管两台机器上的一般问题是NP难的，但我们确定了一个多项式可解的特殊情况。对于一般问题，我们开发了基于优先关系和时间索引的混合整数线性规划模型，以及最大完成时间的下界。我们还提出了一种使用带重复排列编码的遗传算法，以及主动、非延迟和混合调度评估程序。对源自Lawrence和Taillard基准的实例，以及随机生成的广义作业车间实例进行了计算实验，以评估所提出的模型、下界和遗传算法的性能。
英文摘要
We study the job shop scheduling problem with a conflict graph (JSC), in which adjacent jobs in the conflict graph cannot be processed simultaneously on different machines, with the objective of minimizing the makespan. The problem models settings where jobs share additional resources while retaining their individual machine routings. We first investigate its computational complexity and establish a polynomial equivalence between JSC and a variant of the resource-constrained job shop problem with unit-capacity resources. Although the general problem on two machines is NP-hard, we identify a polynomially solvable special case. For the general problem, we develop precedence-based and time-indexed mixed-integer linear formulations, along with lower bounds on the makespan. We also propose a genetic algorithm using permutation-with-repetition encoding and active, non-delay, and hybrid schedule evaluation procedures. Computational experiments on instances derived from the Lawrence and Taillard benchmarks, as well as randomly generated generalized job shop instances, are conducted to evaluate the performance of the proposed formulations, lower bounds, and genetic algorithm.
