Abstract: For a dual-resource flexible job shop scheduling problem where multiple workers may be required to collaborate on each machine,a flexible job shop scheduling problem with worker collaboration flexibility was investigated.Combining the influence of learning effect on workers,an improved learning effect curve of worker skill flexibility was proposed.A mathematical model with maximum completion time,total worker load and total energy consumption minimization as the optimization objectives was established,and an Improved NSGA-II (INSGA-II) was proposed for solving the problem.Four initialization rules to improve the quality and diversity of initial populations were designed,and the adaptive crossover and mutation operators based on Pareto rank were established.To improve the local search capability of the algorithm,three neighborhood search operators based on the optimization objective were constructed.Multiple evaluation metrics were used in the experimental part to compare with the other algorithms,and the experimental results showed that the proposed algorithm was able to effectively solve the dual-resource flexible job shop scheduling problem with workers collaboration and learning effect.

Key words: worker collaborative flexibility, learning effect, non-dominated sorted genetic algorithm-II, dual-resource flexible job shop scheduling problem

摘要： 针对每台机器存在需要多名工人协作操作的双资源柔性作业车间调度问题,研究一种具有工人协作灵活性的柔性作业车间调度问题。结合学习效应对工人操作时间的影响,构建一种改进的工人技能柔性度的学习效应曲线;建立以最大完工时间、工人总负载和总能耗最小化为优化目标的数学模型,并提出一种改进的非支配排序遗传算法进行求解。设计4种初始化规则提高初始种群的质量和多样性,建立基于Pareto等级的自适应交叉、变异算子;为了提高算法的局部搜索能力,构造了3种基于优化目标的邻域搜索算子。在实验部分采用多种评价指标与其他算法进行对比,实验结果表明该算法能够有效求解考虑工人协作与学习效应的双资源柔性作业车间调度问题。

关键词: 工人协作灵活性, 学习效应, 非支配排序遗传算法, 双资源柔性作业车间调度问题