Abstract: Energy costs and production efficiency are key factors in smart manufacturing.In order to reduce electricity costs while improving production efficiency,by taking the Distributed Flexible Flow-shop Scheduling Problem (DFFSP) as the objective,the characteristics of DFFSP were analyzed.Considering the constraint of the Time-of-Use(TOU)electricity tariffs,an integer programming model of DFFSP-TOU was formulated with the objectives of minimizing makespan and total energy consumption.A Multi-objective Learning Monarch Butterfly Optimization algorithm (MOLMBO) based on self-learning mechanism was proposed according to the characteristics of DFFSP-TOU,in which the migration operator and adjusting operator were generated by the information of historical optimal solutions to enhance self-learning and the adaptive ability.Furthermore,the variable neighborhood search strategy was used to improve the performance of local search and enhance the diversity of population.In addition,the right-shift operation was applied to transfer the production from the peak times to reduce the energy consumption.The performance of the proposed algorithm was verified on benchmark problems,the experimental results showed that the MOLMBO was an effective method in addressing DFFSP.

Key words: time-of-use electricity tariffs, distributed flexible flow-shop scheduling, multi-objective optimization, monarch butterfly optimization algorithm, learning mechanism

摘要： 能源成本和生产效率是智能制造的关键,为了在降低电力成本的同时提升生产效率,以分布式制造环境下的柔性流水车间调度问题作为研究对象(DFFSP),重点分析了分布式柔性流水车间调度问题的特性,考虑分时电价(TOU)约束,以最小化最大完工时间和总电力成本为优化指标,建立了DFFSP-TOU问题整数规划模型,根据分时电价下分布式柔性流水车间调度问题特性DFFSP-TOU,提出一种基于自学习机制的多目标帝王蝶优化算法(MOLMBO)。算法的迁移算子和调整算子通过历史最优解的信息自学习生成,以增强该算法的自学习、自适应能力;采用变邻域搜索来提高算法的局部搜索性能和种群多样性;通过右移操作将电价区间在高峰时段的生产转移到电价区间在低谷时段进行生产,减少机器在待机状态下的能耗,进而降低电力成本。实验结果表明MOLMBO算法是求解分布式柔性流水车间调度问题的一种有效的方法。

关键词: 分时电价, 分布式柔性流水车间调度, 多目标优化算法, 帝王蝶优化算法, 学习机制