Abstract: According to the characteristics of Hybrid Flow-Shop Scheduling Problem (HFSP) based on energy saving,the energy consumption composition of HFSP was analyzed.Based on Wagner's modeling idea,a Mixed Integer Linear Programming (MILP) model with the aim of minimizing energy consumption was proposed,and an improved Migrating Birds Optimization (MBO) algorithm was used to solve this problem.In MBO,the initial population was generated randomly and four decoding methods were proposed.Based on critical path,two kinds of move strategies were designed,of which the purpose were to implement the machine turning off-on and to delay the start time of machine respectively.The leader and followers were evolved through the optimal exchange operation and the optimal insertion operation.By using MBO algorithm (with or not with move and machine turning off-on strategies) to test 41 instances,the results showed that the move and machine turning off-on strategies could greatly reduce the total energy consumption,and the effectiveness of MILP model and MBO algorithm were also proved.

Key words: hybrid flow-shop scheduling, energy consumption, mixed integer linear programming, migrating birds optimization algorithm

摘要： 针对面向节能的不相关并行机混合流水车间调度问题的特点,分析了混合流水车间的能耗组成,基于Wagner建模思想提出一种以最小化能耗为目标的混合整数线性规划模型,并提出一种改进的候鸟优化算法求解该问题。在候鸟优化算法中,采用随机策略生成初始种群,提出4种解码方法;基于关键路径的思想设计了两种移动策略,目的分别是调整空闲时间段使其可以实行关机重启策略,以及尽量延迟机床开机;该算法中领飞鸟和跟飞鸟通过最优交换操作和最优插入操作进行进化。通过41组实例对加入移动和关机重启策略的候鸟优化算法,以及没有加入移动和关机重启策略的候鸟优化算法进行测试,证明了所提移动和关机重启策略能够大幅度减少车间总能耗。同时,通过41组实例测试验证了所提模型和算法的有效性和可行性。

关键词: 混合流水车间调度, 能耗, 混合整数线性规划模型, 候鸟优化算法