改进NSGA-Ⅲ的高维多目标柔性作业车间低碳调度方法研究

Research on low-carbon scheduling method for high-dimensional multi-objective flexible job shop improved by NSGA-Ⅲ

针对考虑低碳指标的柔性作业车间调度问题,建立了以碳排放量、机器能耗、完工时间和机器负载为优化目标的高维多目标柔性作业车间低碳调度(MaOFJLCSP)数学模型。鉴于NSGAⅢ在求解上述模型存在初始解质量差和易陷入局部最优的问题,提出一种改进NSGA-Ⅲ(NSGA-Ⅲ-HD)。首先,提出了一种基于混沌映射的实数编码机制,并在此基础上引入立方混沌映射对种群进行初始化,提高初始种群的质量;其次,设计了多种群精英存储的选择策略,在避免算法陷入局部最优的同时丰富了种群的多样性;最后,融合层次分析法和逼近理想解法(AHP-TOPSIS),选出一个更加全面且准确的调度方案。通过基准测试算例Brandimarte数据集和实例数据对改进算法进行验证对比,结果表明,NSGA-Ⅲ-HD在求解MaOFJLCSP时具有较高的优越性。

Aiming at the flexible job shop scheduling problem considering low-carbon indicators,a highdimensional multi-objective flexible job shop low-carbon scheduling(MaOFJLCSP)mathematical model with carbon emissions,machine energy consumption,completion time,and machine load as optimization objectives was established.In view of the problems that NSGA-Ⅲ has poor initial solution quality and is easy to fall into local optimality when solving the above model,an improved NSGA-Ⅲ(NSGA-Ⅲ-HD)is proposed.Firstly,a real number encoding mechanism based on chaos mapping is proposed,and on this basis,cubic chaos mapping is introduced to initialize the population and improve the quality of the initial population.Secondly,a selection strategy for multi-population elite storage is designed to avoid the algorithm falling into the local optimum also enriches the diversity of the population.Finally,the analytic hierarchy process and the approximate ideal solution method(AHP-TOPSIS)are integrated to select a more comprehensive and accurate scheduling plan.The improved algorithm was verified and compared through the benchmark test case Brandimarte data set and instance data.The results show that NSGA-Ⅲ-HD has high superiority in solving MaOFJLCSP.