Title: An Improved NSGA-II with local search for multi-objective energy-efficient flowshop scheduling problem Show Chinese title

Title: 一种带有局部搜索的改进型NSGA-II求解多目标节能流水车间调度问题

Abstract: There has been an increasing concern to reduce the energy consumption in manufacturing and other industries. Energy consumption in manufacturing industries is directly related to efficient schedules. The contribution of this paper includes: i) a permutation flowshop scheduling problem (PFLSP) mathematical model by considering energy consumed by each machine in the system. ii) an improved non-dominated sorted genetic algorithm with Taguchi method with further incorporating local search (NSGA-II_LS) is proposed for the multi-objective PFLSP model. iii) solved 90 benchmarks problems of Taillard (1993) for the minimisation of flowtime (FT) and energy consumption (EC). The performance of the proposed NSGA_LS algorithm is evaluated on the benchmark problems selected from the published literature Li et. al, (2018). From these results, it is noted that the proposed algorithm performed better on both the objectives i.e., FT and EC minimization in 5 out of 9 cases. On FT objective our algorithm performed better in 8 out of 9 cases and on EC objective 5 out of 9 cases. Overall, the proposed algorithm achieved 47% and 15.44% average improvement in FT and EC minimization respectively on the benchmark problems. From the results of 90 benchmark problems, it is observed that average difference in FT and EC between two solutions is decreasing as the problem size increases from 5 machines to 10 machines with an exception in one case. Further, it is observed that the performance of the proposed algorithm is better as the problem size increases in both jobs and machines. These results can act as standard solutions for further research. Show Chinese abstract

Abstract: 近年来，减少制造业及其他行业中的能源消耗问题引起了越来越多的关注。制造业中的能源消耗与高效的调度直接相关。本文的贡献包括：i）通过考虑系统中每台机器所消耗的能量，建立了一个排列流水车间调度问题（PFLSP）的数学模型；ii）提出了一种改进的非支配排序遗传算法，并结合田口方法和局部搜索（NSGA-II_LS），用于多目标PFLSP模型；iii）针对Taillard（1993年）提出的90个基准问题，解决了流时间（FT）和能源消耗（EC）最小化的问题。 所提出的NSGA_LS算法在从已发表文献中选取的基准问题上进行了评估，Li等人（2018年）。从这些结果可以看出，在9个案例中有5个案例中，所提出的算法在两个目标上表现更好，即FT和EC最小化。在FT目标上，我们的算法在9个案例中有8个表现更好，在EC目标上，有5个案例表现更好。总体而言，所提出的算法在基准问题上分别实现了47%和15.44%的平均改善，分别在FT和EC最小化方面。通过对90个基准问题的结果分析发现，在机器数量从5台增加到10台的情况下，除一个例外情况外，两个解之间的FT和EC平均差异逐渐减小。此外，观察到随着作业和机器数量的增加，所提出算法的性能也有所提高。这些结果可以作为进一步研究的标准解决方案。