Flowshop scheduling with improved NSGA-II

In order to test the feasibility and effectiveness of the algorithm in this paper, NSGA-II-ALS was compared with several other genetic algorithms in experiments to analyze the performance of multiple groups of different algorithms.The standard processing times for workpieces on machines are shown in Table 2 'Standard processing schedule'.The objective function values and scheduling order of sparse points obtained by the three algorithms are shown in Table 3 'The optimal solutions obtained by different algorithms'.The Pareto fronts obtained by using the three algorithms for different values is shown in Table 4 ' The Pareto fronts of different algorithms'.For the Pareto fronts obtained by the three algorithms, the spacing distribution SD and the scattering range index SS were calculated. The details are shown in Table 5 'Comparison of evaluation indicators'.

为验证本文所提算法的可行性与有效性，本研究通过实验将 NSGA-II-ALS 算法与其他几种遗传算法进行对比，以分析不同算法组别间的性能表现。表 2 '标准加工时间表' 展示了机床上工件的标准加工时间。表 3 '不同算法获得的最佳解' 展示了三种算法获得的稀疏点目标函数值及调度顺序。表 4 '不同算法的 Pareto 前沿' 展示了采用三种算法针对不同值获得的 Pareto 前沿。针对三种算法获得的 Pareto 前沿，计算了间距分布 SD 和散布范围指数 SS。具体细节见表 5 '评估指标对比'。