This paper discusses a bi-criteria robust job-shop scheduling problem. Uncertain processing times are described by discrete scenario set. Two objectives are to minimize the mean makespan and to minimize the worst-case makespan among all scenarios, which reflect solution optimality and solution robustness, respectively. The NSGA-II algorithm framework is incorporated with local simulated annealing (SA) operators to solve the proposed problem. The Metropolis criterion is defined by considering two objectives in order to evaluate bi-criteria individuals. United-scenario neighborhood structure is used in local SA operators to adapt to the uncertainty described by scenarios. The developed hybrid algorithm was compared with four alternative algorithms to obtain Pareto solution sets for the proposed bi-criteria problem in an extensive experiment. The computational results show that the developed algorithm obviously outperformed other algorithms in all test instances.

中文翻译：

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场景下混合局部模拟退火算子的 NSGA-II 算法解决双准则鲁棒作业车间调度问题


本文讨论了双标准稳健作业车间调度问题。不确定的处理时间由离散场景集描述。两个目标是最小化所有场景中的平均完工时间和最小化最坏情况的完工时间，这分别反映了解决方案的最优性和解决方案的鲁棒性。 NSGA-II 算法框架与局部模拟退火 (SA) 算子相结合来解决所提出的问题。 Metropolis 标准是通过考虑两个目标来定义的，以便评估双标准个体。局部SA算子采用联合场景邻域结构来适应场景描述的不确定性。将所开发的混合算法与四种替代算法进行比较，以在广泛的实验中获得所提出的双标准问题的帕累托解集。计算结果表明，所开发的算法在所有测试实例中均明显优于其他算法。