A multi-objective scheduling problem with specified release times and due dates for individual tasks is analysed in this study. Distinct tardiness value of each task j comprises the part of the objective, while it is desired to identify all non-dominated solutions. Tardiness values for a total number of n tasks complete a single solution making it an n-objective scheduling problem. Tardiness is treated here as a task specific objective, being different in the usual scheduling context. A branch and bound procedure is proposed for individual tardiness of tasks in multi-objective contexts. The procedure is illustrated with an example. Active schedule enumeration scheme with depth-first strategy for branching is used in branching while two different bounding schemes are tested. However, an improved bounding scheme to find better-quality need to be developed. Procedure is found to perform well on small scale problems. For an n-objective problem like this, a more robust data structure may further improve the performance of the procedure.

中文翻译：

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基于个人作业延迟的单机调度问题

在这项研究中分析了具有指定发布时间和各个任务的到期日的多目标计划问题。每个任务j的不同拖延值包括目标的一部分，同时希望识别所有非支配的解决方案。总共n个任务的延迟值完成了一个解决方案，使其成为n目标调度问题。拖延在这里被视为任务特定的目标，在通常的调度上下文中有所不同。针对多目标上下文中任务的个别拖延，提出了分支定界过程。举例说明该过程。在分支中使用具有深度优先策略的主动调度枚举方案，同时测试了两种不同的边界方案。但是，需要开发一种改进的边界方案以找到更好的质量。发现该程序在小规模问题上表现良好。对于这样的n目标问题，更健壮的数据结构可以进一步提高过程的性能。