This paper addresses a permutation flowshop scheduling problem, with the objective of minimizing total weighted squared tardiness. The focus is on providing efficient procedures that can quickly solve medium or even large instances. Within this context, we first present multiple dispatching heuristics. These include general rules suited to various due date-related environments, heuristics developed for the problem with a linear objective function, and procedures that are suitably adapted to take the squared objective into account. Then, we describe several improvement procedures, which use one or more of three techniques. These procedures are used to improve the solution obtained by the best dispatching rule. Computational results show that the quadratic rules greatly outperform the linear counterparts, and that one of the quadratic rules is the overall best performing dispatching heuristic. The computational tests also show that all procedures significantly improve upon the initial solution. The non-dominated procedures, when considering both solution quality and runtime, are identified. The best dispatching rule, and two of the non-dominated improvement procedures, are quite efficient, and can be applied to even very large-sized problems. The remaining non-dominated improvement method can provide somewhat higher quality solutions, but it may need excessive time for extremely large instances.

中文翻译：

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加权平方拖延置换流水车间调度问题的有效程序

本文针对置换流水车间调度问题，以最小化总加权平方拖延为目标。重点是提供可以快速解决中型甚至大型实例的有效程序。在这种情况下，我们首先介绍多种调度启发式方法。这些规则包括适用于各种与截止日期相关的环境的一般规则，针对具有线性目标函数的问题而开发的试探法，以及适合于考虑平方目标的过程。然后，我们描述了几种改进程序，它们使用了三种技术中的一种或多种。这些过程用于改进通过最佳调度规则获得的解决方案。计算结果表明，二次规则大大优于线性规则，二次规则之一是整体上表现最佳的启发式算法。计算测试还表明，在初始解决方案上，所有过程都得到了显着改善。在考虑解决方案质量和运行时间时，应确定非主导过程。最佳调度规则以及两个非主导的改进过程非常有效，甚至可以应用于非常大的问题。其余的非主要改进方法可以提供质量更高的解决方案，但是对于超大型实例，可能需要花费大量时间。最佳调度规则以及两个非主导的改进过程非常有效，甚至可以应用于非常大的问题。其余的非主要改进方法可以提供质量更高的解决方案，但是对于超大型实例，可能需要花费大量时间。最佳调度规则以及两个非主导的改进过程非常有效，甚至可以应用于非常大的问题。其余的非主要改进方法可以提供质量更高的解决方案，但是对于超大型实例，可能需要花费大量时间。