The Job-shop Scheduling Problem (JSP) is a well-known and challenging combinatorial optimization problem in which tasks sharing a machine are to be arranged in a sequence such that encompassing jobs can be completed as early as possible. In this paper, we propose problem decomposition into time windows whose operations can be successively scheduled and optimized by means of multi-shot Answer Set Programming (ASP) solving. Decomposition aims to split highly complex scheduling tasks into better manageable sub-problems with a balanced number of operations so that good quality or even optimal partial solutions can be reliably found in a small fraction of runtime. Problem decomposition must respect the precedence of operations within their jobs and partial schedules optimized by time windows should yield better global solutions than obtainable in similar runtime on the entire instance. We devise and investigate a variety of decomposition strategies in terms of the number and size of time windows as well as heuristics for choosing their operations. Moreover, we incorporate time window overlapping and compression techniques into the iterative scheduling process to counteract window-wise optimization limitations restricted to partial schedules. Our experiments on JSP benchmark sets of several sizes show that successive optimization by multi-shot ASP solving leads to substantially better schedules within the runtime limit than global optimization on the full problem, where the gap increases with the number of operations to schedule. While the obtained solution quality still remains behind a state-of-the-art Constraint Programming system, our multi-shot solving approach comes closer the larger the instance size, demonstrating good scalability by problem decomposition.
翻译:工作商店日程安排问题(JSP)是一个众所周知且具有挑战性的组合优化问题,在这一问题中,共享机器的任务将被排列成能够尽早完成包括工作的任务的顺序。在本文件中,我们建议将问题分解成时间窗口,其操作可以相继安排,并通过多镜头回答设置编程(ASP)解决优化。分解的目的是将高度复杂的日程安排任务分为更易于管理的子问题,同时有均衡的业务数量,这样在运行的一小部分时间里才能可靠地找到优质甚至最佳的局部解决方案。 问题分解必须尊重其工作中的优先业务,而通过时间窗口优化优化而优化的部分时间表应产生比在整个运行的类似时间可以获得的更好的全球解决方案。我们设计并调查了多种拆分解战略,从时间窗口的数量和大小以及选择其操作的超自然学性。此外,我们仍然将时间窗口重叠和压缩技术纳入迭代时间安排进程,以抵消窗口对窗口的优化限制,但仅限于部分时间表。我们在几个更近距离的系统内进行的实验将更接近于更精确的流程,从而通过多镜头来大幅优化全球的流程安排。