In an online environment, jobs arrive over time and there is no information in advance about how many jobs are going to be processed and what their processing times are going to be. In this paper, we study the online scheduling of Boolean Satisfiability (SAT) and Mixed Integer Programming (MIP) instances that are well-known NP-complete problems. Typical online machine scheduling approaches assume that jobs are completed at some point in order to minimize functions related to completion time (e.g., makespan, minimum lateness, total weighted tardiness, etc). In this work, we formalize and present an online over time problem where arriving instances are subject to waiting time constraints. We propose computational approaches that combine the use of machine learning, MIP, and instance interruption heuristics. Unlike other approaches, we attempt to maximize the number of solved instances using single and multiple machine configurations. Our empirical evaluation with well-known SAT and MIP instances, suggest that our interruption heuristics can improve generic ordering policies to solve up to 21.6x and 12.2x more SAT and MIP instances. Additionally, our hybrid approach observed up to 90% of solved instances with respect to a semi clairvoyant policy (SCP).

中文翻译：

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随着时间的推移在线处理组合问题

在在线环境中，作业会随时间到达，并且事先没有有关要处理多少个作业以及它们将要处理的时间的信息。在本文中，我们研究了布尔可满足性（SAT）和混合整数编程（MIP）实例的在线调度，这些实例是众所周知的NP完全问题。典型的在线机器调度方法假设作业在某个时间点完成，以最小化与完成时间有关的功能（例如，制造时间，最小延迟，总加权拖延时间等）。在这项工作中，我们形式化并提出了在线超时问题，其中到达的实例受到等待时间的约束。我们提出了将机器学习，MIP和实例中断启发式方法结合使用的计算方法。与其他方法不同 我们尝试使用单机和多机配置最大化已解决实例的数量。我们对著名的SAT和MIP实例进行的经验评估表明，我们的中断启发法可以改善通用排序策略，以解决多达SAT和MIP实例21.6倍和12.2倍的问题。此外，就半透视策略（SCP）而言，我们的混合方法最多可解决90％的已解决实例。