, Volume 23, Issue 3, pp 310–334 | Cite as

Online over time processing of combinatorial problems

  • Robinson DuqueEmail author
  • Alejandro Arbelaez
  • Juan F. Díaz
Part of the following topical collections:
  1. Topical Collection on Integration of Constraint Programming, Artificial Intelligence, and Operations Research


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).


Online scheduling Combinatorial problems Machine learning Regression models Classification models Runtime estimation Mixed integer programming 



The authors would like to thank the anonymous reviewers for their comments and suggestions which helped to improve the paper. Robinson Duque is supported by the Universidad del Valle and also by Colciencias, the Colombian Administrative Department of Science, Technology and Innovation under the PhD scholarship program.


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© Springer Science+Business Media, LLC, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Universidad del ValleCaliColombia
  2. 2.Cork Institute of TechnologyCorkIreland

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