Advertisement

Constraints

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

Online over time processing of combinatorial problems

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

Abstract

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).

Keywords

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

Notes

Acknowledgments

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.

References

  1. 1.
    Anderson, E.J., & Potts, C.N. (2004). Online scheduling of a single machine to minimize total weighted completion time. Mathematics of Operations Research, 29(3), 686–697.MathSciNetCrossRefzbMATHGoogle Scholar
  2. 2.
    Arpaci-Dusseau, R.H., & Arpaci-Dusseau, A.C. (2014). Operating systems: three easy pieces, chap. Scheduling: Introduction. Arpaci-Dusseau Books.Google Scholar
  3. 3.
    Bartz-Beielstein, T., & Markon, S. (2004). Tuning search algorithms for real-world applications: a regression tree based approach. In Congress on evolutionary computation, 2004. CEC2004, (Vol. 1 pp. 1111–1118). IEEE.Google Scholar
  4. 4.
    Breiman, L. (2001). Random forests. Machine Learning, 45(1), 5–32.CrossRefzbMATHGoogle Scholar
  5. 5.
    Chan, W.T., Chin, F.Y., Ye, D., Zhang, G., Zhang, Y. (2008). On-line scheduling of parallel jobs on two machines. Journal of Discrete Algorithms, 6(1), 3–10.MathSciNetCrossRefzbMATHGoogle Scholar
  6. 6.
    Deng, K., Song, J., Ren, K., Iosup, A. (2013). Exploring portfolio scheduling for long-term execution of scientific workloads in iaas clouds. In Proceedings of the international conference on high performance computing, networking, storage and analysis (p. 55). ACM.Google Scholar
  7. 7.
    Deng, K., Song, J., Ren, K., Iosup, A. (2013). Exploring portfolio scheduling for long-term execution of scientific workloads in iaas clouds. In SC.Google Scholar
  8. 8.
    Deng, K., Verboon, R., Ren, K., Iosup, A. (2013). A periodic portfolio scheduler for scientific computing in the data center. In Workshop on job scheduling strategies for parallel processing (pp. 156–176). Springer.Google Scholar
  9. 9.
    Duque, R., Arbelaez, A., Díaz, J.F. (2017). Off-line and on-line scheduling of SAT instances with time processing constraints, (pp. 524–539). Cham: Springer International Publishing.Google Scholar
  10. 10.
    Graham, R.L., Lawler, E.L., Lenstra, J.K., Kan, A.R. (1979). Optimization and approximation in deterministic sequencing and scheduling: a survey. Annals of Discrete Mathematics, 5, 287–326.MathSciNetCrossRefzbMATHGoogle Scholar
  11. 11.
    Heule, M.J.H., Kullmann, O., Marek, V.W. (2016). Solving and verifying the boolean pythagorean triples problem via cube-and-conquer. In SAT.Google Scholar
  12. 12.
    Hurink, J.L., & Paulus, J.J. (2008). Online scheduling of parallel jobs on two machines is 2-competitive. Operations Research Letters, 36(1), 51–56.MathSciNetCrossRefzbMATHGoogle Scholar
  13. 13.
    Hutter, F., Xu, L., Hoos, H.H., Leyton-Brown, K. (2014). Algorithm runtime prediction: methods & evaluation. Artificial Intelligence, 206, 79–111.MathSciNetCrossRefzbMATHGoogle Scholar
  14. 14.
    Järvisalo, M., Le Berre, D., Roussel, O., Simon, L. (2012). The international sat solver competitions. AI Magazine, 33(1), 89–92.CrossRefGoogle Scholar
  15. 15.
    Kautz, H.A. (2006). Deconstructing planning as satisfiability. In IAAI (pp. 1524–1526).Google Scholar
  16. 16.
    Krueger, P., Lai, T., Dixit-Radiya, V. (1994). Job scheduling is more important than processor allocation for hypercube computers. IEEE Transactions on Parallel and Distributed Systems, 5(5), 488–497.CrossRefGoogle Scholar
  17. 17.
    Lawler, E.L., Lenstra, J.K., Kan, A.H.R., Shmoys, D.B. (1993). Sequencing and scheduling: algorithms and complexity. Handbooks in Operations Research and Management Science, 4, 445–522.CrossRefGoogle Scholar
  18. 18.
    Leyton-Brown, K., Nudelman, E., Shoham, Y. (2009). Empirical hardness models: methodology and a case study on combinatorial auctions. Journal of the ACM (JACM), 56(4), 22.MathSciNetCrossRefzbMATHGoogle Scholar
  19. 19.
    Lynce, I., & Marques-Silva, J. (2006). SAT in bioinformatics: making the case with haplotype inference. In SAT.Google Scholar
  20. 20.
    Pinedo, M.L. (2016). Scheduling: theory, algorithms, and systems, 5th edn. Cham: Springer International Publishing.CrossRefzbMATHGoogle Scholar
  21. 21.
    Prasad, M.R., Biere, A., Gupta, A. (2005). A survey of recent advances in sat-based formal verification. STTT, 7(2), 156–173.CrossRefGoogle Scholar
  22. 22.
    Shen, S., Deng, K., Iosup, A., Epema, D. (2013). Scheduling jobs in the cloud using on-demand and reserved instances. In European conference on parallel processing (pp. 242–254). Springer.Google Scholar
  23. 23.
    Smith-Miles, K., & van Hemert, J.I. (2011). Discovering the suitability of optimisation algorithms by learning from evolved instances. Annals of Mathematics and Artificial Intelligence, 61(2), 87.MathSciNetCrossRefzbMATHGoogle Scholar
  24. 24.
    Srinivasan, S., Kettimuthu, R., Subramani, V., Sadayappan, P. (2002). Characterization of backfilling strategies for parallel job scheduling. In ICPP workshops (pp. 514–522).Google Scholar
  25. 25.
    Sukhija, N., Malone, B., Srivastava, S., Banicescu, I., Ciorba, F.M. (2014). Portfolio-based selection of robust dynamic loop scheduling algorithms using machine learning. In IPDPS workshops.Google Scholar
  26. 26.
    Terekhov, D., Tran, T.T., Down, D.G., Beck, J.C. (2014). Integrating queueing theory and scheduling for dynamic scheduling problems. Journal of Artificial Intelligence Research, 50, 535–572.MathSciNetzbMATHGoogle Scholar
  27. 27.
    Thain, D., Tannenbaum, T., Livny, M. (2005). Distributed computing in practice: the condor experience. Concurrency - Practice and Experience, 17(2-4), 323–356.CrossRefGoogle Scholar
  28. 28.
    Tian, J., Fu, R., Yuan, J. (2014). Online over time scheduling on parallel-batch machines: a survey. Journal of the Operations Research Society of China, 2(4), 445–454.MathSciNetCrossRefzbMATHGoogle Scholar
  29. 29.
    Vielma, J.P. (2015). Mixed integer linear programming formulation techniques. SIAM Review, 57(1), 3–57.Google Scholar
  30. 30.
    Witten, I.H., Frank, E., Hall, M.A. (2011). Data mining: practical machine learning tools and techniques, 3rd edn. San Mateo: Morgan Kaufmann.Google Scholar

Copyright information

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

Authors and Affiliations

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

Personalised recommendations