Failure-Directed Search for Constraint-Based Scheduling

  • Petr VilímEmail author
  • Philippe Laborie
  • Paul Shaw
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9075)


This paper presents a new constraint programming search algorithm that is designed for a broad class of scheduling problems. Failure-directed Search (FDS) assumes that there is no (better) solution or that such a solution is very hard to find. Therefore, instead of looking for solution(s), it focuses on a systematic exploration of the search space, first eliminating assignments that are most likely to fail. It is a “plan B” strategy that is used once a less systematic “plan A” strategy – here, Large Neighborhood Search (LNS) – is not able to improve current solution any more. LNS and FDS form the basis of the automatic search for scheduling problems in CP Optimizer, part of IBM ILOG CPLEX Optimization Studio.

FDS and LNS+FDS (the default search in CP Optimizer) are tested on a range of scheduling benchmarks: Job Shop, Job Shop with Operators, Flexible Job Shop, RCPSP, RCPSP/max, Multi-mode RCPSP and Multi-mode RCPSP/max. Results show that the proposed search algorithm often improves best-known lower and upper bounds and closes many open instances.


Constraint programming Scheduling Search Job shop Job shop with Operators Flexible job shop RCPSP RCPSP/max Multi-mode RCPSP Multi-mode RCPSP/max CPLEX CP optimizer 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Achterberg, T., Koch, T., Martin, A.: Branching rules revisited. Operations Research Letters 33, 42–54 (2004)CrossRefMathSciNetGoogle Scholar
  2. 2.
    Adams, J., Balas, E., Zawack, D.: The shifting bottleneck procedure for job shop scheduling. Management Science 34(3), 391–401 (1988)CrossRefzbMATHMathSciNetGoogle Scholar
  3. 3.
    Agnetis, A., Flamini, M., Nicosia, G., Pacifici, A.: A job-shop problem with one additional resource type. Journal of Scheduling 14, 225–237 (2011)CrossRefzbMATHMathSciNetGoogle Scholar
  4. 4.
    Baptiste, P., Pape, C.L., Nuijten, W.: Constraint-Based Scheduling: Applying Constraint Programming to Scheduling Problems. Kluwer Academic Publishers (2001)Google Scholar
  5. 5.
    Beldiceanu, N., Carlsson, M., Demassey, S., Poder, E.: New filtering for the cumulative constraint in the context of non-overlapping rectangles. Annals of Operations Research 184(1), 27–50 (2011)CrossRefzbMATHMathSciNetGoogle Scholar
  6. 6.
    Boussemart, F., Hemery, F., Lecoutre, C., Saïs, L.: Boosting systematic search by weighting constraints. In: de Mántaras, R.L., Saitta, L. (eds.) ECAI. pp. 146–150. IOS Press (2004)Google Scholar
  7. 7.
    Dechter, R., Meiri, I., Pearl, J.: Temporal constraint networks. Artificial Intelligence 49(1–3), 61–95 (1991)CrossRefzbMATHMathSciNetGoogle Scholar
  8. 8.
    Gomes, C.P., Selman, B., Crato, N., Kautz, H.: Heavy-tailed phenomena in satisfiability and constraint satisfaction problems. J. Autom. Reason. 24(1–2), 67–100 (2000)CrossRefzbMATHMathSciNetGoogle Scholar
  9. 9.
    Jussien, N., Lhomme, O.: Dynamic domain splitting for numeric CSPs. In: Proc. European Conference on Artificial Intelligence, pp. 224–228 (1998)Google Scholar
  10. 10.
    Kolisch, R., Sprecher, A.: PSPLIB - a project scheduling problem library. European Journal of Operational Research 96, 205–216 (1996). CrossRefGoogle Scholar
  11. 11.
    Laborie, P., Godard, D.: Self-adapting large neighborhood search: application to single-mode scheduling problems. In: Proceedings of the 3rd Multidisciplinary International Conference on Scheduling: Theory and Applications (MISTA), pp. 276–284 (2007)Google Scholar
  12. 12.
    Laborie, P., Rogerie, J.: Reasoning with conditional time-intervals. In: Wilson, D., Lane, H.C. (eds.) Proceedings of the 21st International Florida Artificial Intelligence Research Society Conference, pp. 555–560. AAAI Press (2008)Google Scholar
  13. 13.
    Laborie, P., Rogerie, J.: Temporal Linear Relaxation in IBM ILOG CP Optimizer. Journal of Scheduling (2014)Google Scholar
  14. 14.
    Laborie, P., Rogerie, J., Shaw, P., Vilím, P.: Reasoning with conditional time-intervals. part II: an algebraical model for resources. In: Lane, H.C., Guesgen, H.W. (eds.) Proceedings of the 22nd International Florida Artificial Intelligence Research Society Conference. AAAI Press, Sanibel Island, Florida, USA, 19–21 May 2009Google Scholar
  15. 15.
    Lecoutre, C., Saïs, L., Tabary, S., Vidal, V.: Nogood recording from restarts. In: 20th International Joint Conference on Artificial Intelligence (IJCAI 2007), pp. 131–136 (2007)Google Scholar
  16. 16.
    Lhomme, O.: Quick shaving. In: Veloso, M.M., Kambhampati, S. (eds.) AAAI, pp. 411–415. AAAI Press/The MIT Press (2005)Google Scholar
  17. 17.
    Mencía, R., Sierra, M.R., Mencía, C., Varela, R.: A genetic algorithm for job-shop scheduling with operators enhanced by weak lamarckian evolution and search space narrowing. Natural Computing 13, 179–192 (2014)CrossRefMathSciNetGoogle Scholar
  18. 18.
    Michel, L., Van Hentenryck, P.: Activity-based search for black-box constraint programming solvers. In: Beldiceanu, N., Jussien, N., Pinson, É. (eds.) CPAIOR 2012. LNCS, vol. 7298, pp. 228–243. Springer, Heidelberg (2012) CrossRefGoogle Scholar
  19. 19.
    Moskewicz, M.W., Madigan, C.F., Zhao, Y., Zhang, L., Malik, S.: Chaff: engineering an efficient SAT solver. In: Annual ACM IEEE Design Automation Conference, pp. 530–535. ACM (2001)Google Scholar
  20. 20.
    Muller, L.F.: An adaptive large neighborhood search algorithm for the multi-mode RCPSP. Tech. Rep. Report 3.2011, Department of Management Engineering, Technical University of Denmark (2011)Google Scholar
  21. 21.
    Pardalos, P.M., Shylo, O.V.: An algorithm for the job shop scheduling problem based on global equilibrium search techniques. Computational Management Science 3(4), 331–348 (2006)CrossRefzbMATHMathSciNetGoogle Scholar
  22. 22.
    Refalo, P.: Impact-based search strategies for constraint programming. In: Wallace, M. (ed.) CP 2004. LNCS, vol. 3258, pp. 557–571. Springer, Heidelberg (2004) CrossRefGoogle Scholar
  23. 23.
    Schnell, A., Hartl, R.F.: Optimizing the multi-mode resource-constrained project scheduling problem with standard and generalized precedence relations by constraint programming and boolean satisfiability solving techniques (working Paper) (2014)Google Scholar
  24. 24.
    Schutt, A., Feydy, T., Stuckey, P.J.: Explaining time-table-edge-finding propagation for the cumulative resource constraint. In: Gomes, C., Sellmann, M. (eds.) CPAIOR 2013. LNCS, vol. 7874, pp. 234–250. Springer, Heidelberg (2013) CrossRefGoogle Scholar
  25. 25.
    Schutt, A., Feydy, T., Stuckey, P.J., Wallace, M.G.: Solving RCPSP/max by lazy clause generation. Journal of Scheduling 16(3), 273–289 (2013). (Accessed 1 November 2014)
  26. 26.
    Simonis, H., O’Sullivan, B.: Search strategies for rectangle packing. In: Stuckey, P. (ed.) CP 2008. LNCS, vol. 5202, pp. 52–66. Springer, Heidelberg (2008)CrossRefGoogle Scholar
  27. 27.
    Storer, R., Wu, S., Vaccari, R.: New search spaces for sequencing problems with application to job shop scheduling. Management Science 38(10), 1495–1509 (1992)CrossRefzbMATHGoogle Scholar
  28. 28.
    Taillard, E.: Benchmarks for basic scheduling problems. European Journal of Operations Research 64, 278–285 (1993)CrossRefzbMATHGoogle Scholar
  29. 29.
    Torres, P., Lopez, P.: Overview and possible extensions of shaving techniques for job-shop problems. In: Junker, U., Karisch, S., Tschöke, S. (eds.) Proceedings of 2nd International Workshop on the Integration of AI and OR Techniques in Constraint Programming for Combinatorial Optimization Problems, pp. 181–186 (2000)Google Scholar
  30. 30. (Accessed 1 November 2014)
  31. 31. (Accessed 1 November 2014)
  32. 32. (Accessed 1 November 2014)
  33. 33. (Accessed 1 November 2014)
  34. 34. (Accessed 1 November 2014)
  35. 35.
    Vilím, P.: Global Constraints in Scheduling. Ph.D. thesis, Charles University in Prague, Faculty of Mathematics and Physics, Department of Theoretical Computer Science and Mathematical Logic (2007)Google Scholar
  36. 36.
    Vilím, P.: Timetable edge finding filtering algorithm for discrete cumulative resources. In: Achterberg, T., Beck, J. (eds.) CPAIOR 2011. LNCS, vol. 6697, pp. 230–245. Springer, Heidelberg (2011)CrossRefGoogle Scholar
  37. 37.
    Wolf, A.: Impact-based search in constraint-based scheduling. In: Hegering, H., Lehmann, A., Ohlbach, H.J., Scheideler, C. (eds.) Informatik 2008, Beherrschbare Systeme - dank Informatik, Band 2, Beiträge der 38. Jahrestagung der Gesellschaft für Informatik e.V. (GI), in München, 8–13 September, LNI, vol. 134, pp. 523–528. GI (2008)Google Scholar
  38. 38.
    Yamada, T., Nakano, R.: A genetic algorithm applicable to large-scale job-shop problems. In: Männer, R., Manderick, B. (eds.) Proc. 2nd International Workshop on Parallel Problem Solving from Nature, pp. 281–290 (1992)Google Scholar

Copyright information

© Springer International Publishing Switzerland 2015

Authors and Affiliations

  1. 1.IBMPraha 4 - ChodovCzech Republic
  2. 2.IBMGentilly CedexFrance
  3. 3.IBM, Les Taissounieres HB2ValbonneFrance

Personalised recommendations