Skip to main content
SpringerLink
Log in

How efficient is a global constraint in practice?

A fair experimental framework

  • Published:
Constraints Aims and scope Submit manuscript

Abstract

Propagation is at the very core of t can provide signi: it can provide significant performance boosts as long as the search space reduction is not outweighed by the cost for running the propagators. A lot of research effort in the CP community is directed toward improving this trade-off. While experimental evaluation is here of the greatest importance, there exists no systematic and flexible methodology to measure the exact benefits provided by a given (new) filtering procedure. This work proposes such a framework by relying on replaying search trees to obtain more realistic assessments. Reducing propagation overhead is done chiefly by 1) devising more efficient algorithms or by 2) using on-line control policies to limit the propagator activations, i.e., mechanisms to reduce the number of propagator calls. In both cases, obtaining improvements is a long and demanding process with uncertain outcome. We propose a method to assess the potential gain of both approaches before actually starting the endeavor, providing the community with a tool to best direct the research efforts. In order to visualize benefits of actual global constraints and the potential of their improvement, we suggest the use of performance profiles. Our approach is showcased for well-known global constraints: alldifferent, cumulative, binpacking and unary (with transition times).

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7
Fig. 8
Fig. 9
Fig. 10
Fig. 11
Fig. 12
Fig. 13
Fig. 14
Fig. 15
Fig. 16
Fig. 17
Fig. 18
Fig. 19
Fig. 20
Fig. 21
Fig. 22
Fig. 23

Similar content being viewed by others

Notes

  1. The terms constraint and propagator are also used interchangeably in this paper.

  2. Some particular CP approaches, such as the ones using Decision Diagrams [8], perform inference on internal data structures. But in the end, potential partial assignments are removed by propagation (e.g., by removing an arc of a Decision Diagram) and the inference made on Decision Diagrams can always be projected to variable domains.

  3. Notice that a similar reasoning could be done for another example where the left and right tree are attributed to M ∪ ϕ and M ∪ ϕ M , respectively.

  4. 4In principle, one might remove most of the bias by using statistics, i.e., by runningexperiments with many instances and many search strategies. However, this is an expensiveprocess and it is not always viable.

  5. 5With a 2.2 GHz Intel Core i7 processor.

  6. A last solution is to use as a baseline the model that makes use of the constructive disjunction of ϕ 1 and ϕ 2 [29, 36, 61], that only prunes when both algorithm prune. However, in the general case, the time overhead for performing deductions only made by ϕ 1 or ϕ 2 cannot easily be deducted from the propagation time. This penalizes the baseline from a time perspective when it is replayed.

  7. The reader might be surprised by the x-axis of the plots, as there is a change of scale on the right-most side. This helps to have a long-term view of the profiles while keeping the focus on the τ region of interest.

  8. Another way to think of \(\phi _{\mathcal {O}(1)}^{\mathit {cost}}(\tau )\) is to consider additional inference made by ϕ to be integrated into the baseline model.

  9. Accessible at http://performance-profile.info.ucl.ac.be/.

  10. For efficiency reasons, dedicated propagators have been implemented instead of posting reified constraints.

References

  1. Aggoun, A., & Beldiceanu, N. (1993). Extending CHIP in order to solve complex scheduling and placement problems. Mathematical and Computer Modelling, 17(7), 57–73.

    Article  MathSciNet  Google Scholar 

  2. Ait-Kaci, H., & Des Flambertins, F. (1999). Warren’s abstract machine—a tutorial reconstruction (pp. 114). Cambridge: MIT Press Cambridge.

  3. Baptiste, P., & Le Pape, C. (2000). Constraint propagation and decomposition techniques for highly disjunctive and highly cumulative project scheduling problems. Constraints, 5(1–2), 119–139.

    Article  MathSciNet  MATH  Google Scholar 

  4. Baptiste, P., Le Pape, C., & Nuijten, W. (2001). Constraint-based scheduling: applying constraint programming to scheduling problems. In International Series in Operations Research & Management Science (Vol. 39). Springer, Berlin.

  5. Beldiceanu, N., & Contejean, E. (1994). Introducing global constraints in CHIP. Mathematical and Computer Modelling, 20(12), 97–123.

    Article  MATH  Google Scholar 

  6. Benhamou, F. (1996). Heterogeneous constraint solving. In International conference on algebraic and logic programming (pp. 62–76). Springer, Berlin.

  7. Bergman, D., Ciré, A.A., & van Hoeve, W.J. (2014). MDD propagation for sequence constraints. Journal of Artificial Intelligence Research (JAIR), 50, 697–722.

    MathSciNet  MATH  Google Scholar 

  8. Bergman, D., Cire, A.A., van Hoeve, W.J., & Hooker, J. (2016). Decision diagrams for optimization. Springer International Publishing.

  9. Berthold, T., Heinz, S., & Schulz, J. (2011). An approximative criterion for the potential of energetic reasoning. In Theory and practice of algorithms in (computer) systems (pp. 229–239).

  10. Bessière, C., & Debruyne, R. (2005). Optimal and suboptimal singleton arc consistency algorithms. In International joint conference on artificial intelligence (pp. 54–59).

  11. Bessiere, C., & Régin, J.C. (1997). Arc consistency for general constraint networks: preliminary results. In International joint conference on artificial intelligence (pp. 398–404). Citeseer.

  12. Bessiere, C., & Van Hentenryck, P. (2003). To be or not to be... a global constraint. In International conference on principles and practice of constraint programming (pp. 789–794). Springer, Berlin.

  13. Brand, S., Narodytska, N., Quimper, C., Stuckey, P.J., & Walsh, T. (2007). Encodings of the sequence constraint. In International conference on principles and practice of constraint programming (pp. 210–224).

  14. Cheng, K.C.K., & Yap, R.H.C. (2010). An MDD-based generalized arc consistency algorithm for positive and negative table constraints and some global constraints. Constraints, 15(2), 265–304.

    Article  MathSciNet  MATH  Google Scholar 

  15. Dejemeppe, C., Van Cauwelaert, S., & Schaus, P. (2015). The unary resource with transition times. In International conference on principles and practice of constraint programming (pp. 89–104). Springer, Berlin.

  16. Deransart, P., Hermenegildo, M.V., & Maluszynski, J. (2000). Analysis and visualization tools for constraint programming: constraint debugging. In Lecture Notes in Computer Science (Vol. 1870). Springer, Berlin.

  17. Derrien, A., & Petit, T. (2014). A new characterization of relevant intervals for energetic reasoning. In International conference on principles and practice of constraint programming (pp. 289–297). Springer, Berlin.

  18. Dincbas, M., Simonis, H., & Van Hentenryck, P. (1990). Solving large combinatorial problems in logic programming. The Journal of Logic Programming, 8 (1), 75–93.

    Article  MATH  Google Scholar 

  19. Dolan, E.D., & Moré, J.J. (2002). Benchmarking optimization software with performance profiles. Mathematical Programming, 91(2), 201–213.

    Article  MathSciNet  MATH  Google Scholar 

  20. Du Boisberranger, J., Gardy, D., Lorca, X., & Truchet, C. (2013). When is it worthwhile to propagate a constraint? A probabilistic analysis of alldifferent. In Workshop on analytic algorithmics and combinatorics (pp. 80–90). SIAM.

  21. Ducomman, S., Cambazard, H., & Penz, B. (2016). Alternative filtering for the weighted circuit constraint: Comparing lower bounds for the tsp and solving tsptw. In AAAI conference on artificial intelligence.

  22. Erschler, J., & Lopez, P. (1990). Energy-based approach for task scheduling under time and resources constraints. In International workshop on project management and scheduling (pp. 115–121).

  23. Focacci, F., Lodi, A., Milano, M., & Vigo, D. (1999). Solving TSP through the integration of OR and CP techniques. Electronic Notes in Discrete Mathematics, 1, 13–25.

    Article  MathSciNet  MATH  Google Scholar 

  24. Gay, S., Hartert, R., Lecoutre, C., & Schaus, P. (2015). Conflict ordering search for scheduling problems. In International conference on principles and practice of constraint programming (pp. 140–148). Springer.

  25. Gay, S., Hartert, R., & Schaus, P. (2015). Simple and scalable time-table filtering for the cumulative constraint. In International conference on principles and practice of constraint programming (pp. 149–157). Springer, Berlin.

  26. Gay, S., Hartert, R., & Schaus, P. (2015). Time-table disjunctive reasoning for the cumulative constraint. In International conference on integration of artificial intelligence (AI) and operations research (OR) techniques in constraint programming (pp. 157–172). Springer, Berlin.

  27. Harvey, W.D., & Ginsberg, M.L. (1995). Limited discrepancy search. In International joint conference on artificial intelligence (pp. 607–615).

  28. van Hoeve, W.J., Pesant, G., Rousseau, L., & Sabharwal, A. (2006). Revisiting the sequence constraint. In International conference on principles and practice of constraint programming (pp. 620–634).

  29. Jefferson, C., Moore, N.C., Nightingale, P., & Petrie, K.E. (2010). Implementing logical connectives in constraint programming. Artificial Intelligence, 174(16–17), 1407–1429.

    Article  MathSciNet  MATH  Google Scholar 

  30. Kolisch, R., Schwindt, C., & Sprecher, A. (1999). Benchmark instances for project scheduling problems. In Project scheduling (pp. 197–212). Springer, Berlin.

  31. Langevine, L., Deransart, P., & Ducassé, M. (2003). A generic trace schema for the portability of CP(FD) debugging tools. In International workshop on constraint solving and constraint logic programming (pp. 171–195). Springer, Berlin.

  32. Le Pape, C., Couronné, P., Vergamini, D., & Gosselin, V. (1994). Time-versus-capacity compromises in project scheduling. In Workshop of the UK planning and scheduling. Citeseer.

  33. Letort, A., Beldiceanu, N., & Carlsson, M. (2012). A scalable sweep algorithm for the cumulative constraint. In International conference on principles and practice of constraint programming (pp. 439–454). Springer, Berlin.

  34. López-Ortiz, A., Quimper, C.G., Tromp, J., & Van Beek, P. (2003). A fast and simple algorithm for bounds consistency of the alldifferent constraint. In International joint conference on artificial intelligence (Vol. 3, pp. 245–250).

  35. McCreesh, C., & Prosser, P. (2015). A parallel, backjumping subgraph isomorphism algorithm using supplemental graphs. In International conference on principles and practice of constraint programming (pp. 295–312). Springer, Berlin.

  36. Müller, T., & Würtz, J. (1995). Constructive disjunction in oz. In Workshop Logische Programmierung. Citeseer.

  37. OscaR Team: OscaR: Scala in OR (2012). Available from https://bitbucket.org/oscarlib/oscar.

  38. Pelsser, F., Schaus, P., & Régin, J.C. (2013). Revisiting the cardinality reasoning for binpacking constraint. In International conference on principles and practice of constraint programming (pp. 578–586). Springer, Berlin.

  39. Pisinger, D., & Ropke, S. (2010). Large neighborhood search. In Handbook of metaheuristics (pp. 399–419). Springer, Berlin.

  40. Régin, J.C. (1994). A filtering algorithm for constraints of difference in CSPs. In AAAI conference on artificial intelligence (Vol. 94, pp. 362–367).

  41. Reinelt, G. (1991). Tsplib—a traveling salesman problem library. ORSA Journal on Computing, 3(4), 376–384.

    Article  MathSciNet  MATH  Google Scholar 

  42. Schaus, P. (2009). Solving balancing and bin-packing problems with constraint programming. Ph.D. thesis, Université catholique de Louvain, Louvain-la-Neuve.

  43. Schulte, C. (1997). Oz explorer: a visual constraint programming tool. In L. Naish (Ed.), Proceedings of the fourteenth international conference on logic programming (pp. 286–300). Leuven: The MIT Press.

  44. Schulte, C. (1999). Comparing trailing and copying for constraint programming. In International conference on logic programming (Vol. 99, pp. 275–289).

  45. Schulte, C., & Stuckey, P.J. (2005). When do bounds and domain propagation lead to the same search space? ACM Transactions on Programming Languages and Systems, 27(3), 388–425.

    Article  Google Scholar 

  46. Schulte, C., & Tack, G. (2009). Weakly monotonic propagators. In International conference on principles and practice of constraint programming (pp. 723–730). Springer, Berlin.

  47. Shaw, P. (2004). A constraint for bin packing. In International conference on principles and practice of constraint programming (pp. 648–662). Springer, Berlin.

  48. Shishmarev, M., Mears, C., Tack, G, & de la Banda, M.G. (2015). Visual search tree profiling. In International conference on principles and practice of constraint programming. Springer, Berlin.

  49. Shishmarev, M., Mears, C., Tack, G, & de la Banda, M.G. (2016). Learning from learning solvers. In International conference on principles and practice of constraint programming (pp. 455–472). Springer, Berlin.

  50. Shishmarev, M., Mears, C., Tack, G, & de la Banda, M.G. (2016). Visual search tree profiling. Constraints, 21(1), 77–94.

    Article  MathSciNet  MATH  Google Scholar 

  51. Simonis, H., Davern, P., Feldman, J., Mehta, D., Quesada, L., & Carlsson, M. (2010). A generic visualization platform for CP. In International conference on principles and practice of constraint programming (pp. 460–474). Springer, Berlin.

  52. Smith, B.M. (2005). Modelling for constraint programming. In Lecture notes for the first international summer school on constraint programming.

  53. Tack, G. (2009). Constraint propagation—models, techniques, implementation. Ph.D. thesis, Saarland University, Germany.

  54. Van Beek, P. (2006). Backtracking search algorithms. In Handbook of constraint programming (pp. 85–134).

  55. Van Cauwelaert, S., Lombardi, M., & Pierre, S. (2014). Supervised learning to control energetic reasoning: feasibility study. In Proceedings of the doctoral program of CP2014.

  56. Van Cauwelaert, S., Lombardi, M., & Schaus, P. (2015). Understanding the potential of propagators. In International conference on integration of artificial intelligence (AI) and operations research (OR) techniques in constraint programming (pp. 427–436). Springer, Berlin.

  57. Van Cauwelaert, S., Lombardi, M., & Schaus, P. (2016). A visual web tool to perform what-if analysis of optimization approaches. Tech. rep., UCLouvain.

  58. Van Hentenryck, P., & Dincbas, M. (1987). Forward checking in logic programming. In International conference on logic programming (pp. 229–256).

  59. Vilım, P. (2007). Global constraints in scheduling. Ph.D. thesis, Charles University in Prague, Faculty of Mathematics and Physics, Department of Theoretical Computer Science and Mathematical Logic, KTIML MFF, Universita Karlova, Praha 1.

  60. Warren, D. (1983). An abstract Prolog instruction set (Vol. 309). Menlo Park: SRI International.

    Google Scholar 

  61. Würtz, J., & Müller, T. (1996). Constructive disjunction revisited. In Görz, G., & Hölldobler, S. (Eds.) KI-96: Advances in artificial intelligence. KI 1996. Lecture Notes in Computer Science (Lecture Notes in Artificial Intelligence), (Vol. 1137, pp. 377386). Berlin: Springer.

Download references

Author information

Authors and Affiliations

  1. Université Catholique de Louvain, Place Sainte Barbe, 2 bte L5.02.01, 1348, Louvain-la-Neuve, Belgium

    Sascha Van Cauwelaert & Pierre Schaus

  2. Università di Bologna, Viale del Risorgimento 2, Bologna, Italy

    Michele Lombardi

Authors
  1. Sascha Van Cauwelaert
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Michele Lombardi
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Pierre Schaus
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Sascha Van Cauwelaert.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Cauwelaert, S., Lombardi, M. & Schaus, P. How efficient is a global constraint in practice?. Constraints 23, 87–122 (2018). https://doi.org/10.1007/s10601-017-9277-y

Download citation

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10601-017-9277-y

Keywords

Search

Navigation