, Volume 16, Issue 3, pp 228–249 | Cite as

Hybrid search for minimal perturbation in Dynamic CSPs



It is often the case that after a scheduling problem has been solved some small changes occur that make the solution of the original problem not valid. Solving the new problem from scratch can result in a schedule that is very different from the original schedule. In applications such as a university course timetable or flight scheduling, one would be interested in a solution that requires minimal changes for the users. The present paper considers the minimal perturbation problem. It is motivated by scenarios in which a Constraint Satisfaction Problem (CSP) is subject to changes. In particular, the case where some of the constraints are changed after a solution was obtained. The goal is to find a solution to the changed problem that is as similar as possible (e.g. includes minimal perturbations) to the previous solution. Previous studies proposed a formal model for this problem (Barták et al. 2004), a best first search algorithm (Ross et al. 2000), complexity bounds (Hebrard et al. 2005), and branch and bound based algorithms (Barták et al. 2004; Hebrard et al. 2005). The present paper proposes a new approach for solving the minimal perturbation problem. The proposed method interleaves constraint optimization and constraint satisfaction techniques. Our experimental results demonstrate the advantage of the proposed algorithm over former algorithms. Experiments were performed both on random CSPs and on random instances of the Meeting Scheduling Problem.


Dynamic Constraint Satisfaction Problems (CSPs) 


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Barták, R. (1998). Guide to constraint programming.∼bartak/constraints/.
  2. 2.
    Barták, R. (1999). Dynamic constraint models for planning and scheduling problems. In New trends in constraints (pp. 237–255).Google Scholar
  3. 3.
    Barták, R., Muller, T., & Rudova, H. (2004). A new approach to modeling and solving minimal perturbation problems. In Recent advances in constraints (pp. 233–249). Berlin: Springer.CrossRefGoogle Scholar
  4. 4.
    Bessiere, C., & Regin, J. C. (1996). MAC and combined heuristics: Two reasons to forsake FC (and CBJ?) on hard problems. In Proc. second international conference on principles and practice of constraint programming, CP 96 (pp. 61–75). Cambridge, MA.Google Scholar
  5. 5.
    Gent, I. P., & Walsh, T. (1999). CSPLib: A benchmark library for constraints. Technical report, APES-09-1999, 1999. Available from
  6. 6.
    Hebrard, E., Hnich, B., O’Sullivan, B., & Walsh, T. (2005). Finding diverse and similar solutions in constraint programming. In The twentieth national conference on artificial intelligence, AAAI-2005. Pittsburgh, PA, USA.Google Scholar
  7. 7.
    Hebrard, E., O’Sullivan, B., & Walsh, T. (2007). Distance constraints in constraint satisfaction. In The twentieth international joint conference on artificial intelligence, IJCAI-2007. Hyderabab, India.Google Scholar
  8. 8.
    Kondrak, G., & van Beek, P. (1997). A theoretical evaluation of selected backtracking algorithms. Artificial Intelligence, 21, 365–387.CrossRefGoogle Scholar
  9. 9.
    Meisels, A., & Kaplanski, E. (2002). Scheduling agents—Distributed employee timetabling. In Proc. 4th conf. on autom. timetabling, PATAT-2002 (pp. 166–80). Ghent, Belgium.Google Scholar
  10. 10.
    Prosser, P. (1996). An empirical study of phase transitions in binary constraint satisfaction problems. Artificial Intelligence, 81, 81–109.MathSciNetCrossRefGoogle Scholar
  11. 11.
    Roos, N., Ran, Y., & van den Herik, H. J. (2000). Combining local search and constraint propagation to find a minimal change solution for a dynamic csp. In Artificial intelligence: Methodology, systems, applications (pp. 272–282).Google Scholar
  12. 12.
    Roos, N., Ran, Y., & van den Herik, H. J. (2002). Approaches to find a near-minimal change solution for dynamic csps. In Fourth international workshop on integration of AI and OR techniques in constraint programming for combinatorial optimisation problems (pp. 373–387).Google Scholar
  13. 13.
    Russell, S., & Norvig, P. (2005). Artificial intelligence, a modern approach (2nd ed.). Englewood Cliffs: Prentice-Hall.Google Scholar
  14. 14.
    Sakkout, H. E., Richards, T., & Wallace, M. (1998). Minimal perturbation in dynamic scheduling. In Proc. 13th European conference on artificial intelligence, ECAI-98 (pp. 504–508). Brighton.Google Scholar
  15. 15.
    Sakkout, H. E., & Wallace, M. (2000). Probe backtrack search for minimalperturbation in dynamic scheduling. Constraints, 4(5), 359–388.CrossRefGoogle Scholar
  16. 16.
    Schiex, T., & Verfaillie, G. (1994). Nogood recording for static and dynamic constraint satisfaction problem. International Journal on Artificial Intelligence Tools (IJAIT), 3(2), 187–207.CrossRefGoogle Scholar
  17. 17.
    Smith, B. M. (1996). Locating the phase transition in binary constraint satisfactionproblems. Artificial Intelligence, 81, 155–181.MathSciNetCrossRefGoogle Scholar
  18. 18.
    Verfaillie, G., & Jussien, N. (2005). Constraint solving in uncertain and dynamic environments—A survey. Constraints, 10(3), 253–281.MathSciNetMATHCrossRefGoogle Scholar
  19. 19.
    Verfaillie, G., & Schiex, T. (1994). Solution reuse in dynamic constraint satisfaction problems. In Twelfth national conference on artificial intelligence, AAAI-1994 (pp. 307–312).Google Scholar
  20. 20.
    Wallace, R. J., & Freuder, E. (2002). Constraint-based multi-agent meeting scheduling: Effects of agent heterogeneity on performance and privacy loss. In Proc. 3rd workshop on distributed constrait reasoning, DCR-02 (pp. 176–182). Bologna.Google Scholar
  21. 21.
    Wallace, R. J., & Freuder, E. (2005). Constraint-based reasoning and privacy/efficiency tradeoffs in multi-agent problem solving. Artificial Intelligence, 161(1–2), 209–228.MathSciNetMATHCrossRefGoogle Scholar
  22. 22.
    Zivan, R., & Meisels, A. (2006). Message delay and discsp search algorithms. Annals of Mathematics and Artificial Intelligence (AMAI), 46, 415–439.MathSciNetMATHCrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media, LLC 2011

Authors and Affiliations

  1. 1.Department of Industrial Engineering and ManagementBen-Gurion University of the NegevBeer-ShevaIsrael
  2. 2.Department of Computer ScienceBen-Gurion University of the NegevBeer-ShevaIsrael

Personalised recommendations