Air Traffic Controller Shift Scheduling by Reduction to CSP, SAT and SAT-Related Problems

  • Mirko Stojadinović
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8656)

Abstract

In this paper we present our experience in solving Air Traffic Controller Shift Scheduling Problem. We give a formal definition of this optimization problem and introduce three encodings. The encodings make possible to formulate a very wide set of different scheduling requirements. The problem is solved by using SAT, MaxSAT, PB, SMT, CSP and ILP solvers. In combination with these solvers, three different optimization techniques are presented, a basic technique and its two modifications. The modifications use local search to modify some parts of the initial solution. Results indicate that SAT-related approaches outperform other solving methods used and that one of the introduced techniques which uses local search can significantly outperform the basic technique. We have successfully used these approaches to make shift schedules for one air traffic control center.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Apt, K.R.: Principles of constraint programming. Cambridge University Press (2003)Google Scholar
  2. 2.
    Arnvig, M., Beermann, B., Köper, B., Maziul, M., Mellett, U., Niesing, C., Vogt, J.: Managing shiftwork in european atm. Literature Review. European Organisation for the Safety of Air Navigation (2006)Google Scholar
  3. 3.
    Beldiceanu, N., Carlsson, M., Rampon, J.-X.: Global constraint catalog. Technical report, SICS (2005)Google Scholar
  4. 4.
    Berre, D.L., Parrain, A.: The sat4j library, release 2.2. JSAT 7(2-3), 59–64 (2010)Google Scholar
  5. 5.
    Biere, A.: Lingeling, plingeling, picosat and precosat at sat race 2010. FMV Report Series Technical Report 10(1) (2010)Google Scholar
  6. 6.
    Biere, A., Heule, M.J.H., van Maaren, H., Walsh, T. (eds.): Handbook of Satisfiability, February 2009. Frontiers in Artificial Intelligence and Applications, vol. 185. IOS Press, Amsterdam (2009)MATHGoogle Scholar
  7. 7.
    Burke, E.K., De Causmaecker, P., Berghe, G.V., Van Landeghem, H.: The state of the art of nurse rostering. J. Scheduling 7(6), 441–499 (2004)CrossRefMATHGoogle Scholar
  8. 8.
    Chen, J.: A new sat encoding of the at-most-one constraint. In: Proceedings of the 9th International Workshop on Constraint Modelling and Reformulation (2010)Google Scholar
  9. 9.
    Chiarandini, M., Birattari, M., Socha, K., Rossi-Doria, O.: An effective hybrid algorithm for university course timetabling. J. Scheduling 9(5), 403–432 (2006)CrossRefMATHMathSciNetGoogle Scholar
  10. 10.
    Cook, S.A.: The complexity of theorem-proving procedures. In: Harrison, M.A., Banerji, R.B., Ullman, J.D. (eds.) STOC, pp. 151–158. ACM (1971)Google Scholar
  11. 11.
    de Moura, L., Bjørner, N.S.: Z3: An efficient smt solver. In: Ramakrishnan, C.R., Rehof, J. (eds.) TACAS 2008. LNCS, vol. 4963, pp. 337–340. Springer, Heidelberg (2008)CrossRefGoogle Scholar
  12. 12.
    Dutertre, B., De Moura, L.: The yices smt solver, vol. 2, p. 2 (2006), Tool paper at, http://yices.csl.sri.com/tool-paper.pdf
  13. 13.
    Eén, N., Sörensson, N.: An extensible sat-solver. In: Giunchiglia, E., Tacchella, A. (eds.) SAT 2003. LNCS, vol. 2919, pp. 502–518. Springer, Heidelberg (2004)CrossRefGoogle Scholar
  14. 14.
    Eén, N., Sörensson, N.: Temporal induction by incremental sat solving. Electr. Notes Theor. Comput. Sci. 89(4), 543–560 (2003)CrossRefGoogle Scholar
  15. 15.
    Eén, N., Sörensson, N.: Translating pseudo-boolean constraints into sat. JSAT 2(1-4), 1–26 (2006)MATHGoogle Scholar
  16. 16.
    EUROCONTROL. Shiftwork practices study - atm and related industries. DAP/SAF-2006/56 Brussels: EUROCONTROL (2006)Google Scholar
  17. 17.
    Committee for a Review of the En Route Air Traffic Control Complexity and Workload Model. Air traffic controller staffing in the en route domain: A review of the federal aviation administration’s task load model (2010)Google Scholar
  18. 18.
    Gebser, M., Kaufmann, B., Neumann, A., Schaub, T.: clasp: A Conflict-Driven Answer Set Solver. In: Baral, C., Brewka, G., Schlipf, J. (eds.) LPNMR 2007. LNCS (LNAI), vol. 4483, pp. 260–265. Springer, Heidelberg (2007)CrossRefGoogle Scholar
  19. 19.
    Hebrard, E.: Mistral, a constraint satisfaction library. In: Proceedings of the 3rd International CSP Solver Competition, pp. 31–39Google Scholar
  20. 20.
    Klieber, W., Kwon, G.: Efficient cnf encoding for selecting 1 from n objects. In: Proc. International Workshop on Constraints in Formal Verification (2007)Google Scholar
  21. 21.
    Koshimura, M., Zhang, T., Fujita, H., Hasegawa, R.: Qmaxsat: A partial max-sat solver. JSAT 8(1/2), 95–100 (2012)MathSciNetGoogle Scholar
  22. 22.
    Marques-Silva, J.: The msuncore maxsat solver. In: SAT 2009 competitive events booklet: preliminary version, p. 151 (2009)Google Scholar
  23. 23.
    Merchez, S., Lecoutre, C., Boussemart, F.: Abscon: A prototype to solve csps with abstraction. In: Walsh, T. (ed.) CP 2001. LNCS, vol. 2239, pp. 730–744. Springer, Heidelberg (2001)CrossRefGoogle Scholar
  24. 24.
    Nethercote, N., Stuckey, P.J., Becket, R., Brand, S., Duck, G.J., Tack, G.R.: Minizinc: Towards a standard cp modelling language. In: Bessière, C. (ed.) CP 2007. LNCS, vol. 4741, pp. 529–543. Springer, Heidelberg (2007)CrossRefGoogle Scholar
  25. 25.
    Roussel, O., Lecoutre, C.: Xml representation of constraint networks: Format xcsp 2.1. CoRR, abs/0902.2362 (2009)Google Scholar
  26. 26.
    Schulte, C., Lagerkvist, M., Tack, G.: Gecode (2006), Software download and online material at the website, http://www.gecode.org
  27. 27.
    Sinz, C.: Towards an optimal cnf encoding of boolean cardinality constraints. In: van Beek, P. (ed.) CP 2005. LNCS, vol. 3709, pp. 827–831. Springer, Heidelberg (2005)CrossRefGoogle Scholar
  28. 28.
    Stojadinović, M., Marić, F.: mesat: Multiple encodings of csp to sat. Constraints (2014), doi:10.1007/s10601-014-9165-7Google Scholar
  29. 29.
    Tamura, N., Banbara, M.: Sugar: A csp to sat translator based on order encoding. In: Proceedings of the Third Constraint Solver Competition, pp. 65–69 (2008)Google Scholar
  30. 30.
    Tanjo, T., Tamura, N., Banbara, M.: Sugar++: a sat-based max-csp/cop solver. In: Proc. the Third International CSP Solver Competition, pp. 144–151 (2008)Google Scholar
  31. 31.
    EATCHIP Human Resources Team. Ats manpower planning in practice: Introduction to a qualitative and quantitative staffing methodology. HUM.ET1.ST02.2000-REP-01 Brussels: EUROCONTROL (1998)Google Scholar

Copyright information

© Springer International Publishing Switzerland 2014

Authors and Affiliations

  • Mirko Stojadinović
    • 1
  1. 1.Faculty of MathematicsUniversity of BelgradeSerbia

Personalised recommendations