A Multi-Agent Problem in a New Depiction

  • Krystian JobczykEmail author
  • Antoni Ligȩza
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 10842)


This paper contains a new depiction of the Multi-Agent Problem as motivated by the so-called Nurse Rostering Problem, which forms a workable subcase of this general problem of Artificial Intelligence. Multi-Agent Problem will be presented as a scheduling problem with an additional planning component. The next, the problem will be generalized and different constraints will be put forward. Finally, some workable subcases of Multi-Agent Problem will be implemented in PROLOG-solvers.


  1. 1.
    Armstrong, W.: Determinates of the utility function. Econ. J. 49, 453–467 (1939)CrossRefGoogle Scholar
  2. 2.
    Armstrong, W.: Uncertainty and the utility function. Econ. J. 58, 1–10 (1949)CrossRefGoogle Scholar
  3. 3.
    Burke, E.K., Curtois, T., Qu, R., Vanden Berghe, G.: A scatter search approach to the nurse rostering problem. J. Oper. Res. Soc. 61, 1667–1679 (2010)CrossRefGoogle Scholar
  4. 4.
    Cheang, B., Li, H., Lim, A., Rodrigues, B.: Nurse rostering problems—a bibliographic survey. Eur. J. Oper. Res. 151, 447–460 (2003)MathSciNetCrossRefGoogle Scholar
  5. 5.
    Davidson, D.: Hempel on explaining action. In: Essays on Actiona and Events, pp. 261–275 (1976)CrossRefGoogle Scholar
  6. 6.
    Dechter, R., Meiri, I., Pearl, J.: On fuzzy temporal constraints networks. Temporal Constraints Netw. 49(1–3), 61–95 (1991)zbMATHGoogle Scholar
  7. 7.
    Ernst, A.T., Jiang, H., Krishnamoorthy, M., Sier, D.: Staff scheduling and rostering: a review of applications, methods and models. Eur. J. Oper. Res. 153(1), 3–27 (2004)MathSciNetCrossRefGoogle Scholar
  8. 8.
    Halpern, J.Y.: Defining relative likehood in partially-ordered preferential structure. J. Artif. Intell. Res. 7, 1–24 (1997)CrossRefGoogle Scholar
  9. 9.
    Jobczyk, K., Ligeza, A.: Fuzzy-temporal approach to the handling of temporal interval relations and preferences. In: Proceeding of INISTA, pp. 1–8 (2015)Google Scholar
  10. 10.
    Jobczyk, K., Ligeza, A.: A general method of the hybrid controller construction for temporal planning with preferences. In: Proceeding of FedCSIS, pp. 61–70 (2016)Google Scholar
  11. 11.
    Jobczyk, K., Ligeza, A.: Multi-valued Halpern-Shoham logic for temporal Allen’s relations and preferences. In: Proceedings of the Annual International Conference of Fuzzy Systems (FuzzIEEE) (2016, page to appear)Google Scholar
  12. 12.
    Jobczyk, K., Ligeza, A.: Towards a new convolution-based approach to the specification of STPU-solutions. In: FUZZ-IEEE, pp. 782–789 (2016)Google Scholar
  13. 13.
    Jobczyk, K., Ligȩza, A., Bouzid, M., Karczmarczuk, J.: Comparative approach to the multi-valued logic construction for preferences. In: Rutkowski, L., Korytkowski, M., Scherer, R., Tadeusiewicz, R., Zadeh, L.A., Zurada, J.M. (eds.) ICAISC 2015. LNCS (LNAI), vol. 9119, pp. 172–183. Springer, Cham (2015). Scholar
  14. 14.
    Khatib, L., Morris, P., Morris, R., Rossi, F.: Temporal reasoning about preferences. In: Proceedings of IJCAI-01, pp. 322–327 (2001)Google Scholar
  15. 15.
    Leierson, C.E., Saxe, J.B.: A mixed-integer linear programming problem which is efficiently solvable. In: Proceedings 21st Annual Allerton Conference on Communications, Control, and Computing, pp. 204–213 (1983)Google Scholar
  16. 16.
    Liao, Y.Z., Wong, C.K.: An algorithm to compact a VLSI symbolic layout with mixed constraints. IEEE Trans. Comput. Aided Des. Integr. Circuits Syst. 2(2), 62–69 (1983)CrossRefGoogle Scholar
  17. 17.
    Métivier, J.-P., Boizumault, P., Loudni, S.: Solving nurse rostering problems using soft global constraints. In: Gent, I.P. (ed.) CP 2009. LNCS, vol. 5732, pp. 73–87. Springer, Heidelberg (2009). Scholar
  18. 18.
    Qu, R., He, F.: A hybrid constraint programming approach for nurse rostering problems. Technical report, School of Computer Science, Nottingham (2008)Google Scholar
  19. 19.
    Ramsey, F.: A mathematical theory and saving. Econ. J. 38, 543–59 (1928)CrossRefGoogle Scholar
  20. 20.
    Rossi, F., Yorke-Smith, N., Venable, K.: Temporal reasoning with preferences and uncertainty. In: Proceedings of AAAI, vol. 8, pp. 1385–1386 (2003)Google Scholar
  21. 21.
    Shostak, R.: Deciding linear inequalities by computing loop residues. J. ACM 28(4), 769–779 (1981)MathSciNetCrossRefGoogle Scholar
  22. 22.
    Traverso, P., Ghallab, M., Nau, D.: Automated Planning: Theory and Practice. Elsevier, New York City (2004, 1997)Google Scholar
  23. 23.
    van Benthem, J.: Dynamic logic for belief revision. J. Appl. Non-Class. Log. 17(2), 119–155 (2007)MathSciNetzbMATHGoogle Scholar
  24. 24.
    van Benthem, J., Gheerbrant, A.: Game: solution, epistemic dynamics, and fixed-point logics. Fundam. Inform. 100, 19–41 (2010)MathSciNetzbMATHGoogle Scholar
  25. 25.
    Vidal, T., Fargier, H.: Handling contingency in temporal constraints networks: from consistency to controllabilities. J. Exp. Tech. Artif. Intell. 11(1), 23–45 (1999)CrossRefGoogle Scholar

Copyright information

© Springer International Publishing AG, part of Springer Nature 2018

Authors and Affiliations

  1. 1.University of Caen NormandyCaenFrance
  2. 2.AGH University of Science and TechnologyKrakówPoland

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