Annals of Operations Research

, Volume 218, Issue 1, pp 147–163 | Cite as

The generalized balanced academic curriculum problem with heterogeneous classes



We propose an extension of the Generalized Balanced Academic Curriculum Problem (GBACP), a relevant planning problem arising in many universities. The problem consists of assigning courses to teaching terms and years, satisfying a set of precedence constraints and balancing students’ load among terms. Differently from the original GBACP formulation, in our case, the same course can be assigned to different years for different curricula (i.e., the predetermined sets of courses from which a student can choose), leading to a more complex solution space.

The problem is tackled by both Integer Programming (IP) methods and combinations of metaheuristics based on local search. The experimental analysis shows that the best results are obtained by means of a two-stage metaheuristic that first computes a solution for the underlying GBACP and then refines it by searching in the extended solution space.


Timetabling Simulated Annealing Academic Planning Mixed integer quadratic programming 


  1. Aarts, E. H. L., & Korst, J. (1989). Simulated annealing and Boltzmann machines. New York: Wiley. Google Scholar
  2. Birattari, M., Stützle, T., Paquete, L., & Varrentrapp, K. (2002). A racing algorithm for configuring metaheuristics. In W. B. Langdon, E. Cantú-Paz, K. Mathias, R. Roy, D. Davis, R. Poli, K. Balakrishnan, V. Honavar, G. Rudolph, J. Wegener, L. Bull, M. A. Potter, A. C. Schultz, J. F. Miller, E. Burke, & N. Jonoska (Eds.), GECCO 2002: proceedings of the genetic and evolutionary computation conference (pp. 11–18). New York: Kaufmann. Google Scholar
  3. Burke, E. K., Mareček, J., Parkes, A. J., & Rudová, H. (2012). A branch-and-cut procedure for the Udine course timetabling problem. Annals of Operations Research, 194, 71–87. CrossRefGoogle Scholar
  4. Castro, C., & Manzano, S. (2001). Variable and value ordering when solving balanced academic curriculum problems. In 6th workshop of the ERCIM working group on constraints. Google Scholar
  5. Castro, C., Crawford, B., & Monfroy, E. (2007). A quantitative approach for the design of academic curricula. In Lecture notes in computer science: Vol. 4558. Human interface and the management of information. Interacting in information environments (pp. 279–288). Berlin: Springer. CrossRefGoogle Scholar
  6. Černý, V. (1985). Thermodynamical approach to the traveling salesman problem: an efficient simulation algorithm. Journal of Optimization Theory and Applications, 45(1), 41–51. CrossRefGoogle Scholar
  7. Chiarandini, M., Di Gaspero, L., Gualandi, S., & Schaerf, A. (2011). The balanced academic curriculum problem revisited. Journal of Heuristics (30 pp.). doi:10.1007/s10732-011-9158-2. Google Scholar
  8. Cioppa, T. M., & Lucas, T. W. (2007). Efficient nearly orthogonal and space-filling Latin hypercubes. Technometrics, 49(1), 45–55. CrossRefGoogle Scholar
  9. Conover, W. (1999). Practical nonparametric statistics (3rd ed.). New York: Wiley. Google Scholar
  10. Di Gaspero, L., & Schaerf, A. (2003). EasyLocal++: an object-oriented framework for flexible design of local search algorithms. Software, Practice & Experience, 33(8), 733–765. CrossRefGoogle Scholar
  11. Di Gaspero, L., & Schaerf, A. (2008). Hybrid local search techniques for the generalized balanced academic curriculum problem. In M. Blesa Aguilera, C. Blum, C. Cotta, A. Fernández Leiva, J. Gallardo Ruiz, A. Roli, & M. Sampels (Eds.), Lecture notes in computer science: Vol. 5296. 5th int. workshop on hybrid metaheuristics (HM-2008) (pp. 146–157). Berlin: Springer. CrossRefGoogle Scholar
  12. Gent, I. P., & Walsh, T. (1999). CSPLib: a benchmark library for constraints (Technical report). APES-09-1999. Available from A shorter version appears in Lecture notes in computer science: Vol. 1713. Proceedings of the 5th international conference on principles and practices of constraint programming (CP-99) (pp. 480–481). Berlin: Springer. Google Scholar
  13. Hnich, B., Kızıltan, Z., & Walsh, T. (2002). Modelling a balanced academic curriculum problem. In N. Jussien & F. Laburthe (Eds.), Proceedings of the fourth international workshop on integration of AI and OR techniques in constraint programming for combinatorial optimisation problems (CP-AI-OR’02) (pp. 121–131). Google Scholar
  14. Kirkpatrick, S., Gelatt, C. D. Jr., & Vecchi, M. P. (1983). Optimization by simulated annealing. Science, 220, 671–680. CrossRefGoogle Scholar
  15. Lambert, T., Castro, C., Monfroy, E., & Saubion, F. (2006). Solving the balanced academic curriculum problem with an hybridization of genetic algorithm and constraint propagation. In Lecture notes in computer science: Vol. 4029. Artificial intelligence and soft computing—ICAISC 2006 (pp. 410–419). Berlin: Springer. CrossRefGoogle Scholar
  16. McCollum, B., Schaerf, A., Paechter, B., McMullan, P., Lewis, R., Parkes, A. J., Di Gaspero, L., Qu, R., & Burke, E. K. (2010). Setting the research agenda in automated timetabling: the second international timetabling competition. INFORMS Journal on Computing, 22(1), 120–130. CrossRefGoogle Scholar
  17. Monette, J., Schaus, P., Zampelli, S., Deville, Y., & Dupont, P. (2007). A CP approach to the balanced academic curriculum problem. In B. Benhamou, B. Choueiry, & B. Hnich (Eds.), Symcon’07, the seventh international workshop on symmetry and constraint satisfaction problems. Google Scholar
  18. Sanchez, S. M. (2005). NOLH designs spreadsheet. Visited on May 13, 2011. Last updated on April 7, 2006.
  19. van Laarhoven, P. J. M., & Aarts, E. H. L. (1987). Simulated annealing: theory and applications. Norwell: Reidel/Kluwer. CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media New York 2013

Authors and Affiliations

  • Sara Ceschia
    • 1
  • Luca Di Gaspero
    • 1
  • Andrea Schaerf
    • 1
  1. 1.DIEGMUniversity of UdineUdineItaly

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