Minimization of the Weighted Total Sparsity of Cosmonaut Training Courses

  • Alexander Lazarev
  • Nail Khusnullin
  • Elena MusatovaEmail author
  • Denis Yadrentsev
  • Maxim Kharlamov
  • Konstantin Ponomarev
Conference paper
Part of the Communications in Computer and Information Science book series (CCIS, volume 974)


The paper is devoted to a cosmonaut training planning problem, which is some kind of resource-constrained project scheduling problem (RCPSP) with a new goal function. Training of each cosmonaut is divided into special courses. To avoid too sparse courses, we introduce a special objective function—the weighted total sparsity of training courses. This non-regular objective function requires the development of new methods that differ from methods for solving the thoroughly studied RCPSP with the makespan criterion. New heuristic algorithms for solving this problem are proposed. Their efficiency is verified on real-life data. In a reasonable time, the algorithms let us find a solution that is better than the solution found with the help of the solver CPLEX CP Optimizer.


Resource-constrained project scheduling problem Heuristic algorithms Planning Priority rule 


  1. 1.
    Artigues, C., Demassey, S., Neron, E. (eds.): Resource-Constrained Project Scheduling: Models, Algorithms, Extensions and Applications. Wiley-ISTE, Hoboken-London (2008)Google Scholar
  2. 2.
    Bartusch, M., Mohring, R.H., Radermache, F.J.: Scheduling project networks with resource constraints and time windows. Ann. Oper. Res. 16, 201–240 (1988)MathSciNetCrossRefGoogle Scholar
  3. 3.
    Brucker, P., Drexl, A., Mohring, R., Neumann, K., Pesch, E.: Resource-constrained project scheduling: notation, classification, models, and methods. Eur. J. Oper. Res. 112, 3–41 (1999)CrossRefGoogle Scholar
  4. 4.
    Debels, D., Vanhoucke, M.: A decomposition-based genetic algorithm for the resource-constrained project-scheduling problem. Oper. Res. 55(3), 457–469 (2007)CrossRefGoogle Scholar
  5. 5.
    Dechter, R.: Constraint Processing. Morgan Kaufmann Publishers, San Francisco (2003)zbMATHGoogle Scholar
  6. 6.
    Homberger, J.: A multi-agent system for the decentralized resource-constrained multi-project scheduling problem. Int. Trans. Oper. Res. 14, 565–589 (2007)CrossRefGoogle Scholar
  7. 7.
    Kolisch, R.: Serial and project scheduling methods revisited: theory and computation. Eur. J. Oper. Res. 90, 320–333 (1996)CrossRefGoogle Scholar
  8. 8.
    Kolisch, R., Hartmann, S.: Experimental investigation of heuristics for resource-constrained project scheduling: an update. Eur. J. Oper. Res. 174(1), 23–37 (2006)CrossRefGoogle Scholar
  9. 9.
    Lazarev, A.A., et al.: Mathematical modeling of the astronaut training scheduling. UBS 63, 129–154 (2016)Google Scholar
  10. 10.
    Musatova, E., Lazarev, A., Ponomarev, K., Yadrentsev, D., Bronnikov, S., Khusnullin, N.: A mathematical model for the astronaut training scheduling problem. IFAC PapersOnLine 49(12), 221–225 (2016)CrossRefGoogle Scholar
  11. 11.
    Valls, V., Quintanilla, M.S., Ballestin, F.: Resource-constrained project scheduling: a critical activity reordering heuristic. Eur. J. Oper. Res. 149(2), 282–301 (2003)MathSciNetCrossRefGoogle Scholar
  12. 12.
  13. 13.

Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  • Alexander Lazarev
    • 1
    • 2
    • 3
  • Nail Khusnullin
    • 1
  • Elena Musatova
    • 1
    Email author
  • Denis Yadrentsev
    • 4
  • Maxim Kharlamov
    • 4
  • Konstantin Ponomarev
    • 4
  1. 1.V.A. Trapeznikov Institute of Control Science of Russian Academy of SciencesMoscowRussia
  2. 2.Lomonosov Moscow State UniversityMoscowRussia
  3. 3.International Laboratory of Decision Choice and AnalysisNational Research University Higher School of EconomicsMoscowRussia
  4. 4.Yu.A. Gagarin Research & Test Cosmonaut Training CenterStar CityRussia

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