Skip to main content
Log in

Approximate solution of a resource-constrained scheduling problem

  • Published:
Journal of Heuristics Aims and scope Submit manuscript

Abstract

This paper is devoted to the approximate solution of a strongly NP-hard resource-constrained scheduling problem which arises in relation to the operability of certain high availability real time distributed systems. We present an algorithm based on the simulated annealing metaheuristic and, building on previous research on exact solution methods, extensive computational results demonstrating its practical ability to produce acceptable solutions, in a precisely defined sense. Additionally, our experiments are in remarkable agreement with certain theoretical properties of our simulated annealing scheme. The paper concludes with a short discussion on further research.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  • Aarts, E.H.L., van Laarhoven, P.J.M.: Statistical cooling: a general approach to combinatorial optimization problems. Philips J. Res. 40, 193–226 (1985)

    MathSciNet  Google Scholar 

  • Cerny, V.: Thermodynamical approach to the traveling salesman problem: an efficient simulation algorithm. J. Optim. Theory Appl. 5, 41–51 (1985)

    Article  MathSciNet  Google Scholar 

  • Demange, M., Paschos, V.T.: On an approximation measure founded on the links between optimization and polynomial approximation theory. Theor. Comput. Sci. 158, 117–141 (1996)

    Article  MATH  MathSciNet  Google Scholar 

  • Garey, M.R., Johnson, D.S.: Computers and Intractability—A Guide to the Theory of NP-Completeness. Freeman, New York (1979)

    MATH  Google Scholar 

  • Hajek, B., Sasaki, G.: Simulated annealing—to cool or not. Syst. Control Lett. 12, 443–447 (1989)

    Article  MATH  MathSciNet  Google Scholar 

  • Kemeny, J.G., Snell, J.L.: Finite Markov Chains. The University Series in Undergraduate Mathematics. D. van Nostrand Company/Princeton, New Jersey (1960)

    MATH  Google Scholar 

  • Kirkpatrick, S., Gelatt, C.D. Jr.: Vecchi, M.P.: Optimization by simulated annealing. Science (May 1983)

  • Lundy, M., Mees, A.: Convergence of an annealing algorithm. Math. Program. 34, 111–124 (1986)

    Article  MATH  MathSciNet  Google Scholar 

  • Möbius, A., Neklioudov, A., Díaz-Sánchez, A., Hoffman, K.H., Fachat, A., Schreiber, M.: Optimization by thermal cycling. Phys. Rev. Lett. 79, 4297–4301 (1997)

    Article  Google Scholar 

  • Monnot, J., Paschos, V.T., Toulouse, S.: Approximation Polynomiale des Problèmes NP-Difficiles. Optima Locaux et Rapport Différentiel. Hermès Science Publications, Lavoisier (2003)

    MATH  Google Scholar 

  • Schrijver, A.: Theory of Linear and Integer Programming. Wiley-Interscience Series in Discrete Mathematics and Optimization. Wiley, New York (1986)

    MATH  Google Scholar 

  • Sirdey, R., Kerivin, H.: A branch-and-cut algorithm for a resource-constrained scheduling problem. PRAIRO Oper. Res. 41, 235–251 (2007)

    Article  MathSciNet  Google Scholar 

  • Sirdey, R., Plainfossé, D., Gauthier, J.-P.: A practical approach to combinatorial optimization problems encountered in the design of a high availability distributed system. In: Proceedings of the International Network Optimization Conference, pp. 532–539 (2003)

  • Sirdey, R., Carlier, J., Nace, D.: A fast heuristic for a resource-constrained scheduling problem. Technical Report PE/BSC/INF/017254 V01/EN, Service d’architecture BSC, Nortel GSM Access R&D, France (2005)

  • Sirdey, R., Carlier, J., Kerivin, H., Nace, D.: On a resource-constrained scheduling problem with application to distributed systems reconfiguration. Eur. J. Oper. Res. 183, 546–563 (2007)

    Article  MATH  MathSciNet  Google Scholar 

  • Triki, E., Colette, Y., Siarry, P.: A theoretical study on the behavior of simulated annealing leading to a new cooling schedule. Eur. J. Oper. Res. 166, 77–92 (2005)

    Article  MATH  Google Scholar 

  • van Laarhoven, P.J.M., Aarts, E.H.L.: Simulated Annealing: Theory and Applications. Mathematics and its Applications. Kluwer Academic, Dordrecht (1987)

    MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Renaud Sirdey.

Additional information

This research was supported in part by Association Nationale de la Recherche Technique grant CIFRE-121/2004.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Sirdey, R., Carlier, J. & Nace, D. Approximate solution of a resource-constrained scheduling problem. J Heuristics 15, 1–17 (2009). https://doi.org/10.1007/s10732-007-9052-0

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10732-007-9052-0

Keywords

Navigation