[go: up one dir, main page]
More Web Proxy on the site http://driver.im/ Skip to main content

Advertisement

Log in

Simulated annealing algorithm for the robust spanning tree problem

  • Published:
Journal of Heuristics Aims and scope Submit manuscript

Abstract

This paper addresses the robust spanning tree problem with interval data, i.e. the case of classical minimum spanning tree problem when edge weights are not fixed but take their values from some intervals associated with edges. The problem consists of finding a spanning tree that minimizes so-called robust deviation, i.e. deviation from an optimal solution under the worst case realization of interval weights. As it was proven in Kouvelis and Yu (Robust Discrete Optimization and Its Applications, Kluwer Academic, Norwell, 1997), the problem is NP-hard, therefore it is of great interest to tackle it with some metaheuristic approach, namely simulated annealing, in order to calculate an approximate solution for large scale instances efficiently. We describe theoretical aspects and present the results of computational experiments. To the best of our knowledge, this is the first attempt to develop a metaheuristic approach for solving the robust spanning tree problem.

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

Access this article

Subscribe and save

Springer+ Basic
£29.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or eBook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Price includes VAT (United Kingdom)

Instant access to the full article PDF.

Similar content being viewed by others

Explore related subjects

Discover the latest articles, news and stories from top researchers in related subjects.

References

  • Aron, I., van Hentenryck, P.: A constraint satisfaction approach to the robust spanning tree problem with interval data. In: Proceedings of the 18th Conference on Uncertainty in Artificial Intelligence, Computer Science Department, Brown University, Maz, Edmonton, Canada, August 1–4, 2002

  • Aron, I., van Hentenryck, P.: On the complexity of the robust spanning tree problem with interval data. Oper. Res. Lett. 32, 36–40 (2004)

    Article  MATH  MathSciNet  Google Scholar 

  • Ben-Tal, A., Nemirovski, A.: Robust solutions to uncertain programs. Oper. Res. Lett. 25, 1–13 (1999)

    Article  MATH  MathSciNet  Google Scholar 

  • Ben-Tal, A., Nemirovski, A.: Robust solutions of linear programming problems contaminated with uncertain data. Math. Program. 88, 411–424 (2000)

    Article  MATH  MathSciNet  Google Scholar 

  • Garey, M., Johnson, D.: Computers and Intractability. A Guide to the Theory of NP-Completeness. Freeman, San Francisco (1979)

    MATH  Google Scholar 

  • Kasperski, A., Zielinski, P.: An approximation algorithm for interval data minmax regret combinatorial optimization problems. Inf. Process. Lett. 97, 177–180 (2006)

    Article  MathSciNet  Google Scholar 

  • Kirkpatrick, S.: Optimization by simulated annealing—quantitative studies. J. Stat. Phys. 34, 975–986 (1984)

    Article  MathSciNet  Google Scholar 

  • Kirkpatrick, S., Gelatt, C., Vecchi, M.: Optimization by simulated annealing. Science 220, 671–680 (1983)

    Article  MathSciNet  Google Scholar 

  • Kouvelis, P., Yu, G.: Robust Discrete Optimization and Its Applications. Kluwer Academic, Norwell (1997)

    MATH  Google Scholar 

  • Kozina, G., Perepelitsa, V.: Interval spanning tree problem: solvability and computational complexity. Interval Comput. 1, 42–50 (1994)

    MathSciNet  Google Scholar 

  • Kruskal, J.B.: On the shortest spanning subtree of a graph and the traveling salesman problem. Proc. Am. Math. Soc. 7, 48–50 (1956)

    Article  MathSciNet  Google Scholar 

  • Montemanni, R.: A Benders decomposition approach for the robust spanning tree problem with interval data. Eur. J. Oper. Res. 174, 1479–1490 (2006)

    Article  MATH  MathSciNet  Google Scholar 

  • Montemanni, R., Gambardella, L.: A branch and bound algorithm for the robust spanning tree problem with interval data. Eur. J. Oper. Res. 161, 771–779 (2005)

    Article  MATH  MathSciNet  Google Scholar 

  • Neumann, F., Wegener, I.: Randomized local search, evolutionary algorithms, and the minimum spanning tree problem. In: Deb et al. (eds.) GECCO 2004. LNCS, vol. 3102, pp. 713–724. Springer, Berlin (2004)

    Google Scholar 

  • Nikulin, Y.: Robustness in combinatorial optimization and scheduling theory: an extended annotated bibliography. Manuskripte aus den Instituten für Betriebswirtschaftslehre No. 606, Christian-Albrechts-Universität zu Kiel, Germany (2006). Available on-line: http://www.optimization-online.org/DB_HTML/2004/11/995.html

  • Prim, R.C.: Shortest connection networks and some generalizations. Bell Syst. Technol. J. 36, 1389–1401 (1957)

    Google Scholar 

  • Steiner, S., Radzik, T.: Solving the biobjective minimum spanning tree problem using a k-best algorithm. Technical Report TR-03-06, Department of Computer Science King’s College London (2003)

  • van Laarhoven, P., Aarts, E.: Simulated Annealing: Theory and Applications. Reidel, Dordrecht (1987)

    MATH  Google Scholar 

  • Wegener, I.: Simulated annealing beats metropolis in combinatorial optimization. Report No. 8, Electronic Colloquium on Computational Complexity, Dortmund, Germany (2004)

  • Yaman, H., Karasan, O., Pinar, M.: The robust spanning tree problem with interval data. Oper. Res. Lett. 29, 31–40 (2001)

    Article  MATH  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Yury Nikulin.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Nikulin, Y. Simulated annealing algorithm for the robust spanning tree problem. J Heuristics 14, 391–402 (2008). https://doi.org/10.1007/s10732-007-9057-8

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10732-007-9057-8

Keywords