Towards an Accurate Solution of Wireless Network Design Problems

  • Fabio D’AndreagiovanniEmail author
  • Ambros M. Gleixner
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9849)


The optimal design of wireless networks has been widely studied in the literature and many optimization models have been proposed over the years. However, most models directly include the signal-to-interference ratios representing service coverage conditions. This leads to mixed-integer linear programs with constraint matrices containing tiny coefficients that vary widely in their order of magnitude. These formulations are known to be challenging even for state-of-the-art solvers: the standard numerical precision supported by these solvers is usually not sufficient to reliably guarantee feasible solutions. Service coverage errors are thus commonly present. Though these numerical issues are known and become evident even for small-sized instances, just a very limited number of papers has tried to tackle them, by mainly investigating alternative non-compact formulations in which the sources of numerical instabilities are eliminated. In this work, we explore a new approach by investigating how recent advances in exact solution algorithms for linear and mixed-integer programs over the rational numbers can be applied to analyze and tackle the numerical difficulties arising in wireless network design models.


Linear programming Precise solutions Network design Wireless telecommunications systems 


  1. 1.
    Achterberg, T.: SCIP: solving constraint integer programs. Math. Prog. Comput. 1(1), 1–41 (2009)MathSciNetCrossRefzbMATHGoogle Scholar
  2. 2.
    Amaldi, E., Capone, A., Malucelli, F., Mannino, C.: Optimization problems and models for planning cellular networks. In: Resende, M., Pardalos, P. (eds.) Handbook of Optimization in Telecommunication, pp. 917–939. Springer, Heidelberg (2006)CrossRefGoogle Scholar
  3. 3.
    Applegate, D.L., Cook, W., Dash, S., Espinoza, D.G.: QSopt_ex (2007).
  4. 4.
    Bauschert, T., Büsing, C., D’Andreagiovanni, F., Koster, A.M.C.A., Kutschka, M., Steglich, U.: Network planning under demand uncertainty with robust optimization. IEEE Commun. Mag. 52, 178–185 (2014)CrossRefGoogle Scholar
  5. 5.
    Capone, A., Chen, L., Gualandi, S., Yuan, D.: A new computational approach for maximum link activation in wireless networks under the sinr model. IEEE Trans. Wirel. Commun. 10(5), 1368–1372 (2011)CrossRefGoogle Scholar
  6. 6.
    Cook, W., Koch, T., Steffy, D.E., Wolter, K.: An exact rational mixed-integer programming solver. In: Günlük, O., Woeginger, G.J. (eds.) IPCO 2011. LNCS, vol. 6655, pp. 104–116. Springer, Heidelberg (2011)CrossRefGoogle Scholar
  7. 7.
    Cook, W., Koch, T., Steffy, D.E., Wolter, K.: A hybrid branch-and-bound approach for exact rational mixed-integer programming. Math. Prog. Comp. 5, 305–344 (2013)MathSciNetCrossRefzbMATHGoogle Scholar
  8. 8.
    D’Andreagiovanni, F.: On improving the capacity of solving large-scale wireless network design problems by genetic algorithms. In: Di Chio, C., et al. (eds.) EvoApplications 2011, Part II. LNCS, vol. 6625, pp. 11–20. Springer, Heidelberg (2011)CrossRefGoogle Scholar
  9. 9.
    D’Andreagiovanni, F.: Pure 0–1 programming approaches to wireless network design. 4OR-Q. J. Oper. Res. 10(2), 211–212 (2012). doi: 10.1007/s10288-011-0162-z CrossRefGoogle Scholar
  10. 10.
    D’Andreagiovanni, F.: Revisiting wireless network jamming by SIR-based considerations and multiband robust optimization. Optim. Lett. 9(8), 1495–1510 (2015)MathSciNetCrossRefzbMATHGoogle Scholar
  11. 11.
    D’Andreagiovanni, F., Mannino, C., Sassano, A.: Negative cycle separation in wireless network design. In: Pahl, J., Reiners, T., Voß, S. (eds.) INOC 2011. LNCS, vol. 6701, pp. 51–56. Springer, Heidelberg (2011)CrossRefGoogle Scholar
  12. 12.
    D’Andreagiovanni, F., Mannino, C., Sassano, A.: GUB covers and power indexed formulations for wireless network design. Manage. Sci. 59(1), 142–156 (2013)CrossRefGoogle Scholar
  13. 13.
    Dely, P., D’Andreagiovanni, F., Kassler, A.: Fair optimization of mesh-connected WLAN hotspots. Wirel. Commun. Mob. Com. 15(5), 924–946 (2015)CrossRefGoogle Scholar
  14. 14.
    Dhiflaoui, M., Funke, S., Kwappik, C., Mehlhorn, K., Seel, M., Schömer, E., Schulte, R., Weber, D.: Certifying and repairing solutions to large LPs: How good are LP-solvers? In: Proceedings of SODA 2003, pp. 255–256. SIAM (2003)Google Scholar
  15. 15.
    Espinoza, D.G.: On Linear Programming, Integer Programming and Cutting Planes. Ph.D. thesis, Georgia Institute of Technology (2006)Google Scholar
  16. 16.
    Gleixner, A.M., Steffy, D.E., Wolter, K.: Improving the accuracy of linear programming solvers with iterative refinement. In: Proceedings ISSAC 2012, Grenoble (2012)Google Scholar
  17. 17.
    Gleixner, A.M., Steffy, D.E., Wolter, K.: Iterative refinement for linear programming. INFORMS J. Comput. 28(3), 449–464 (2016)MathSciNetCrossRefGoogle Scholar
  18. 18.
    GNU Multiple Precision Arithmetic Library Version.
  19. 19.
  20. 20.
    Kennington, J., Olinick, E., Rajan, D.: Wireless Network Design: Optimization Models and Solution Procedures. Springer, Heidelberg (2010)zbMATHGoogle Scholar
  21. 21.
    Koch, T.: The final NETLIB-LP results. Oper. Res. Lett. 32(2), 138–142 (2004)MathSciNetCrossRefzbMATHGoogle Scholar
  22. 22.
    Mannino, C., Rossi, F., Smriglio, S.: The network packing problem in terrestrial broadcasting. Oper. Res. 54(6), 611–626 (2006)CrossRefzbMATHGoogle Scholar
  23. 23.
    Mannino, C., Rossi, F., Smriglio, S.: A unified view in planning broadcasting networks. DIS Technical report, vol. 8. Aracne Editrice, Roma (2007)Google Scholar
  24. 24.
    Neumaier, A., Shcherbina, O.: Safe bounds in linear and mixed-integer linear programming. Math. Program. 99(2), 283–296 (2004)MathSciNetCrossRefzbMATHGoogle Scholar
  25. 25.
    Rappaport, T.S.: Wireless Communications: Principles and Practice. Prentice Hall, Upper Saddle River (2001)zbMATHGoogle Scholar
  26. 26.
    SCIP: Solving Constraint Integer Programs.
  27. 27.
    SoPlex. The Sequential object-oriented simPlex.

Copyright information

© Springer International Publishing Switzerland 2016

Authors and Affiliations

  • Fabio D’Andreagiovanni
    • 1
    • 2
    • 3
    Email author
  • Ambros M. Gleixner
    • 1
  1. 1.Department of Mathematical OptimizationZuse Institute Berlin (ZIB)BerlinGermany
  2. 2.DFG Research Center MATHEON, Einstein Center for Mathematics (ECMath)BerlinGermany
  3. 3.Institute for System Analysis and Computer ScienceNational Research Council of Italy (IASI-CNR)RomeItaly

Personalised recommendations