Journal of Heuristics

, Volume 17, Issue 5, pp 615–635 | Cite as

An adaptive multi-start graph partitioning algorithm for structuring cellular networks

  • Matías Toril
  • Volker Wille
  • Iñigo Molina-Fernández
  • Chris Walshaw


In mobile network design, the problem of assigning network elements to controllers when defining network structure can be modeled as a graph partitioning problem. In this paper, a comprehensive analysis of a sophisticated graph partitioning algorithm for grouping base stations into packet control units in a mobile network is presented. The proposed algorithm combines multi-level and adaptive multi-start schemes to obtain high quality solutions efficiently. Performance assessment is carried out on a set of problem instances built from measurements in a live network. Overall results confirm that the proposed algorithm finds solutions better than those obtained by the classical multi-level approaches and much faster than classical multi-start approaches. The analysis of the optimization surface shows that the best local minima values follow a Gumbel distribution, which justifies the stagnation of naive multi-start approaches after a few attempts. Likewise, the analysis shows that the best local minima share strong similarities, which is the reason for the superiority of adaptive multi-start approaches. Finally, a sensitivity analysis shows the best internal parameter settings in the algorithm.


Mobile network Optimization Graph partitioning Multi-level refinement Adaptive multi-start 


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  1. Bhattacharjee, P.S., Saha, D., Mukherjee, A.: An approach for location area planning in a personal communication services network (PCSN). IEEE Trans. Wirel. Commun. 3(4), 1176–1187 (2004) CrossRefGoogle Scholar
  2. Boender, C.G.E., Rinnooy Kan, A.H.G., Timmer, G.T., Stougie, L.: A stochastic method for global optimization. Math. Program. 22, 125–140 (1982) MathSciNetzbMATHCrossRefGoogle Scholar
  3. Boese, K.D., Khang, A., Muddu, S.: A new adaptive multi-start technique for combinatorial global optimizations. Oper. Res. Lett. 16, 101–113 (1994) MathSciNetzbMATHCrossRefGoogle Scholar
  4. Demirkol, I., Ersoy, C., Caglayan, M.U., Delic, H.: Location area planning and cell-to-switch assignment in cellular networks. IEEE Trans. Wirel. Commun. 3(3), 880–890 (2004) CrossRefGoogle Scholar
  5. Donath, W.E., Hoffman, A.J.: Lower bounds for the partitioning of graphs. IBM J. Res. Dev. 17(5), 420–425 (1973) MathSciNetzbMATHCrossRefGoogle Scholar
  6. Ernst, A., Jiang, H., Krishnamoorthy, M.: Exact solutions to task allocation problems. Manag. Sci. 52(10), 1634–1646 (2006) CrossRefGoogle Scholar
  7. Ferreira, C.E., Martin, A., de Souza, C.C., Weismantel, R., Wolsey, L.A.: The node capacitated graph partitioning problem: a computational study. Math. Program. 81(2), 229–256 (1998) zbMATHCrossRefGoogle Scholar
  8. Fiduccia, C., Mattheyses, R.: A linear time heuristic for improving network partitions. In: Proc. 19th ACM/IEEE Design Automation Conference, pp. 175–181 (1982) Google Scholar
  9. Gondim, P.: Genetic algorithms and location area partitioning problem in cellular networks. In: Proc. 46th IEEE Vehicular Technology Conference, pp. 1835–1838 (1996) Google Scholar
  10. Gupta, A.: Fast and effective algorithms for graph partitioning and sparse matrix ordering. IBM J. Res. Dev. 41(1/2), 171–184 (1997) CrossRefGoogle Scholar
  11. Hagen, L., Kahng, A.: Combining problem reduction and adaptive multi-start: a new technique for superior iterative partitioning. IEEE Trans. Comput.-Aided Des. Integr. Circuits Syst. 16(7), 709–717 (1997) CrossRefGoogle Scholar
  12. Hendrickson, B., Leland, R.: A multilevel algorithm for partitioning graphs. In: Proc. 1995 ACM/IEEE Conference on Supercomputing. ACM, New York (1995) Google Scholar
  13. Karypis, G., Kumar, V.: A fast and high quality multilevel scheme for partitioning irregular graphs. SIAM J. Sci. Comput. 20(1), 359–392 (1998a) MathSciNetCrossRefGoogle Scholar
  14. Karypis, G., Kumar, V.: Multilevel k-way partitioning scheme for irregular graphs. J. Parallel Distrib. Comput. 48(1), 96–129 (1998b) MathSciNetCrossRefGoogle Scholar
  15. Kernighan, B.W., Lin, S.: An efficient heuristic procedure for partitioning graphs. Bell Syst. Tech. J. 49, 291–307 (1970) zbMATHGoogle Scholar
  16. Krishnan, R., Ramanathan, R., Steentrup, M.: Optimization algorithms for large self-structuring networks. In: Proc. INFOCOM’99, vol. 1, pp. 71–78 (1999) Google Scholar
  17. Laiho, J., Wacker, A., Novosad, T.: Radio Network Planning and Optimisation for UMTS. Wiley, New York (2002) Google Scholar
  18. Lisser, A., Rendl, F.: Graph partitioning using linear and semidefinite programming. Math. Program. 95(1), 91–101 (2003) MathSciNetzbMATHCrossRefGoogle Scholar
  19. Lusa, A., Potts, C.: A variable neighbourhood search algorithm for the constrained task allocation problem. J. Oper. Res. Soc. 59(6), 812–822 (2008) zbMATHCrossRefGoogle Scholar
  20. Merchant, A., Sengupta, B.: Assignment of cells to switches in PCS networks. IEEE/ACM Trans. Netw. 3(5), 521–526 (1995) CrossRefGoogle Scholar
  21. Mishra, AR: Advanced Cellular Network Planning and Optimisation. Wiley, New York (2007) Google Scholar
  22. Mouly, M., Pautet, M.B.: The GSM System for Mobile Communications. Cell & Sys. Telecom Publishing, Palaiseau (1992) Google Scholar
  23. Pierre, S., Houeto, F.: A tabu-search approach for assigning cells to switches in cellular mobile networks. Comput. Commun. 25(5), 465–478 (2002) CrossRefGoogle Scholar
  24. Plehn, J.: The design of location areas in a GSM-network. In: Proc. 45th IEEE Vehicular Technology Conference, pp. 871–875 (1995) Google Scholar
  25. Rolland, E., Pirkul, H., Glover, F.: Tabu search for graph partitioning. Ann. Oper. Res. 63, 209–232 (1996) zbMATHCrossRefGoogle Scholar
  26. Saha, D., Mukherjee, A., Bhattacharjee, P.S.: A simple heuristic for assignment of cells to switches in a PCS network. Wirel. Pers. Commun. 12, 209–224 (2000) CrossRefGoogle Scholar
  27. Schloegel, K., Karypis, G., Kumar, V.: Graph partitioning for high performance scientific simulations. In: Dongarra, J., Foster, I., Fox, G., Kennedy, K., White, A. (eds.) CRPC Parallel Computing Handbook. Morgan Kaufmann, San Mateo (2000) Google Scholar
  28. Sherali, H.D., Smith, J.C.: Improving discrete model representations via symmetry considerations. Manag. Sci. 47(10), 1396–1407 (2001) CrossRefGoogle Scholar
  29. Toril, M.: Self-tuning algorithms for the assignment of packet control units and handover parameters in GERAN. Ph.D. thesis, University of Málaga (2007) Google Scholar
  30. Toril, M., Wille, V., Barco, R.: Optimization of the assignment of cells to packet control units in GERAN. IEEE Commun. Lett. 10(3), 219–221 (2006) CrossRefGoogle Scholar
  31. Toril, M., Wille, V., Molina-Fernández, I., Walshaw, C.: An adaptive multi-start graph partitioning algorithm for structuring cellular networks. Tech. Rep. IC-10-01, University of Málaga (2010).
  32. Walshaw, C.: Multilevel refinement for combinatorial optimisation problems. Ann. Oper. Res. 131, 325–372 (2004) MathSciNetzbMATHCrossRefGoogle Scholar
  33. Walshaw, C., Cross, M.: Mesh partitioning: a multilevel balancing and refinement algorithm. SIAM J. Sci. Comput. 22(1), 63–80 (2000) MathSciNetzbMATHCrossRefGoogle Scholar
  34. Walshaw, C., Everett, M.G.: Multilevel landscapes in combinatorial optimisation. Tech. Rep. 02/IM/93 (2002) Google Scholar

Copyright information

© Springer Science+Business Media, LLC 2010

Authors and Affiliations

  • Matías Toril
    • 1
  • Volker Wille
    • 2
  • Iñigo Molina-Fernández
    • 1
  • Chris Walshaw
    • 3
  1. 1.Communications Engineering Dept.University of MálagaMálagaSpain
  2. 2.Performance ServicesNokia Siemens NetworksHuntingdonUK
  3. 3.School of Computing and Mathematical SciencesUniversity of GreenwichLondonUK

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