Journal of Heuristics

, Volume 16, Issue 3, pp 259–288 | Cite as

A comparison of problem decomposition techniques for the FAP

  • Gualtiero Colombo
  • Stuart M. Allen


This paper proposes a problem decomposition approach to solve hard Frequency Assignment Problem instances with standard meta-heuristics. The proposed technique aims to divide the initial problem into a number of easier subproblems, solve them and then recompose the partial solutions into one of the original problem. We consider the COST-259 MI-FAP instances and other Cardiff University test problems in order to simulate larger and more realistic networks. For both benchmarks the standard implementations of meta-heuristics do not generally produce a satisfactory performance within reasonable times of execution. However, the decomposed assignment approach can improve their results, both in terms of solution quality and runtime.

Frequency assignment Problem decomposition Graph partitioning Simulated annealing 


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  1. Aardal, K.I., van Hoesel, C.P.M., Jansen, B.: A branch-and-cut algorithm for the frequency assignment problem, R.M. 96\11 (1996) Google Scholar
  2. Abbiw-Jackson, R., Golden, B., Raghavan, S., Wasil, E.: A divide-and-conquer local search heuristic for data visualization. Comput. Oper. Res. 33(11), 3070–3087 (2006) zbMATHCrossRefGoogle Scholar
  3. Allen, S.M., Dunkin, N., Hurley, S., Smith, D.: Frequency assignment problems: benchmarks and lower bounds. University of Glamorgan (1998) Google Scholar
  4. Angelsmark, O., Thapper, J.: Partitioning Based Algorithms for Some Colouring Problems. Lecture Notes in Computer Science, vol. 3978, pp. 44–58 (2006) Google Scholar
  5. Beckmann, D., Killat, U.: Frequency planning with respect to interference minimization in cellular radio networks. Tech. Rep. 8th COST 259 Meeting, Vienna, Austria (1999) Google Scholar
  6. Borovska, P.: Solving the travelling salesman problem in parallel by genetic algorithm on multicomputer cluster. In: Proc. of the International Conference on Computer Systems and Technologies CompSysTech’06, Veliko Tarnovo, Bulgaria, 2006 Google Scholar
  7. Brandes, U., Gaertler, M., Wagner, D.: Experiments on graph clustering algorithms. In: Proc. of the 11th Annual European Symposium on Algorithms, Budapest, 2003 Google Scholar
  8. Cardiff University Condor Pool., accessed on 1st June 2007
  9. Cheng, C.B., Wang, K.P.: Solving a vehicle routing problem with time windows by a decomposition technique and a genetic algorithm. Expert Syst. Appl. 36(4), 7758–7763 (2009) CrossRefMathSciNetGoogle Scholar
  10. Colombo, G.: A genetic algorithm for frequency assignment with problem decomposition. Int. J. Mob. Netw. Des. Innov. 1(2), 102–112 (2006) CrossRefGoogle Scholar
  11. Colombo, G., Allen, S.M.: Problem decomposition for minimum interference frequency assignment. In: Proc. of the 2007 IEEE Congress in Evolutionary Computation, Singapore, 2007 Google Scholar
  12. Colombo, G.: A decomposition approach for the frequency assignment problem. Ph.D. Thesis, Cardiff University, UK (2008) Google Scholar
  13. Correia, L.M. (ed.): Wireless Flexible Personalised Communications. Wiley, Chichester (2001) Google Scholar
  14. Crainic, T.G., Toulouse, M.: Parallel Strategies for Meta-heuristic. State-of-the-Art Handbook in Metaheuristics, edited by Glover, F., Kochenberger, G., Kluwer Academic, Dordrecht (2002) Google Scholar
  15. Crompton, W., Hurley, W.S., Stephens, N.M.: A parallel genetic algorithm for frequency assignment problems. In: Proc. of the IMAC-IEEE Conference on Signal Processing, Robotics and Neural Networks, Lille, France, 1994 Google Scholar
  16. Eisenblatter, A.: Frequency assignment in GSM networks: Models, heuristics, and lower bounds. Ph.D. Thesis, Technische Universitat Berlin, Berlin, Germany (2001) Google Scholar
  17. FAP web—A website about Frequency Assignment Problems., accessed on 1st June 2007
  18. Gendreau, M., Guertin, F., Potvin, J.Y., Taillard, E.: Parallel tabu search for real-time vehicle routing and dispatching. Transp. Sci. 33(4), 381–390 (1999) zbMATHCrossRefGoogle Scholar
  19. Gonzales Hernandez, L.F., Corne, D.W.: Evolutionary divide and conquer for the set-covering problem. In: Lecture Notes in Computer Science, vol. 1143, pp. 198–208 (1996) Google Scholar
  20. Hale, W.K.: Frequency assignment: Theory and applications. Proc. IEEE 68(12), 1497–1514 (1980) CrossRefGoogle Scholar
  21. Hellebrandt, M., Heller, H.: A new heuristic method for frequency assignment. Tech. Report TD(00) 003, COST259, Valencia, Spain (Jan. 2000) Google Scholar
  22. Hurley, S., Smith, D.: Meta-heuristics and channel assignment. In: Hurley, S., Leese, R. (eds.) Methods and Algorithms for Radio Channel Assignment. Oxford University Press, Oxford (2002) Google Scholar
  23. Hurley, S., Smith, D., Thiel, S.U.: FASoft: A system for discrete channel frequency assignment. Radio Sci. 32(5), 1921–1939 (1997) CrossRefGoogle Scholar
  24. Gendron, B., Crainic, T.G.: Parallel branch-and-bound algorithms: Survey and synthesis. Oper. Res. 42(6), 1042–1066 (1994) zbMATHCrossRefMathSciNetGoogle Scholar
  25. Karaoglu, N., Manderick, B.: FAPSTER—a genetic algorithm for frequency assignment problem. In: Proc. of the 2005 Genetic and Evolutionary Computation Conference, Washington D.C., USA, 2005 Google Scholar
  26. Karp, R.M.: Probabilistic analysis of partitioning algorithms for the traveling-salesman problem in the plane. Math. Oper. Res. 2(3), 209–224 (1977) zbMATHCrossRefMathSciNetGoogle Scholar
  27. Koster, A.M.C.A., van Hoesel, C.P.M., Kolen, A.W.J.: Solving partial constraint satisfaction problems with tree decomposition. Networks 40(3), 170–180 (2002) zbMATHCrossRefMathSciNetGoogle Scholar
  28. Kravets, V.L., Sergienko, I.V.: Decomposition method of solving a class of combinatorial optimization problems. Cybern. Syst. Anal. 19(6), 833–837 (1983) zbMATHCrossRefMathSciNetGoogle Scholar
  29. Mannino, C., Sassano, A.: An enumerative algorithm for the frequency assignment problem. Discrete Appl. Math. 129(1), 155–169 (2003) zbMATHCrossRefMathSciNetGoogle Scholar
  30. Mannino, C., Oriolo, G., Ricci, F.: Solving stability problems on a superclass of interval graphs. T.R. n. 511, Vito Volterra (2002) Google Scholar
  31. Montemanni, R., Moon, J.N., Smith, D.H.: An improved tabu search algorithm for the fixed-spectrum frequency-assignment problem. IEE Trans. Veh. Technol. 52(3), 891–901 (2003) CrossRefGoogle Scholar
  32. Pardalos, P., Rappe, J., Resende, M.: An exact parallel algorithm for the maximum clique problem. In: De Leone, P.P.R., Murl’i, A., Toraldo, G. (eds.) High Performance Algorithms and Software in Nonlinear Optimization. Kluwer, Dordrecht (1998) Google Scholar
  33. Pekny, J.F., Miller, D.L.: An exact parallel algorithm for the resource constrained traveling salesman problem with application to scheduling with an aggregate deadline. In: Proc. of the 1990 ACM Annual Conference on Cooperation, Washington, D.C., USA, 1990 Google Scholar
  34. Ralphs, T.K.: Parallel branch and cut for capacitated vehicle routing. Parallel Comput. 29(5), 607–629 (2003) CrossRefGoogle Scholar
  35. Schabauer, H., Schikuta, E., Weishaupl, T.: Solving very large traveling salesman problems by SOM parallelization on cluster architectures. In: Proc. of Sixth International Conference on the Parallel and Distributed Computing, Applications and Technologies, Vienna, Austria, 2005 Google Scholar
  36. Taillard, E.D.: Parallel iterative search methods for vehicle routing problems. Networks 23, 661–673 (1993) zbMATHCrossRefGoogle Scholar
  37. Taillard, E.D.: Parallel taboo search techniques for the job shop scheduling problem. ORSA J. Comput. 6(2), 108–117 (1994) zbMATHGoogle Scholar
  38. Talbi, E.G., Mostaghim, S., Okabe, T., Ishibuchi, H., Rudolph, G., Coello, C.A.: Parallel approaches for multiobjective optimization. In: Lecture Notes in Computer Science, vol. 5252, pp. 349–372 (2008) Google Scholar
  39. Toulouse, M., Thulasiraman, K., Glover, F.: Multi-level cooperative search: a new paradigm for combinatorial optimization and an application to graph partitioning. In: Lecture Notes in Computer Science, vol. 1685, pp. 533–542 (1999) Google Scholar
  40. Valenzuela, C.L., Jones, A.J.: Evolutionary divide and conquer (I): A novel genetic approach to the TSP. Evol. Comput. 1(4), 313–333 (1993) CrossRefGoogle Scholar
  41. van Dongen, S.: A cluster algorithm for graphs. Technical Report INS-R0010, National Research Institute for Mathematics and Computer Science in the Netherlands, Amsterdam (2000) Google Scholar
  42. Walshaw, C.: A multilevel approach to the graph colouring problem. Tech. Rep. 01/IM/69, University of Greenwich, London (2001) Google Scholar
  43. Zhang, Y.: Parallel algorithms for combinatorial search problems. Ph.D. Thesis, University of California at Berkeley (1989) Google Scholar

Copyright information

© Springer Science+Business Media, LLC 2009

Authors and Affiliations

  1. 1.Centre for Intelligent Network Design, School of Computer ScienceCardiff UniversityCardiffUK

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