Hybrid Metaheuristics for the Graph Partitioning Problem

Part of the Studies in Computational Intelligence book series (SCI, volume 434)

Abstract

The Graph Partitioning Problem (GPP) is one of the most studied NP-complete problems notable for its broad spectrum of applicability such as in VLSI design, data mining, image segmentation, etc. Due to its high computational complexity, a large number of approximate approaches have been reported in the literature. Hybrid algorithms that are based on adaptations of popular metaheuristic techniques have shown to provide outstanding performance in terms of partition quality. In particular, it is the hybrids between well-known metaheuristics and multilevel strategies that report partitions of the minimal cut-size value. However, metaheuristic hybrids generally require more computing time than those based on greedy heuristics which can generate partitions of acceptable quality in a matter of seconds even for very large graphs. This chapter is dedicated to a review on some representative hybrid metaheuristic approaches including genetic local search, basic multilevel search and recent development on hybrid multilevel search.

Keywords

Tabu Search Memetic Algorithm Graph Partitioning Graph Partitioning Problem Fiedler Vector 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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References

  1. 1.
    Alpert, J.C., Kahng, B.A.: Recent directions in netlist partitioning: A survey. Integration, the VLSI Journal 19(12), 1–81 (1995)MATHCrossRefGoogle Scholar
  2. 2.
    Alpert, J.C., Hagen, W.L., Kahng, B.A.: A hybrid multilevel/genetic approach for circuit partitioning. In: Proceedings of the IEEE Asia Pacific Conference on Circuits and Systems, pp. 298–301 (1996)Google Scholar
  3. 3.
    Barake, M., Chardaire, P., McKeown, G.P.: The PROBE metaheuristic for the multiconstraint knapsack problem. In: Resende, M.G.C., de Sousa, J.P. (eds.) Metaheuritics, pp. 19–36. Springer (2004)Google Scholar
  4. 4.
    Barnard, T.S., Simon, D.H.: A Fast Multilevel Implementation of Recursive Spectral Bisection for Partitioning Unstructured Problems. In: Proceedings of the 6th SIAM Conference on Parallel Processing for Scientific Computing, pp. 711–718 (1993)Google Scholar
  5. 5.
    Baños, R., Gil, C., Ortega, J., Montoya, F.G.: Multilevel Heuristic Algorithm for Graph Partitioning. In: Raidl, G.R., Cagnoni, S., Cardalda, J.J.R., Corne, D.W., Gottlieb, J., Guillot, A., Hart, E., Johnson, C.G., Marchiori, E., Meyer, J.-A., Middendorf, M. (eds.) EvoIASP 2003, EvoWorkshops 2003, EvoSTIM 2003, EvoROB/EvoRobot 2003, EvoCOP 2003, EvoBIO 2003, and EvoMUSART 2003. LNCS, vol. 2611, pp. 143–153. Springer, Heidelberg (2003)CrossRefGoogle Scholar
  6. 6.
    Battiti, R., Bertossi, A.: Differential Greedy for the 0-1 Equicut Problem. In: Proceedings of the DIMACS Workshop on Network Design: Connectivity and Facilities Location, pp. 3–21 (1997)Google Scholar
  7. 7.
    Battiti, R., Bertossi, A.: Greedy, prohibition, and reactive heuristics for graph partitioning. IEEE Transactions on Computers 48(4), 361–385 (1999)CrossRefGoogle Scholar
  8. 8.
    Battiti, R., Bertossi, A., Cappelletti, A.: Multilevel reactive tabu search for graph partitioning. Preprint UTM 554. Dip. Mat., University Trento, Italy (1999)Google Scholar
  9. 9.
    Benlic, U., Hao, J.K.: An effective multilevel tabu search approach for balanced graph partitioning. Computers and Operations Research 38(7), 1066–1075 (2010)MathSciNetCrossRefGoogle Scholar
  10. 10.
    Benlic, U., Hao, J.K.: An Effective Multilevel Memetic Algorithm for Balanced Graph Partitioning. In: ICTAI, vol. (1), pp. 121–128 (2010)Google Scholar
  11. 11.
    Benlic, U., Hao, J.K.: A multilevel memetic approach for improving graph k-partitions. To appear in IEEE Transactions on Evolutionary Computation (2011)Google Scholar
  12. 12.
    Brandt, A., McCormick, S., Ruge, J.: Algebraic multigrid (AMG) for sparse matrix equations. In: Evans, D.J. (ed.) Sparsity and its Applications, pp. 257–284 (1984)Google Scholar
  13. 13.
    Brandt, A.: Algebraic multigrid theory: The symmetric case. In: Preliminary Proceedings of the International Multigrid Congerence, vol. 19, pp. 23–56 (1986)Google Scholar
  14. 14.
    Bui, T.N., Moon, B.R.: Genetic Algorithm and Graph Partitioning. IEEE Transactions on Computers 45(7), 841–855 (1996)MathSciNetMATHCrossRefGoogle Scholar
  15. 15.
    Chardaire, P., Barake, M., McKeown, G.P.: A PROBE-based heuristic for graph partitioning. IEEE Transactions on Computers 56(12), 1707–1720 (2007)MathSciNetCrossRefGoogle Scholar
  16. 16.
    Ciarlet, P., Lamour, F.: On the validity of a front-oriented approach to partitioning large sparse graphs with a connectivity. Numerical Algorithms 12(1), 193–214 (1996)MathSciNetMATHCrossRefGoogle Scholar
  17. 17.
    Chevalier, C., Safro, I.: Comparison of Coarsening Schemes for Multilevel Graph Partitioning. In: Stützle, T. (ed.) LION 3. LNCS, vol. 5851, pp. 191–205. Springer, Heidelberg (2009)CrossRefGoogle Scholar
  18. 18.
    Eshelman, L.J.: The CHC adaptive search algorithm: How to have a safe search when engaging in non-traditional genetic recombination. In: Rawlings, G.J.E. (ed.) Foundations of Genetic Algorithms, pp. 265–283 (1991)Google Scholar
  19. 19.
    Garbers, J., Prome, H.J., Steger, A.: Finding clusters in VLSI circuits. In: Proceedings of IEEE International Conference on Computer Aided Design, pp. 520–523 (1990)Google Scholar
  20. 20.
    Gusfield, D.: Partition-Distance: A Problem and Class of Perfect Graphs Arising in Clustering. Information Processing Letters 82(3), 159–164 (2002)MathSciNetMATHCrossRefGoogle Scholar
  21. 21.
    Fiduccia, C., Mattheyses, R.: A linear-time heuristics for improving network partitions. In: Proceedings of the 19th Design Automation Conference, pp. 171–185 (1982)Google Scholar
  22. 22.
    Hagen, L., Kahng, A.: A new approach to effective circuit clustering. In: Proceedings of IEEE International Conference on Computer Aided Design, pp. 422–427 (1992)Google Scholar
  23. 23.
    Hendrickson, B., Leland, R.: A multilevel algorithm for partitioning graphs. In: Proceedings of Supercomputing, CDROM (1995)Google Scholar
  24. 24.
    Holtgrewe, M., Sanders, P., Schulz, C.: Engineering a scalable high quality graph partitioner. In: Proceedings of IEEE International Parallel & and Distributed Processing Symposium, pp. 1–12 (2010)Google Scholar
  25. 25.
    Johnson, D.S., Aragon, C.R., Mcgeoch, L.A., Schevon, C.: Optimization by Simulated Annealing: An Experimental Evaluation; Part-I, Graph Partitioning. Operations Research 37, 865–892 (1989)MATHCrossRefGoogle Scholar
  26. 26.
    Jones, T., Forrest, S.: Fitness Distance Correlation as a Measure of Problem Difficulty for Genetic Algorithms. In: Proceedings of the 6th International Conference on Genetic Algorithms, pp. 184–192. Morgan Kaufmann (1995)Google Scholar
  27. 27.
    Karypis, G., Kumar, V.: A Fast and High Quality Multilevel Scheme for Partitioning Irregular Graphs. SIAM Journal on Scientific Computing 20(1), 359–392 (1998)MathSciNetCrossRefGoogle Scholar
  28. 28.
    Karypis, G., Kumar, V.: Multilevel k-way Partitioning Scheme for Irregular Graphs. Journal of Parallel and Distributed Computing 48(1), 96–129 (1998)MathSciNetCrossRefGoogle Scholar
  29. 29.
    Kernighan, B.W., Lin, S.: An efficient heuristic procedure for partitioning graphs. Bell System Technical Journal 49, 291–307 (1970)MATHGoogle Scholar
  30. 30.
    Küçükpetek, S., Polat, F., Oğuztüzün, H.: Multilevel graph partitioning: an evolutionary approach. Journal of the Operational Research Society 56, 549–562 (2005)MATHCrossRefGoogle Scholar
  31. 31.
    Krishnarnurthy, B.: An Improved Min-Cut Algorithm for Partitioning VLSI Networks. IEEE Transactions on Computers 33, 438–446 (1984)CrossRefGoogle Scholar
  32. 32.
    Merz, P., Freisleben, B.: Fitness Landscapes, Memetic Algorithms. and Greedy Operators for Graph Bipartitioning. Journal of Evolutionary Computation 8(1), 61–91 (2000)Google Scholar
  33. 33.
    Lü, Z., Hao, J.K.: A Memetic Algorithm for Graph Coloring. European Journal of Operational Research 203(1), 241–250 (2010)MathSciNetMATHCrossRefGoogle Scholar
  34. 34.
    Nascimento, M., de Carvalho, A.: Spectral methods for graph clustering: A survey. European Journal of Operational Research 211(2011), 221–231 (2010)Google Scholar
  35. 35.
    Papadimitriou, C., Steiglitz, K.: Combinatorial Optimization: Algorithms and Complexity. Prentice-Hall (1982)Google Scholar
  36. 36.
    Pellegrini, F.: Scotch home page, http://www.labri.fr/pelegrin/scotch
  37. 37.
    Safro, I., Dorit, R., Brandt, A.: Multilevel algorithms for linear ordering problems. Journal of Experimental Algorithmics 13, 1–14 (2008)Google Scholar
  38. 38.
    Sanchis, L.: Multiple-Way Network Partitioning. IEEE Transactions on Computers 38(1), 62–81 (1989)MATHCrossRefGoogle Scholar
  39. 39.
    Sanchis, L.: Multiple-Way Network Partitioning with Different Cost Functions. IEEE Transactions on Computers 42(12), 1500–1504 (1993)CrossRefGoogle Scholar
  40. 40.
    Schloegel, K., Karypis, G., Kumar, V.: Graph partitioning for high performance scientific simulations. In: Dongarra, J., et al. (eds.) CRPC Parallel Computing Handbook. Morgan Kaufmann (2000)Google Scholar
  41. 41.
    Simon, H., Teng, S.H.: How good is recursive bisection. SIAM J. Sci. Comput. 18(5), 1436–1445 (1997)Google Scholar
  42. 42.
    Shi, J., Malik, J.: Normalized Cuts and Image Segmentation. In: Proceedings of the IEEE Computer Society Conference on Computer Vision and Pattern Recognition, pp. 731–737 (1997)Google Scholar
  43. 43.
    Słowik, A., Białko, M.: Partitioning of VLSI Circuits on Subcircuits with Minimal Number of Connections Using Evolutionary Algorithm. In: Rutkowski, L., Tadeusiewicz, R., Zadeh, L.A., Żurada, J.M. (eds.) ICAISC 2006. LNCS (LNAI), vol. 4029, pp. 470–478. Springer, Heidelberg (2006)CrossRefGoogle Scholar
  44. 44.
    Soper, A.J., Walshaw, C., Cross, M.: A Combined Evolutionary Search and Multilevel Optimisation Approach to Graph-partitioning. Journal of Global Optimization 29(2), 225–241 (2004)MathSciNetMATHCrossRefGoogle Scholar
  45. 45.
    Sun, L., Leng, M.: An Effective Multi-Level Algorithm Based on Simulated Annealing for Bisecting Graph. In: Yuille, A.L., Zhu, S.-C., Cremers, D., Wang, Y. (eds.) EMMCVPR 2007. LNCS, vol. 4679, pp. 1–12. Springer, Heidelberg (2007)CrossRefGoogle Scholar
  46. 46.
    Viswanathan, N., Alpert, C.J., Sze, C., Li, Z., Nam, G.J., Roy, J.A.: The ISPD-2011 Routability-Driven Placement Contest and Benchmark Suite. In: Proc. ACM International Symposium on Physical Design, pp. 141–146 (2011)Google Scholar
  47. 47.
    Walshaw, C.: Multilevel refinement for combinatorial optimisation problems. Annals of Operations Research 131, 325–372 (2004)MathSciNetMATHCrossRefGoogle Scholar
  48. 48.
    Walshaw, C., Cross, M.: JOSTLE: Parallel Multilevel Graph-Partitioning Software – An Overview. In: Magoules, F. (ed.) Mesh Partitioning Techniques and Domain Decomposition Techniques, pp. 27–58 (2007)Google Scholar
  49. 49.
    Zha, H., He, X., Ding, C., Simon, H., Gu, M.: Bipartite Graph Partitioning and Data Clustering. In: Proceedings of the ACM 10th International Conference on Information and Knowledge, pp. 25–31 (2001)Google Scholar

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© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  1. 1.LERIAUniversity of AngersAngers Cedex 01France

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