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Hybrid Metaheuristics pp 417–432Cite as

Predicting Metaheuristic Performance on Graph Coloring Problems Using Data Mining

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

Abstract

This chapter illustrates the benefits of using data mining methods to gain greater understanding of the strengths and weaknesses of a metaheuristic across the whole of instance space. Using graph coloring as a case study, we demonstrate how the relationships between the features of instances and the performance of algorithms can be learned and visualized. The instance space (in this case, the set of all graph coloring instances) is characterized as a high-dimensional feature space, with each instance summarized by a set of metrics selected as indicative of instance hardness. We show how different instance generators produce instances with various properties, and how the performance of algorithms depends on these properties. Based on a set of tested instances, we reveal the generalized boundary in instance space where an algorithm can be expected to perform well. This boundary is called the algorithm footprint in instance space. We show how data mining methods can be used to visualize the footprint and relate its boundary to properties of the instances. In this manner, we can begin to develop a good understanding of the strengths and weaknesses of a set of algorithms, and identify opportunities to develop new hybrid approaches that exploit the combined strength and improve the performance across a broad instance space.

Keywords

  • Travel Salesman Problem
  • Betweenness Centrality
  • Algorithm Performance
  • Graph Coloring
  • Quadratic Assignment Problem

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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  • DOI: 10.1007/978-3-642-30671-6_16
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References

  1. Wolpert, D.H., Macready, W.G.: No free lunch theorems for optimization. IEEE Transactions on Evolutionary Computation 1(1), 67–82 (1997)

    CrossRef  Google Scholar 

  2. Culberson, J.: On the futility of blind search: An algorithmic view of ’no free lunch’. Evolutionary Computation 6(2), 109–127 (1998)

    CrossRef  Google Scholar 

  3. Blum, C., Roli, A.: Hybrid metaheuristics: An introduction. In: Hybrid Metaheuristics, pp. 1–30 (2008)

    Google Scholar 

  4. Talbi, E.: A taxonomy of hybrid metaheuristics. Journal of Heuristics 8(5), 541–564 (2002)

    CrossRef  Google Scholar 

  5. Burke, E., Kendall, G., Newall, J., Hart, E., Ross, P., Schulenburg, S.: Hyper-heuristics: An emerging direction in modern search technology. International Series in Operations Research and Management Science, pp. 457–474 (2003)

    Google Scholar 

  6. Leyton-Brown, K., Nudelman, E., Shoham, Y.: Learning the Empirical Hardness of Optimization Problems: The Case of Combinatorial Auctions. In: Van Hentenryck, P. (ed.) CP 2002. LNCS, vol. 2470, pp. 556–572. Springer, Heidelberg (2002)

    CrossRef  Google Scholar 

  7. Leyton-Brown, K., Nudelman, E., Andrew, G., McFadden, J., Shoham, Y.: A portfolio approach to algorithm selection. In: International Joint Conference on Artificial Intelligence, vol. 18, pp. 1542–1543 (2003)

    Google Scholar 

  8. Xu, L., Hutter, F., Hoos, H.H., Leyton-Brown, K.: SATzilla-07: The Design and Analysis of an Algorithm Portfolio for SAT. In: Bessière, C. (ed.) CP 2007. LNCS, vol. 4741, pp. 712–727. Springer, Heidelberg (2007)

    CrossRef  Google Scholar 

  9. Hooker, J.: Testing heuristics: We have it all wrong. Journal of Heuristics 1(1), 33–42 (1995)

    MathSciNet  MATH  CrossRef  Google Scholar 

  10. Corne, D.W., Reynolds, A.P.: Optimisation and Generalisation: Footprints in Instance Space. In: Schaefer, R., Cotta, C., Kołodziej, J., Rudolph, G. (eds.) PPSN XI, Part I. LNCS, vol. 6238, pp. 22–31. Springer, Heidelberg (2010)

    CrossRef  Google Scholar 

  11. Smith-Miles, K.A., Lopes, L.B.: Measuring instance difficulty for combinatorial optimization problems. Computers and Operations Research 39(5), 875–889 (2012)

    MathSciNet  CrossRef  Google Scholar 

  12. Macready, W., Wolpert, D.: What makes an optimization problem hard. Complexity 5, 40–46 (1996)

    MathSciNet  Google Scholar 

  13. van Hemert, J., Urquhart, N.: Phase Transition Properties of Clustered Travelling Salesman Problem Instances Generated with Evolutionary Computation. In: Yao, X., Burke, E.K., Lozano, J.A., Smith, J., Merelo-Guervós, J.J., Bullinaria, J.A., Rowe, J.E., Tiňo, P., Kabán, A., Schwefel, H.-P. (eds.) PPSN 2004. LNCS, vol. 3242, pp. 151–160. Springer, Heidelberg (2004)

    CrossRef  Google Scholar 

  14. Smith-Miles, K., van Hemert, J., Lim, X.Y.: Understanding TSP Difficulty by Learning from Evolved Instances. In: Blum, C., Battiti, R. (eds.) LION 4. LNCS, vol. 6073, pp. 266–280. Springer, Heidelberg (2010)

    CrossRef  Google Scholar 

  15. Smith-Miles, K., van Hemert, J.: Discovering the suitability of optimisation algorithms by learning from evolved instances. Annals of Mathematics and Artificial Intelligence (in press)

    Google Scholar 

  16. Merz, P., Freisleben, B.: Fitness landscape analysis and memetic algorithms for the quadratic assignment problem. IEEE Transactions on Evolutionary Computation 4(4), 337–352 (2000)

    CrossRef  Google Scholar 

  17. Merz, P.: Advanced fitness landscape analysis and the performance of memetic algorithms. Evolutionary Computation 12(3), 303–325 (2004)

    MathSciNet  CrossRef  Google Scholar 

  18. Achlioptas, D., Naor, A., Peres, Y.: Rigorous location of phase transitions in hard optimization problems. Nature 435(7043), 759–764 (2005)

    CrossRef  Google Scholar 

  19. Cheeseman, P., Kanefsky, B., Taylor, W.: Where the really hard problems are. In: Proceedings of the 12th IJCAI, pp. 331–337 (1991)

    Google Scholar 

  20. Smith-Miles, K., James, R., Giffin, J., Tu, Y.: Understanding the Relationship between Scheduling Problem Structure and Heuristic Performance using Knowledge Discovery. LNCS (2009) (in press)

    Google Scholar 

  21. Smith-Miles, K.: Towards insightful algorithm selection for optimisation using meta-learning concepts. In: IEEE International Joint Conference on Neural Networks, IJCNN 2008 (IEEE World Congress on Computational Intelligence), pp. 4118–4124 (2008)

    Google Scholar 

  22. Smith-Miles, K., Lopes, L.: Generalising Algorithm Performance in Instance Space: A Timetabling Case Study. In: Coello, C.A.C. (ed.) LION 2011. LNCS, vol. 6683, pp. 524–538. Springer, Heidelberg (2011)

    CrossRef  Google Scholar 

  23. Hill, R., Reilly, C.: The effects of coefficient correlation structure in two-dimensional knapsack problems on solution procedure performance. Management Science, 302–317 (2000)

    Google Scholar 

  24. Pardalos, P., Mavridou, T., Xue, J.: The graph coloring problem: A bibliographic survey, vol. 2. Kluwer Academic Publishers (1998)

    Google Scholar 

  25. Galinier, P., Hertz, A.: A survey of local search methods for graph coloring. Computers & Operations Research 33(9), 2547–2562 (2006)

    MathSciNet  MATH  CrossRef  Google Scholar 

  26. Brélaz, D.: New methods to color the vertices of a graph. Communications of the ACM 22(4), 251–256 (1979)

    MATH  CrossRef  Google Scholar 

  27. Hertz, A., Werra, D.: Using tabu search techniques for graph coloring. Computing 39(4), 345–351 (1987)

    MathSciNet  MATH  CrossRef  Google Scholar 

  28. Johnson, D., Aragon, C., McGeoch, L., Schevon, C.: Optimization by simulated annealing: an experimental evaluation; part ii, graph coloring and number partitioning. Operations Research, 378–406 (1991)

    Google Scholar 

  29. Chiarandini, M., Stützle, T., et al.: An application of iterated local search to graph coloring problem. In: Proceedings of the Computational Symposium on Graph Coloring and its Generalizations, pp. 7–8. Citeseer (2002)

    Google Scholar 

  30. Hamiez, J.-P., Hao, J.-K.: Scatter Search for Graph Coloring. In: Collet, P., Fonlupt, C., Hao, J.-K., Lutton, E., Schoenauer, M. (eds.) EA 2001. LNCS, vol. 2310, pp. 168–213. Springer, Heidelberg (2002)

    CrossRef  Google Scholar 

  31. Galinier, P., Hao, J.: Hybrid evolutionary algorithms for graph coloring. Journal of Combinatorial Optimization 3(4), 379–397 (1999)

    MathSciNet  MATH  CrossRef  Google Scholar 

  32. Fleurent, C., Ferland, J.: Genetic and hybrid algorithms for graph coloring. Annals of Operations Research 63(3), 437–461 (1996)

    MATH  CrossRef  Google Scholar 

  33. Blöchliger, I., Zufferey, N.: A graph coloring heuristic using partial solutions and a reactive tabu scheme. Computers & Operations Research 35(3), 960–975 (2008)

    MathSciNet  MATH  CrossRef  Google Scholar 

  34. Hooker, J.: Needed: An empirical science of algorithms. Operations Research, 201–212 (1994)

    Google Scholar 

  35. Culberson, J.: Graph coloring page (2006), http://www.cs.ualberta.ca/~joe/Coloring

  36. Culberson, J., Beacham, A., Papp, D.: Hiding our colors. In: CP 1995 Workshop on Studying and Solving Really Hard Problems. Citeseer (1995)

    Google Scholar 

  37. Mohar, B.: The laplacian spectrum of graphs. Graph Theory, Combinatorics, and Applications 2, 871–898 (1991)

    MathSciNet  Google Scholar 

  38. Biggs, N.: Algebraic graph theory, vol. 67. Cambridge Univ. Pr. (1993)

    Google Scholar 

  39. Rice, J.: The Algorithm Selection Problem. Advances in Computers 15, 65–117 (1976)

    CrossRef  Google Scholar 

  40. Smith-Miles, K.: Cross-disciplinary perspectives on meta-learning for algorithm selection. ACM Computing Surveys 41(1) (2008)

    Google Scholar 

  41. Kohonen, T.: Self-organized formation of topologically correct feature maps. Biological Cybernetics 43(1), 59–69 (1982)

    MathSciNet  MATH  CrossRef  Google Scholar 

  42. Somine, V.: Eudaptics software Gmbh

    Google Scholar 

  43. Knowles, J., Corne, D.: Towards landscape analyses to inform the design of a hybrid local search for the multiobjective quadratic assignment problem. Soft Computing Systems: Design, Management and Applications, 271–279 (2002)

    Google Scholar 

  44. Bierwirth, C., Mattfeld, D.C., Watson, J.-P.: Landscape Regularity and Random Walks for the Job-Shop Scheduling Problem. In: Gottlieb, J., Raidl, G.R. (eds.) EvoCOP 2004. LNCS, vol. 3004, pp. 21–30. Springer, Heidelberg (2004)

    CrossRef  Google Scholar 

  45. Schiavinotto, T., Stützle, T.: A review of metrics on permutations for search landscape analysis. Comput. Oper. Res. 34(10), 3143–3153 (2007)

    MATH  CrossRef  Google Scholar 

  46. Lopes, L., Smith-Miles, K.: Generating applicable synthetic instances for branch problems, under review (2011)

    Google Scholar 

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Authors and Affiliations

  1. School of Mathematical Sciences, Monash University, Melbourne, Victoria, 3800, Australia

    Kate Smith-Miles, Brendan Wreford, Leo Lopes & Nur Insani

Authors
  1. Kate Smith-Miles
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  2. Brendan Wreford
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  3. Leo Lopes
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  4. Nur Insani
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Correspondence to Kate Smith-Miles .

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  1. , Cite Scientifique, University of Lille 1, Bat.M3, Villeneuve d'Ascq, 59655, France

    El-Ghazali Talbi

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Smith-Miles, K., Wreford, B., Lopes, L., Insani, N. (2013). Predicting Metaheuristic Performance on Graph Coloring Problems Using Data Mining. In: Talbi, EG. (eds) Hybrid Metaheuristics. Studies in Computational Intelligence, vol 434. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-30671-6_16

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  • DOI: https://doi.org/10.1007/978-3-642-30671-6_16

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