Advertisement

The Algorithm Selection Problem on the Continuous Optimization Domain

  • Mario A. Muñoz
  • Michael Kirley
  • Saman K. Halgamuge
Conference paper
Part of the Studies in Computational Intelligence book series (SCI, volume 445)

Abstract

The problem of algorithm selection, that is identifying the most efficient algorithm for a given computational task, is non-trivial. Meta-learning techniques have been used successfully for this problem in particular domains, including pattern recognition and constraint satisfaction. However, there has been a paucity of studies focused specifically on algorithm selection for continuous optimization problems. This may be attributed to some extent to the difficulties associated with quantifying problem “hardness” in terms of the underlying cost function. In this paper, we provide a survey of the related literature in the continuous optimization domain. We discuss alternative approaches for landscape analysis, algorithm modeling and portfolio development. Finally, we propose a meta-learning framework for the algorithm selection problem in the continuous optimization domain.

Keywords

Algorithm Selection Fitness Landscape Continuous Optimization Combinatorial Auction Landscape Analysis 
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.
This is a preview of subscription content, log in to check access.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Achiloptas, D., Naor, A., Peres, Y.: Rigorous location of phase transitions in hard optimization problems. Nature 435, 759–764 (2005)CrossRefGoogle Scholar
  2. 2.
    Anderson, E.: Markov chain modelling of the solution surface in local search. J. Oper. Res. Soc. 53(6), 630–636 (2002)zbMATHCrossRefGoogle Scholar
  3. 3.
    Angel, E., Zissimopoulos, V.: On the hardness of the quadratic assignment problem with metaheuristics. Heuristics 8(4), 399–414 (2002)CrossRefGoogle Scholar
  4. 4.
    Bartz-Beielstein, T., Markon, S.: Tuning search algorithms for real-world applications: a regression tree based approach. In: CEC 2004, vol. 1, pp. 1111–1118 (2004)Google Scholar
  5. 5.
    Bartz-Beielstein, T., Parsopoulos, K., Vrahatis, M.: Analysis of particle swarm optimization using computational statistics. In: ICNAAM 2004, pp. 34–37 (2004)Google Scholar
  6. 6.
    Beck, J., Watson, J.: Adaptive search algorithms and Fitness-Distance correlation. In: Proc. 5th Metaheuristics Int. Conf. (2003)Google Scholar
  7. 7.
    Borenstein, Y., Poli, R.: Fitness Distributions and GA Hardness. 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. 11–20. Springer, Heidelberg (2004)CrossRefGoogle Scholar
  8. 8.
    Borenstein, Y., Poli, R.: Information landscapes. In: GECCO 2005, pp. 1515–1522. ACM (2005)Google Scholar
  9. 9.
    Borenstein, Y., Poli, R.: Kolmogorov complexity, optimization and hardness. In: CEC 2006, pp. 112–119 (2006)Google Scholar
  10. 10.
    Boukeas, G., Halatsis, C., Zissimopoulos, V., Stamatopoulos, P.: Measures of Intrinsic Hardness for Constraint Satisfaction Problem Instances. In: Van Emde Boas, P., Pokorný, J., Bieliková, M., Štuller, J. (eds.) SOFSEM 2004. LNCS, vol. 2932, pp. 184–195. Springer, Heidelberg (2004)CrossRefGoogle Scholar
  11. 11.
    Branke, J., Schmidt, C.: Faster convergence by means of fitness estimation. Soft Comput. 9(1), 13–20 (2005)CrossRefGoogle Scholar
  12. 12.
    Brooks, C., Durfee, E.: Using Landscape Theory to Measure Learning Difficulty for Adaptive Agents. In: Alonso, E., Kudenko, D., Kazakov, D. (eds.) AAMAS 2000 and AAMAS 2002. LNCS (LNAI), vol. 2636, pp. 291–305. Springer, Heidelberg (2003)CrossRefGoogle Scholar
  13. 13.
    Carchrae, T., Beck, J.: Low knowledge algorithm control. In: AAAI 2004, pp. 49–54 (2004)Google Scholar
  14. 14.
    Carchrae, T., Beck, J.: Applying machine learning to low-knowledge control of optimization algorihms. Comput. Intell. 21(4), 372–387 (2005)MathSciNetCrossRefGoogle Scholar
  15. 15.
    Davidor, Y.: Epistasis variance: A viewpoint on GA-hardness. In: Foundations of Genetic Algorithms. Morgan Kaufmann (1991)Google Scholar
  16. 16.
    Eiben, A., Hinterding, R., Michalewicz, Z.: Parameter control in evolutionary algorithms. IEEE Trans. Evol. Comput. 3(2), 124–141 (1999)CrossRefGoogle Scholar
  17. 17.
    Eremeev, A.V., Reeves, C.R.: Non-parametric Estimation of Properties of Combinatorial Landscapes. In: Cagnoni, S., Gottlieb, J., Hart, E., Middendorf, M., Raidl, G.R. (eds.) EvoIASP 2002, EvoWorkshops 2002, EvoSTIM 2002, EvoCOP 2002, and EvoPlan 2002. LNCS, vol. 2279, pp. 31–40. Springer, Heidelberg (2002)CrossRefGoogle Scholar
  18. 18.
    Eremeev, A.V., Reeves, C.R.: On Confidence Intervals for the Number of Local Optima. 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. 224–235. Springer, Heidelberg (2003)CrossRefGoogle Scholar
  19. 19.
    Fonlupt, C., Robilliard, D., Preux, P.: A Bit-Wise Epistasis Measure for Binary Search Spaces. In: Eiben, A.E., Bäck, T., Schoenauer, M., Schwefel, H.-P. (eds.) PPSN 1998. LNCS, vol. 1498, pp. 47–56. Springer, Heidelberg (1998)CrossRefGoogle Scholar
  20. 20.
    Francois, O., Lavergne, C.: Design of evolutionary algorithms-A statistical perspective. IEEE Trans. Evol. Comput. 5(2), 129–148 (2001)CrossRefGoogle Scholar
  21. 21.
    Galván-López, E., McDermott, J., O’Neill, M., Brabazon, A.: Defining locality as a problem difficulty measure in genetic programming. Genet. Program Evolvable Mach. 12(4), 365–401 (2011)CrossRefGoogle Scholar
  22. 22.
    Garnier, J., Kallel, L.: Efficiency of local search with multiple local optima. SIAM J. Discrete Math. 15(1), 122–141 (2002)MathSciNetzbMATHCrossRefGoogle Scholar
  23. 23.
    Gomes, C., Selman, B.: Algorithm portfolios. Artif. Intell. 126(1-2), 43–62 (2001)MathSciNetzbMATHCrossRefGoogle Scholar
  24. 24.
    Graff, M., Poli, R.: Practical performance models of algorithms in evolutionary program induction and other domains. Artif. Intell. 174, 1254–1276 (2010)MathSciNetzbMATHCrossRefGoogle Scholar
  25. 25.
    Grobler, J., Engelbrecht, A., Kendall, G., Yadavalli, V.: Alternative hyper-heuristic strategies for multi-method global optimization. In: CEC 2010, pp. 1–8 (2010)Google Scholar
  26. 26.
    He, J., Reeves, C., Witt, C., Yao, X.: A note on problem difficulty measures in black-box optimization: Classification, realizations and predictability. Evol. Comput. 15(4), 435–443 (2007)CrossRefGoogle Scholar
  27. 27.
    Heckendorn, R., Whitley, D.: Predicting epistasis from mathematical models. Evol. Comput. 7(1), 69–101 (1999)CrossRefGoogle Scholar
  28. 28.
    Hilario, M., Kalousis, A., Nguyen, P., Woznica, A.: A data mining ontology for algorithm selection and meta-mining. In: SoKD 2009, pp. 76–87 (2009)Google Scholar
  29. 29.
    Hough, P., Williams, P.: Modern machine learning for automatic optimization algorithm selection. In: INFORMS AI/DM Workshop (2006)Google Scholar
  30. 30.
    Hutter, F., Hamadi, Y., Hoos, H.H., Leyton-Brown, K.: Performance Prediction and Automated Tuning of Randomized and Parametric Algorithms. In: Benhamou, F. (ed.) CP 2006. LNCS, vol. 4204, pp. 213–228. Springer, Heidelberg (2006)CrossRefGoogle Scholar
  31. 31.
    Hutter, F., Hamadi, Y., Hoos, H., Leyton-Brown, K.: Performance prediction and automated tuning of randomized and parametric algorithms: An initial investigation. In: The AAAI Workshop on Learning for Search: Schedule (2006)Google Scholar
  32. 32.
    Hutter, F., Hoos, H., Leyton-Brown, K.: Tradeoffs in the empirical evaluation of competing algorithm designs. Tech. Rep. TR-2009-21, The University of British Columbia (2009)Google Scholar
  33. 33.
    Jansen, T.: On classifications of fitness functions. Tech. Rep. CI-76/99, University of Dortmund (1999)Google Scholar
  34. 34.
    Jones, T., Forrest, S.: Fitness distance correlation as a measure of problem difficulty for genetic algorithms. In: GECCO 1995, pp. 184–192. Morgan Kaufmann Publishers Inc. (1995)Google Scholar
  35. 35.
    Jong, K.D.: Parameter setting in EAs: a 30 year perspective. In: Parameter Setting in Evolutionary Algorithms, Stud. Comput Intell., vol. 54, pp. 1–18. Springer (2005)Google Scholar
  36. 36.
    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)CrossRefGoogle Scholar
  37. 37.
    Leyton-Brown, K., Nudelman, E., Shoham, Y.: Empirical hardness models: Methodology and a case study on combinatorial auctions. J. ACM 56(4), 22:1–22:52 (2009)Google Scholar
  38. 38.
    Liu, L., Abbass, H., Green, D., Zhong, W.: Motif difficulty (MD): a predictive measure of problem difficulty for evolutionary algorithms using network motifs. Evol. Comput. 20(3), 321–347 (2012)Google Scholar
  39. 39.
    Lunacek, M., Whitley, D.: The dispersion metric and the CMA evolution strategy. In: GECCO 2006, pp. 477–484. ACM, New York (2006)CrossRefGoogle Scholar
  40. 40.
    Merkuryeva, G., Bolshakovs, V.: Structural analysis of benchmarking fitness landscapes. Scientific Journal of Riga Technical University: Computer Sciences 42, 81–86 (2010)CrossRefGoogle Scholar
  41. 41.
    Mersmann, O., Bischl, B., Trautmann, H., Preuss, M., Weihs, C., Rudolph, G.: Exploratory landscape analysis. In: GECCO 2011, pp. 829–836. ACM (2011)Google Scholar
  42. 42.
    Messelis, T., Haspeslagh, S., Bilgin, B., Causmaecker, P.D., Berghe, G.V.: Towards prediction of algorithm performance in real world optimisation problems. In: BNAIC 2009, pp. 177–183 (2009)Google Scholar
  43. 43.
    Molina, D., Herrera, F., Lozano, M.: Adaptive local search parameters for real-coded memetic algorithms. In: CEC 2005, vol. 1, pp. 888–895 (2005)Google Scholar
  44. 44.
    Muñoz, M., Kirley, M., Halgamuge, S.: Landscape characterization of numerical optimization problems using biased scattered data. In: CEC 2012, pp. 2162–2169 (2012)Google Scholar
  45. 45.
    Muñoz, M.A., Kirley, M., Halgamuge, S.K.: A Meta-learning Prediction Model of Algorithm Performance for Continuous Optimization Problems. In: Coello Coello, C.A., Cutello, V., Deb, K., Forrest, S., Nicosia, G., Pavone, M. (eds.) PPSN 2012, Part I. LNCS, vol. 7491, pp. 226–235. Springer, Heidelberg (2012)Google Scholar
  46. 46.
    Müller, C.L., Sbalzarini, I.F.: Global Characterization of the CEC 2005 Fitness Landscapes Using Fitness-Distance Analysis. In: Di Chio, C., Cagnoni, S., Cotta, C., Ebner, M., Ekárt, A., Esparcia-Alcázar, A.I., Merelo, J.J., Neri, F., Preuss, M., Richter, H., Togelius, J., Yannakakis, G.N. (eds.) EvoApplications 2011, Part I. LNCS, vol. 6624, pp. 294–303. Springer, Heidelberg (2011)CrossRefGoogle Scholar
  47. 47.
    Naudts, B., Kallel, L.: A comparison of predictive measures of problem difficulty in evolutionary algorithms. IEEE Trans. Evol. Comput. 4(1), 1–15 (2000)CrossRefGoogle Scholar
  48. 48.
    Naudts, B., Suys, D., Verschoren, A.: Epistasis as a basic concept in formal landscape analysis. In: GECCO 1997, pp. 65–72. Morgan Kaufmann (1997)Google Scholar
  49. 49.
    Özcan, E., Bilgin, B., Korkmaz, E.E.: Hill Climbers and Mutational Heuristics in Hyperheuristics. In: Runarsson, T.P., Beyer, H.-G., Burke, E.K., Merelo-Guervós, J.J., Whitley, L.D., Yao, X. (eds.) PPSN 2006. LNCS, vol. 4193, pp. 202–211. Springer, Heidelberg (2006)CrossRefGoogle Scholar
  50. 50.
    Pedersen, M.: Tuning & simplifying heuristical optimization. PhD thesis, University of Southampton (2009)Google Scholar
  51. 51.
    Peng, F., Tang, K., Chen, G., Yao, X.: Population-Based algorithm portfolios for numerical optimization. IEEE Trans. Evol. Comput. 14(5), 782–800 (2010)CrossRefGoogle Scholar
  52. 52.
    Petrovic, S., Epstein, S., Wallace, R.: Learning a mixture of search heuristics. In: CP 2007 (2007)Google Scholar
  53. 53.
    Reeves, C.: Fitness landscapes. In: Search Methodologies, pp. 587–610. Springer (2005)Google Scholar
  54. 54.
    Reeves, C., Eremeev, A.: Statistical analysis of local search landscapes. J. Oper. Res. Soc. 55(7), 687–693 (2004)zbMATHCrossRefGoogle Scholar
  55. 55.
    Reeves, C., Wright, C.: An experimental design perspective on genetic algorithms. In: Foundations of Genetic Algorithms, vol. 3, pp. 7–22. Morgan Kaufmann (1995)Google Scholar
  56. 56.
    Rice, J.: The algorithm selection problem. In: Adv. Comput., vol. 15, pp. 65–118. Elsevier (1976)Google Scholar
  57. 57.
    Rice, J.: Methodology for the algorithm selection problem. In: Proc. IFIP TC 2.5 Working Conference on Performance Evaluation of Numerical Software (1979)Google Scholar
  58. 58.
    Rochet, S., Venturini, G., Slimane, M., El Kharoubi, E.M.: A Critical and Empirical Study of Epistasis Measures for Predicting GA Performances: A Summary. In: Hao, J.-K., Lutton, E., Ronald, E., Schoenauer, M., Snyers, D. (eds.) AE 1997. LNCS, vol. 1363, pp. 275–285. Springer, Heidelberg (1998)CrossRefGoogle Scholar
  59. 59.
    Rockmore, D., Kostelec, P., Hordijk, W., Stadler, P.: Fast fourier transform for fitness landscapes. Appl. Comput. Harmon Anal. 12(1), 57–76 (2002)MathSciNetzbMATHCrossRefGoogle Scholar
  60. 60.
    Seo, D., Moon, B.: An Information-Theoretic analysis on the interactions of variables in combinatorial optimization problems. Evol. Comput. 15(2), 169–198 (2007)CrossRefGoogle Scholar
  61. 61.
    Smith, T., Husbands, P., Layzell, P., O’Shea, M.: Fitness landscapes and evolvability. Evol. Comput. 10(1), 1–34 (2002)CrossRefGoogle Scholar
  62. 62.
    Smith-Miles, K.: Cross-disciplinary perspectives on meta-learning for algorithm selection. ACM Comput. Surv. 41(1), 6:1–6:25 (2009)Google Scholar
  63. 63.
    Smith-Miles, K., Hemert, J.v.: Discovering the suitability of optimisation algorithms by learning from evolved instances. Ann. Math. Artif. Intel. 61(2), 87–104 (2011)zbMATHCrossRefGoogle Scholar
  64. 64.
    Stadler, P.: Landscapes and their correlation functions. J. Math. Chem. 20(1), 1–45 (1996)MathSciNetzbMATHCrossRefGoogle Scholar
  65. 65.
    Streeter, M., Golovin, D., Smith, S.: Combining multiple heuristics online. In: AAAI 2007, vol. 2, pp. 1197–1203. AAAI Press (2007)Google Scholar
  66. 66.
    Tomassini, M., Vanneschi, L., Collard, P., Clergue, M.: A study of fitness distance correlation as a difficulty measure in genetic programming. Evolutionary Computation 13(2), 213–239 (2005)CrossRefGoogle Scholar
  67. 67.
    Vanneschi, L.: Investigating problem hardness of real life applications. In: Genetic Programming Theory and Practice V, Genetic and Evolutionary Computation, pp. 107–124. Springer, US (2008)CrossRefGoogle Scholar
  68. 68.
    Vanneschi, L., Clergue, M., Collard, P., Tomassini, M., Vérel, S.: Fitness Clouds and Problem Hardness in Genetic Programming. In: Deb, K., Tari, Z. (eds.) GECCO 2004. LNCS, vol. 3103, pp. 690–701. Springer, Heidelberg (2004)CrossRefGoogle Scholar
  69. 69.
    Vanneschi, L., Tomassini, M., Collard, P., Vérel, S.: Negative Slope Coefficient: A Measure to Characterize Genetic Programming Fitness Landscapes. In: Collet, P., Tomassini, M., Ebner, M., Gustafson, S., Ekárt, A. (eds.) EuroGP 2006. LNCS, vol. 3905, pp. 178–189. Springer, Heidelberg (2006)CrossRefGoogle Scholar
  70. 70.
    Vanneschi, L., Valsecchi, A., Poli, R.: Limitations of the fitness-proportional negative slope coefficient as a difficulty measure. In: GECCO 2009, pp. 1877–1878. ACM, New York (2009)CrossRefGoogle Scholar
  71. 71.
    Vassilev, V., Fogarty, T., Miller, J.: Information characteristics and the structure of landscapes. Evol. Comput. 8(1), 31–60 (2000)CrossRefGoogle Scholar
  72. 72.
    Vassilev, V., Fogarty, T., Miller, J.: Smoothness, ruggedness and neutrality of fitness landscapes: from theory to application. In: Advances in Evolutionary Computing, pp. 3–44. Springer, New York (2003)CrossRefGoogle Scholar
  73. 73.
    Vassilevska, V., Williams, R., Woo, S.: Confronting hardness using a hybrid approach. In: Proc. 17th Ann. ACM-SIAM Symp. Discrete Algorithms, pp. 1–10. ACM, New York (2006)Google Scholar
  74. 74.
    Vrugt, J., Robinson, B., Hyman, J.: Self-Adaptive multimethod search for global optimization in Real-Parameter spaces. IEEE Trans. Evol. Comput. 13(2), 243–259 (2009)CrossRefGoogle Scholar
  75. 75.
    Watson, J., Beck, J., Howe, A., Whitley, L.: Problem difficulty for tabu search in job-shop scheduling. Artif. Intell. 143(2), 189–217 (2003)MathSciNetzbMATHCrossRefGoogle Scholar
  76. 76.
    Weinberger, E.: Correlated and uncorrelated fitness landscapes and how to tell the difference. Biol. Cybern. 63(5), 325–336 (1990)zbMATHCrossRefGoogle Scholar
  77. 77.
    Weinberger, E., Stadler, P.: Why some fitness landscapes are fractal. J. Theor. Biol. 163(2), 255–275 (1993)CrossRefGoogle Scholar
  78. 78.
    Wolpert, D., Macready, W.: No free lunch theorems for optimization. IEEE Trans. Evol. Comput. 1(1), 67–82 (1997)CrossRefGoogle Scholar
  79. 79.
    Yeguas, E., Joan-Arinyo, R., Luzón, M.V.: Modeling the performance of evolutionary algorithms on the root identification problem: A case study with PBIL and CHC algorithms. Evol. Comput. 19(1), 107–135 (2011)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  • Mario A. Muñoz
    • 1
  • Michael Kirley
    • 2
  • Saman K. Halgamuge
    • 1
  1. 1.Department of Mechanical EngineeringThe University of MelbourneParkvilleAustralia
  2. 2.Department of Computing and Information SystemsThe University of MelbourneParkvilleAustralia

Personalised recommendations

Cite paper

Buy options