A Survey of Meta-heuristics Used for Computing Maximin Latin Hypercube

  • Arpad Rimmel
  • Fabien Teytaud
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8600)

Abstract

Finding maximin latin hypercube is a discrete optimization problem believed to be NP-hard. In this paper, we compare different meta-heuristics used to tackle this problem: genetic algorithm, simulated annealing and iterated local search. We also measure the importance of the choice of the mutation operator and the evaluation function. All the experiments are done using a fixed number of evaluations to allow future comparisons. Simulated annealing is the algorithm that performed the best. By using it, we obtained new highscores for a very large number of latin hypercubes.

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References

  1. 1.
    Bates, S.J., Sienz, J., Toropov, V.V.: Formulation of the optimal latin hypercube design of experiments using a permutation genetic algorithm. AIAA 2011, 1–7 (2004)Google Scholar
  2. 2.
    Bohachevsky, I.O., Johnson, M.E., Stein, M.L.: Generalized simulated annealing for function optimization. Technometrics 28(3), 209–217 (1986)CrossRefMATHGoogle Scholar
  3. 3.
    Goldberg, D.E., Holland, J.H.: Genetic algorithms and machine learning. Machine Learning 3(2), 95–99 (1988)CrossRefGoogle Scholar
  4. 4.
    Grosso, A., Jamali, A., Locatelli, M.: Finding maximin latin hypercube designs by iterated local search heuristics. European Journal of Operational Research 197(2), 541–547 (2009)CrossRefMATHGoogle Scholar
  5. 5.
    Holland, J.H.: Adaptation in natural and artificial systems: An introductory analysis with applications to biology, control, and artificial intelligence. U. Michigan Press (1975)Google Scholar
  6. 6.
    Husslage, B., Rennen, G., Van Dam, E.R., Den Hertog, D.: Space-filling Latin hypercube designs for computer experiments. Tilburg University (2006)Google Scholar
  7. 7.
    Husslage, B.G., Rennen, G., van Dam, E.R., den Hertog, D.: Space-filling latin hypercube designs for computer experiments. Optimization and Engineering 12(4), 611–630 (2011)CrossRefMATHGoogle Scholar
  8. 8.
    Jin, R., Chen, W., Sudjianto, A.: An efficient algorithm for constructing optimal design of computer experiments. Journal of Statistical Planning and Inference 134(1), 268–287 (2005)CrossRefMATHMathSciNetGoogle Scholar
  9. 9.
    Johnson, M.E., Moore, L.M., Ylvisaker, D.: Minimax and maximin distance designs. Journal of Statistical Planning and Inference 26(2), 131–148 (1990)CrossRefMathSciNetGoogle Scholar
  10. 10.
    Liefvendahl, M., Stocki, R.: A study on algorithms for optimization of latin hypercubes. Journal of Statistical Planning and Inference 136(9), 3231–3247 (2006)CrossRefMATHMathSciNetGoogle Scholar
  11. 11.
    Lourenço, H.R., Martin, O.C., Stützle, T.: Iterated local search. International series in operations research and management science, pp. 321–354 (2003)Google Scholar
  12. 12.
    McKay, M.D., Beckman, R.J., Conover, W.J.: Comparison of three methods for selecting values of input variables in the analysis of output from a computer code. Technometrics 21(2), 239–245 (1979)MATHMathSciNetGoogle Scholar
  13. 13.
    Morris, M.D., Mitchell, T.J.: Exploratory designs for computational experiments. Journal of Statistical Planning and Inference 43(3), 381–402 (1995)CrossRefMATHMathSciNetGoogle Scholar
  14. 14.
    Van Dam, E.R., Husslage, B., Den Hertog, D., Melissen, H.: Maximin latin hypercube designs in two dimensions. Operations Research 55(1), 158–169 (2007)CrossRefMATHMathSciNetGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2014

Authors and Affiliations

  • Arpad Rimmel
    • 1
  • Fabien Teytaud
    • 2
  1. 1.Supélec E3SFrance
  2. 2.Univ. Lille Nord de FranceFrance

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