Optimizing Latin hypercube designs by particle swarm

详细信息    查看全文

• 作者：Ray-Bing Chen (1)
  Dai-Ni Hsieh (2)
  Ying Hung (3)
  Weichung Wang (4)
  
• 关键词：Latin hypercube design ; Particle swarm optimization ; Graphic processing unit (GPU)
• 刊名：Statistics and Computing
• 出版年：2013
• 出版时间：September 2013
• 年：2013
• 卷：23
• 期：5
• 页码：663-676
• 全文大小：794KB
• 参考文献：1. Bratton, D., Kennedy, J.: Defining a standard for particle swarm optimization. In: IEEE Swarm Intelligence Symposium. SIS 2007, pp. 120鈥?27. IEEE, Piscataway (2007) CrossRef
  2. Bates, S.J., Sienz, J., Toropov, V.V.: Formulation of the optimal Latin hypercube design of experiments using a permutation genetic algorithm. In: AIAA 2004-2011, pp. 1鈥? (2004)
  3. Engelbrecht, A.P.: Fundamentals of Computational Swarm Intelligence. Wiley, Hoboken (2006)
  4. Fang, K.-T., Ma, C.-X., Winker, P.: Centered L2-discrepancy of random sampling and Latin hypercube design, and construction of uniform designs. Math. Comput. 71, 275鈥?96 (2002)
  5. Grosso, A., Jamali, A.R.M.J.U., Locatelli, M.: Finding maximin Latin hypercube designs by iterated local search heuristics. Eur. J. Oper. Res. 197(2), 541鈥?47 (2009) CrossRef
  6. Hung, Y., Wang, W.: Accelerating parallel particle swarm optimization via GPU. Optim. Methods Softw. 27(1), 33鈥?1 (2012) CrossRef
  7. Jin, R., Chen, W., Sudjianto, A.: An efficient algorithm for constructing optimal design of computer experiments. J. Stat. Plan. Inference 134(1), 268鈥?87 (2005) CrossRef
  8. Joseph, V.R., Hung, Y.: Orthogonal-maximin Latin hypercube designs. Stat. Sin. 18, 171鈥?86 (2008)
  9. Kennedy, J., Eberhart, R.C.: Particle swarm optimization. In: Proceedings of IEEE International Conference on Neural Networks, vol.聽4, pp. 1942鈥?948. IEEE, Piscataway (1995) CrossRef
  10. Kennedy, M., O鈥橦agan, A.: Predicting the output from a complex computer code when fast approximations are available. Biometrika 87, 1鈥?3 (2000) CrossRef
  11. Liefvendahl, M., Stocki, R.: A study on algorithms for optimization of Latin hypercubes. J. Stat. Plan. Inference 136(9), 3231鈥?247 (2006) CrossRef
  12. Morris, M.D., Mitchell, T.J.: Exploratory designs for computational experiments. J. Stat. Plan. Inference 43(3), 381鈥?02 (1995) CrossRef
  13. Santner, T.J., Williams, B.J., Notz, W.I.: The Design and Analysis of Computer Experiments. Springer, New York (2003) CrossRef
  14. Tang, B.: Orthogonal array-based Latin hypercubes. J. Am. Stat. Assoc. 88(424), 1392鈥?397 (1993) CrossRef
  15. Toala, D.J.J., Bressloff, N.W., Keanea, A.J., Holden, C.M.E.: The development of a hybridized particle swarm for kriging hyperparameter tuning. Eng. Optim. 43(6), 675鈥?99 (2011) CrossRef
  16. van Dam, E.R., Husslage, B., den Hertog, D., Melissen, H.: Maximin Latin hypercube designs in two dimensions. Oper. Res. 55(1), 158鈥?69 (2007) CrossRef
  17. van Dam, E.R., Rennen, G., Husslage, B.: Bounds for maximin Latin hypercube designs. Oper. Res. 57(3), 595鈥?08 (2009) CrossRef
  18. van den Bergh, F.: An analysis of particle swarm optimizers. Ph.D. Thesis, University of Pretoria (2006)
  19. van聽den Bergh, F., Engelbrecht, A.P.: A new locally convergent particle swarm optimiser. In: IEEE International Conference on Systems, Man and Cybernetics, p. 3 (2002)
  20. Viana, F.A.C., Venter, G., Balabanov, V.: An algorithm for fast optimal Latin hypercube design of experiments. Int. J. Numer. Methods Eng. 82(2), 135鈥?56 (2010)
  21. Ye, K.Q., Li, W., Sudjianto, A.: Algorithmic construction of optimal symmetric Latin hypercube designs. J. Stat. Plan. Inference 90(1), 145鈥?59 (2000) CrossRef
  
• 作者单位：Ray-Bing Chen (1)
  Dai-Ni Hsieh (2)
  Ying Hung (3)
  Weichung Wang (4)
  
  1. Department of Statistics, National Cheng Kung University, Tainan, 701, Taiwan
  2. Institute of Statistical Science, Academia Sinica, Taipei, 115, Taiwan
  3. Department of Statistics and Biostatistics, Rutgers University, Piscataway, NJ, 08854, USA
  4. Department of Mathematics, National Taiwan University, Taipei, 106, Taiwan
  

文摘

Latin hypercube designs (LHDs) are widely used in many applications. As the number of design points or factors becomes large, the total number of LHDs grows exponentially. The large number of feasible designs makes the search for optimal LHDs a difficult discrete optimization problem. To tackle this problem, we propose a new population-based algorithm named LaPSO that is adapted from the standard particle swarm optimization (PSO) and customized for LHD. Moreover, we accelerate LaPSO via a graphic processing unit (GPU). According to extensive comparisons, the proposed LaPSO is more stable than existing approaches and is capable of improving known results.