• OpenAccess
  • Application of Multi-Gene Genetic Programming in Kriging Interpolation  [ICGG 2015]
  • DOI: 10.4236/gep.2015.35004   PP.27 - 34
  • Author(s)
  • Changik Han, Ende Wang, Jianming Xia, Sunggi Yun
  • A key stage for Kriging interpolation is the estimating of variogram model, which characterizes the spatial behavior of the variables of interest. But most traditional kriging interpolation has finite types of empirical variogram model, and sometimes, the optimal type of variogram model can not be find, which result in decreasing interpolation accuracy. In this paper, we explore the use of Multi-Gene Genetic Programming (MGGP) to automatically find an empirical variogram model that fits on an experimental variogram. Empirical variogram estimation based on MGGP, in contrast with traditional method need not select type of basic variogram model and can directly get both the functional type as well as the coefficients of the optimal variogram. The results of case study show that the proposed method can avoid the subjectivity in choosing the type of variogram models and can adaptively fit variogram according to the real data structure, which improves the interpolation accuracy of kriging significantly.

  • MGGP, Kriging Interpolation, Variogram
  • References
  • [1]
    Chiles, J.P. and Pierre, D. (1999) Geostatistics: Modeling Spatial Uncertainty. Wiley, New York.
    Oliver, M.A. (2010) Ch. B6: The Variogram & Kriging. In: Handbook of Applied Spatial Analysis: Software Tools, Methods and Applications, Springer, Berlin, 319-352.
    Zhang, R.Z. (2005) Spatial Variability Theory and Application. Science Press, Beijing.
    Koza, J.P. (1992) Genetic Programming: On the Programming of Computers by Means of Natural Selection. MIT Press, Cambridge.
    Gandomi, A.H. and Alavi, A.M. (2012) A New Multi-Gene Genetic Programming Approach to Nonlinear System Modeling. Part I: Materials and Structural Engineering Problems. Neural Computing and Applications, 21, 171-187.
    Searson, D.P., Leahy, D.E. and Willis, M.J. (2010) GPTIPS: An Open Source Genetic Programming Toolbox for Multigene Symbolic Regression. Proceedings of the International MultiConference of Engineers and Computer Scientists (IMECS 2010), Hong Kong, 77-80.
    Garg, A., Garg, A. and Tai, M. (2014) A Multi-Genetic Programming Model for Estimating Stress-Dependent Soil Water Retention Curves. Computational Geosciences, 18, 45-56.
    Clark, I., Harper, W.V. and Ohio, C. (2000) Practical Geostatistics 2000. Ecosse North America Llc, Greyden Press.
    Casal, R.F. and Fernández, M.F. (2014) Nonparametric Bias-Corrected Variogram Estimation under Non-Constant Trend. Stochastic Environmental Research and Risk Assessment, 28, 1247-1259.
    Lark, R.M. (2000) Estimating Variogram of Soil Properties by the Method-of-Moments and Maximum Likelihood. European Journal of Soil Science, 51, 717-728.

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