A Comparison of Genetic Algorithms and Particle Swarm Optimization to Estimate Cluster-Based Kriging Parameters

Kriging is one of the most used spatial estimation methods in real-world applications. Some kriging parameters must be estimated in order to reach a good accuracy in the interpolation process, however, this task remains a challenge. Various optimization methods have been tested to find good parameters of the kriging process. In recent years, many authors are using bio-inspired techniques and achieving good results in estimating these parameters in comparison with traditional techniques. This paper presents a comparison between well known bio-inspired techniques such as Genetic Algorithms and Particle Swarm Optimization in the estimation of the essential kriging parameters: nugget, sill, range, angle, and factor. In order to perform the tests, we proposed a methodology based on the cluster-based kriging method. Considering the Friedman test, the results showed no statistical difference between the evaluated algorithms in optimizing kriging parameters. On the other hand, the Particle Swarm Optimization approach presented a faster convergence, which is important in this high-cost computational problem.

[1]  Zhuming Bi,et al.  Modelling and verification of fatigue damage for compliant mechanisms , 2019, Robotica.

[2]  Tomislav Hengl,et al.  A Practical Guide to Geostatistical Mapping , 2009 .

[3]  Qing Chen,et al.  GA-based Kriging for isoline drawing , 2010, 2010 The 2nd Conference on Environmental Science and Information Application Technology.

[4]  Mohsen Nasseri,et al.  The use of a genetic algorithm-based search strategy in geostatistics: application to a set of anisotropic piezometric head data , 2012, Comput. Geosci..

[5]  Kusum Deep,et al.  A new mutation operator for real coded genetic algorithms , 2007, Appl. Math. Comput..

[6]  Zhongqi Wang,et al.  Optimization of riveting parameters using Kriging and particle swarm optimization to improve deformation homogeneity in aircraft assembly , 2017 .

[7]  N. Cressie.  Fitting variogram models by weighted least squares , 1985 .

[8]  Edson Koiti Kudo Yasojima,et al.  CAM-ADX: A New Genetic Algorithm with Increased Intensification and Diversification for Design Optimization Problems with Real Variables , 2019, Robotica.

[9]  Kusum Deep,et al.  A new crossover operator for real coded genetic algorithms , 2007, Appl. Math. Comput..

[10]  An Intelligent Improvement on the Reliability of Ordinary Kriging Estimates by a GA , 2010, 2010 Second WRI Global Congress on Intelligent Systems.

[11]  Francky Fouedjio,et al.  A spectral clustering approach for multivariate geostatistical data , 2017, International Journal of Data Science and Analytics.

[12]  Mohsen Nasseri,et al.  Cluster-based ordinary kriging of piezometric head in West Texas/New Mexico - Testing of hypothesis , 2008 .

[13]  Keith C. Clarke,et al.  An automatic variogram modeling method with high reliability fitness and estimates , 2018, Comput. Geosci..

[14]  J. Gibbons,et al.  Nonparametric statistics : an introduction , 1993 .

[15]  Ítalo Gomes Gonçalves,et al.  A machine learning approach to the potential-field method for implicit modeling of geological structures , 2017, Comput. Geosci..

[16]  Luca Scrucca,et al.  GA: A Package for Genetic Algorithms in R , 2013 .