Comparison of Nonlinear Two-Dimensional Modeling of Gravimetric Data of Western Anatolia, Turkey, Using Non-Dominated Sorting Genetic Algorithm and Single-Objective Genetic Algorithm

Document Type : Research Article

Authors

1 Department of Mining Exploration Engineering, Faculty of Mining, Petroleum and Geophysics Engineering, Shahrood University of Technology, Shahrood, Iran.

2 Department of Mining Engineering, Faculty of Technical Engineering, Malayer University, Malayer, Iran.

Abstract

Studying the bedrock geometry in mining and oil exploration operations to obtain its 2D pattern requires nonlinear reverse computations. Local optimization methods for solving nonlinear inverse problems are based on linearizing the changes of the model similar to a primary model and finding an objective function of minimum error from the model’s parameters; however, these optimization methods are not able to select a suitable primary function that is close enough to the general optimal value. That is to say, every objective function can have several minimum and maximum solutions. The lowest minimum is called the global minimum while the rest of them are named local minimums. Therefore, in local inverse methods, the objective is to find the minimum of an objective function, and also an objective function might have a few local minimums with different values. In this case, it is not suitable to use gradient-based methods for exploration purposes, unless the primary model is very close to the actual answer; which is outside the control of geological structures or the geometry of the subsurface. Despite the easy execution and high convergence rate of the local methods, there is the possibility of being trapped in local minimums because these methods are dependent on the primary model and also finding more than one optimized point in 2D or 3D simulations; this is why local optimization methods are considered deterministic algorithms. Multi-objective and single-objective metaheuristic optimization algorithms are capable of searching the feasible region and they also provide a solution independent of the primary model. Searching the feasible region means finding all the feasible solutions for a problem and each point in this region is representing a solution that can be ranked based on its value. One of the important differences between local optimization and metaheuristic methods is constraining. Constraining metaheuristic global optimization methods are only used for constraining the feasible region based on previous knowledge or estimation relations; which is very different from constraining local optimization that is used for stabilizing inverse simulation. The algorithms used in the present work included a non-dominated sorting genetic algorithm (NSGA-II) and single-objective genetic algorithm, which were used to estimate the depth. The NSGA-II is commonly used to solve problems with multiple, typically conflicting, objective functions. This algorithm is capable of being developed and also has a high potential for solving unbounded multi-objective problems. In addition, the single-objective genetic algorithm (GA) is capable of modeling and solving complex problems. In the present study, both algorithms were verified and validated using the data produced by an imaginary and complex synthetic model. In order for a more precise examination of the performance of both algorithms, the imaginary synthetic data were used both with no noise and with up to 10% Gaussian white noise (GWN). Accordingly, the modeling results indicated a good consistence between the algorithms and the primary model; so that, the root mean square error parameter for the data obtained from the initial data of the synthetic model ranged from 0.05 to 0.35mGal for the NSGA-II and from 0.07 to 0.52mGal for the GA. Also, this parameter didn't exceed 72.4 in the NSGA-II and didn't exceed 93.8 in the GA. Based on the gravimetric modeling of the Western Anatolia, Turkey, the results obtained from both algorithms under similar conditions in terms of parameter settings and number of algorithm executions indicated good performance of the NSGA-II algorithm compared to the single-objective algorithm.

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References

Atashpaz-Gargari, E., & Lucas, C. (2007). Imperialist competitive algorithm: an algorithm for optimization inspired by imperialist competition, IEEE Congress on Evolutionary Computation, 4661-4667.
Barbosa, V. C. F., & Silva, J. B. C. (1994). Generalized compact gravity inversion. Geophysics, 59(1), 57-68.
Barbosa, V. C. F., Silva, J. B. C., & Medeiros, W. E. (1997). Gravity inversion of basement relief using approximate equality constraints on depths. Geophysics, 62(6), 1745-1757.
Barbosa, V. C. F., & Silva, J. B. C. (2011). Reconstruction of geologic bodies in depth associated with a sedimentary basin using gravity and magnetic data. Geophysical Prospecting, 59(6), 1021-1034.
Bijani, R., Lelievre, P., Neto, C. F., & Farquharson, C. G. (2017). Physical-property-, lithology- and surface-geometry-based joint inversion using Pareto Multi-Objective Global Optimization. Geophysics Journal International, 209, 730–748.
Boschetti, F., Mike, D., & Ron, L. (1997). Inversion of potential field data by genetic algorithms. Geophysical Prospecting, 45(3), 461-478.
Bozkurt, E. (2001). Neotectonics of Turkey – A synthesis. Geodinamica Acta, 14, 3–30.
Bozkurt, E., & Sözbilir, H. (2004). Tectonic evolution of the Gediz Graben: field evidence for anepisodic, two extension in western Turkey. Geological Magazine, 141, 63–79.
Bozkurt, E., & Sözbilir, H. (2006). Evolution of the large-scale active Manisa Fault, Southwest Turkey: implications on fault development and regional tectonics. Geodinamica Acta, 19, 427–453.
Deb, k. (2001). Multiobjective Optimization Using Evolutionary Algorithms. U.K., Chichester:Wiley.
Deb, K., Pratab, A., Agarwal, S., & Meyarivan, T. (2002). A fast and elitist multiobjective genetic algorithm: NSGA-II. IEEE transaction on evolutionary computation, 6(2), 182- 197.
Ekinci, Y. L., Balkaya, C., Gokturkler, G., & Ozyalin, S. (2020). Gravity Data Inversion for the Basement Relief Delineation through Global Optimization: A Case Study from the Aegean Graben System, western Anatolia, Turkey., Published by Oxford University Press on behalf of The Royal Astronomical Society. Evolutionary Computation, IEEE Transactions on., 6, 182-197.
Goldberg, D. E. (1989). Genetic algorithms in search, optimization, and machine learning., Reading, MA: Addison Wesley.
Gallardo-Delgado, L. A., Pérez-Flores, M. A., & Gómez-Treviño. E. (2003). A versatile algorithm for joint 3D inversion of gravity and magnetic data. Geophysics, 68(3), 949-959.
Holland, J.H. (1992) Genetic Algorithms. Scientific American, 267, 66-72. http://dx.doi.org/10.1038/scientificamerican0792-66
Jie, X., & Tao, Z. (2015). Multiobjective particle swarm inversion algorithm for two-dimensional magnetic data. Applied. Geophysics, 12(2), 127–136.
Özkaymak, Ç., & Sözbilir, H. (2008). Stratigraphic and structural evidence for fault reactivation: the active Manisa fault zone, western Anatolia. Turkish Journal of Earth Sciences, 17, 615–635.
Pallero, J. LG., Fernandez-Martinez, J. L., Bonvalot, S., & Fudym, O. (2015). Gravity inversion and uncertainty assessment of basement relief via Particle Swarm Optimization. Journal of Applied Geophysics, 116, 180-191.
Roy, K., & Kumar, K. (2007). Potential theory in applied geophysics. Springer Science & Business Media.
Schwarzbach, C., Borner, R., & Spitzer, K. (2005). Two-dimensional inversion of direct current resistivity data using a parallel, multi-objective genetic algorithm. Geophysical Journal International, 162, 685–695.
Sen, M. K., & Stoffa, P. L. (1995). Global optimization methods in geophysical inversion, Elsevier Science.
Shaw, R., & Srivastava, S. (2007). Particle swarm optimization: A new tool to invert geophysical data. Geophysics, 72(2), 75–F83.
Sheta, A., & Turabieh, H. (2006). A comparison between genetic algorithms and sequential quadratic programming in solving constrained optimization problems. International Journal on artificial intelligence and machine learning, 6(1), 67-74.
Sivanandam, S. N., & Deepa, S. N. (2007). Introduction to Genetic Algorithms. Springer, Berlin Heidelberg.
Snieder, R. (1998). The role of nonlinearity in inverse problems. Inverse Problems, 14(3), 387-404.
Sözbilir, H., Sarı, B., Uzel, B., Sümer, Ö., & Akkiraz, S. (2011). Tectonic implications of transtensional supradetachment basin development in an extension-parallel transfer zone: the Kocaçay Basin, western Anatolia, Turkey. Basin Research, 23, 423–448.
Srinivas, N., & Deb, K. (1995). Multiobjective function optimization using nondominated sorting genetic algorithms. Evol. Comput., 2(3), 221–248.
Tarantola, A. (2005). Inverse problem theory and methods for model parameter estimation. Society for Industrial and Applied Mathematics.
Telford, W. M., Geldart, L.P., & Sheriff, R. E. (1990). Applied geophysics Vol.1. Cambridge university press.
Uzel, B., & Sözbilir, H. (2008). A First record of strike-slip basin in western Anatolia and its tectonic implication: the Cumaovası basin as an example. Turkish Journal of Earth Sciences, 17, 559–591.
Yang, X. S. (2010). Engineering Optimization: An Introduction with etaheuristic Applications, Published by John Wiley & Sons, New Jersey.
Yeh, J. Y., & Lin, W. S. (2007a). Using simulation technique and genetic algorithm to improve the quality care of a hospital emergency department‖. Journal of expert systems with applications, 32(4), 1073-1083.
Yuan, S., Tian, N., Chen, Y., Liu, H., & Liu, Z. (2008). Nonlinear geophysical inversion based on ACO with hybrid techniques. In Natural Computation, ICNC'08., Fourth International Conference., (4) 530-534., IEEE.
Zitzler, E. (1999). Evolutionary Algorithms for Multi Objective Optimization: Methods and Applications, PhD thesis, Swiss Federal Institute of Technology, Zurich, Switzerland.
Zitzler, E., Deb, K., & Thiele, L. (2000). Comparison of multiobjective evolutionary algorithms:Empirical results. transaction on evolutionary computation, 8(2), 173-195.
 
Journal of the Earth and Space Physics
Volume 49, Issue 2
online publication date: 30 Aug 2023
August 2023
Pages 275-292

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