Water Resources Management

, Volume 33, Issue 2, pp 847–861 | Cite as

Modeling Groundwater Quality Parameters Using Hybrid Neuro-Fuzzy Methods

  • Ozgur Kisi
  • Armin Azad
  • Hamed KashiEmail author
  • Amir Saeedian
  • Seyed Ali Asghar Hashemi
  • Salar Ghorbani


In this study, the application of four evolutionary algorithms, continuous genetic algorithm (CGA), particle swarm optimization (PSO), ant colony optimization for continuous domains (ACOR), and differential evolution (DE) were considered for training and optimization of adaptive neuro-fuzzy inference system (ANFIS) to model groundwater quality variables. At first, using correlation and sensitivity analysis, the best inputs were selected to estimate electrical conductivity (EC), sodium adsorption ratio (SAR) and total hardness (TH). After that, the quality variables were modeled by simple ANFIS and the ANFIS trained by evolutionary algorithms. Finally, the models’ performances were evaluated using determination coefficient (R2), root mean square error (RMSE), and mean absolute percentage error (MAPE) and sensitivity analysis. Results indicated that: 1) All the suggested algorithms improved the ANFIS performance in the modeling of EC and TH. Also, in SAR, CGA and PSO had a better performance than existing algorithms of ANFIS. 2) CGA with the most appropriate results, was the best algorithm in improving ANFIS performance for modeling the groundwater quality variables such that the amounts of R2, RMSE, and MAPE were improved by 0.14, 35.4, and 0.59 for TH, by 0.13, 226 (μmho Cm−1), 2.16 for EC, and by 0.15, 690, and 19.04 for SAR, respectively. 3) Sensitivity analysis showed that the results obtained by correlation analysis was dependable and could be used as a primary step in choosing the best input data for prediction of groundwater quality variables.


Ant colony optimization for continuous domains Continuous genetic algorithm Differential evolution Partial swarm optimization ANFIS Groundwater quality variables 



The authors would like to thank the Isfahan Regional Water Authority for providing the necessary data to carry out this investigation.

Compliance with Ethical Standards

Conflict of Interest



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Copyright information

© Springer Nature B.V. 2018

Authors and Affiliations

  1. 1.School of Natural Sciences and EngineeringIlia State UniversityTbilisiGeorgia
  2. 2.Department of Civil EngineeringSemnan UniversitySemnanIran
  3. 3.Depatment of Plant ScienceTechnology University of MunichMunichGermany
  4. 4.Agriculture Research and Education Organization - Natural Resources Research Center of Semnan ProvinceSemnanIran

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