Skip to main content
SpringerLink
Log in

Groundwater management using a new coupled model of meshless local Petrov-Galerkin method and modified artificial bee colony algorithm

  • Original paper
  • Published:
Computational Geosciences Aims and scope Submit manuscript

Abstract

To develop sustainable groundwater management strategies, generally coupled simulation-optimization (SO) models are used. In this study, a new SO model is developed by coupling moving least squares (MLS)-based meshless local Petrov-Galerkin (MLPG) method and modified artificial bee colony (MABC) algorithm. The MLPG simulation model utilizes the advantages of meshless methods over the grid-based techniques such as finite difference (FDM) and finite element method (FEM). For optimization, the basic artificial bee colony algorithm is modified to balance the exploration and exploitation capacity of the model more effectively. The performance of the developed MLPG-MABC model is investigated by applying it to hypothetical and field problems with three different management scenarios. The model results are compared with other available SO model solutions for its accuracy. Further, sensitivity analyses of various model parameters are carried out to check the robustness of the SO model. The proposed model gave quite promising results, showing the applicability of the present approach.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Ahlfeld, D.P., Mulvey, J.M., Pinder, G.F.: Designing optimal strategies for contaminated groundwater remediation. Adv. Water Resour. 9, 77–84 (1986)

    Article  Google Scholar 

  2. Akay, B., Karaboga, D.: A modified artificial bee colony algorithm for real-parameter optimization. Inf. Sci. (Ny). 192, 120–142 (2012)

    Article  Google Scholar 

  3. Atluri, S.N.: The Meshless Method (MLPG) for Domain and BIE Discretizations. Tech Science Press, Forsyth (2004)

    Google Scholar 

  4. Atluri, S.N., Zhu, T.: A new meshless local Petrov-Galerkin (MLPG) approach in computational mechanics. Comput. Mech. 22, 117–127 (1998)

    Article  Google Scholar 

  5. Atluri, S.N., Kim, H.-G., Cho, J.Y.: A critical assessment of the truly meshless local Petrov-Galerkin (MLPG), and local boundary integral equation (LBIE) methods. Comput. Mech. 24, 348–372 (1999)

    Article  Google Scholar 

  6. Atluri, S.N., Shen, S.: The meshless local Petrov-Galerkin (MLPG) method: a simple & less-costly alternative to the finite element and boundary element methods. Comput. Mech. 3, 11–51 (2002)

  7. Ayvaz, M.T.: Application of harmony search algorithm to the solution of groundwater management models. Adv. Water Resour. 32, 916–924 (2009)

    Article  Google Scholar 

  8. Bäck, T.: Evolutionary Algorithms in Theory and Practice: Evolution Strategies, Evolutionary Programming, Genetic Algorithms. Oxford University Press, Oxford (1996)

    Google Scholar 

  9. Bear, J.: Dynamics of Fluids in Porous Media. Elsevier, New York (1972)

    Google Scholar 

  10. Census 2011 India: Villages & towns in Parkal Mandal of Warangal, Andhra Pradesh. http://www.census2011.co.in/data/subdistrict/4679-parkal-warangal-andhra-pradesh.html

  11. Ciftci, E., Avci, C.B., Borekci, O.S., Sahin, A. U.: Assessment of advective–dispersive contaminant transport in heterogeneous aquifers using a meshless method. Environ. Earth Sci. 67, 2399–2409 (2012)

    Article  Google Scholar 

  12. Cyriac, R., Rastogi, A.K.: Optimization of pumping policy using coupled finite element-particle swarm optimization modelling. ISH. J. Hydraul. Eng. 22, 88–99 (2016)

    Google Scholar 

  13. Dougherty, D.E., Marryott, R.A.: Optimal groundwater management: 1. Simulated annealing. Water Resour. Res. 27, 2493–2508 (1991)

    Article  Google Scholar 

  14. El-Ghandour, H.A., Elsaid, A.: Groundwater management using a new coupled model of flow analytical solution and particle swarm optimization. Int. J. Water Resour. Environ. Eng. 5, 1–11 (2013)

    Article  Google Scholar 

  15. Gaur, S., Chahar, B.R., Graillot, D.: Analytic elements method and particle swarm optimization based simulation–optimization model for groundwater management. J. Hydrol. 402, 217–227 (2011)

    Article  Google Scholar 

  16. Gaur, S., Ch, S., Graillot, D., Chahar, B.R., Kumar, D.N.: Application of artificial neural networks and particle swarm optimization for the management of groundwater resources. Water Resour. Manag. 27, 927–941 (2013)

    Article  Google Scholar 

  17. Guneshwor, S.L., Eldho, T.I., Vinod Kumar, A.: Coupled groundwater flow and contaminant transport simulation in a confined aquifer using meshfree radial point collocation method (RPCM). Eng. Anal. Bound. Elem. 66, 20–33 (2016)

    Article  Google Scholar 

  18. Indian Standard IS: 1172:2007: Code of basic requirements for water supply, drainage and sanitation, New Delhi (2010)

  19. Jones, L., Willis, R., Yeh, W.W.-G.: Optimal control of nonlinear groundwater hydraulics using differential dynamic programming. Water Resour. Res. 23, 2097–2106 (1987)

    Article  Google Scholar 

  20. Karaboga, D.: An idea based on honey bee swarm for numerical optimization. Technical Report-TR06, Erciyes University, Engineering Faculty, Computer Engineering Department (2005)

  21. Karaboga, D., Akay, B.: A comparative study of artificial bee colony algorithm. Appl. Math. Comput. 214, 108–132 (2009)

    Google Scholar 

  22. Karaboga, D., Akay, B.: A modified artificial bee colony (ABC) algorithm for constrained optimization problems. Appl. Soft Comput. 11, 3021–3031 (2011)

    Article  Google Scholar 

  23. Karaboga, D., Gorkemli, B., Ozturk, C., Karaboga, N.: A comprehensive survey: artificial bee colony (ABC) algorithm and applications. Artif. Intell. Rev. 42, 21–57 (2014)

    Article  Google Scholar 

  24. Ketabchi, H., Ataie-Ashtiani, B.: Assessment of a parallel evolutionary optimization approach for efficient management of coastal aquifers. Environ. Model. Softw. 74, 21–38 (2015)

    Article  Google Scholar 

  25. Ketabchi, H., Ataie-Ashtiani, B.: Evolutionary algorithms for the optimal management of coastal groundwater: a comparative study toward future challenges. J. Hydrol. 520, 193–213 (2015)

    Article  Google Scholar 

  26. Kourakos, G., Harter, T.: Parallel simulation of groundwater non-point source pollution using algebraic multigrid preconditioners. Comput. Geosci. 18, 851–867 (2014)

    Article  Google Scholar 

  27. Lancaster, P., Salkauskas, K.: Surfaces generated by moving least squares methods. Math. Comput. 37, 141–158 (1981)

    Article  Google Scholar 

  28. Li, J., Chen, Y., Pepper, D.: Radial basis function method for 1-D and 2-D groundwater contaminant transport modeling. Comput. Mech. 32, 10–15 (2003)

    Article  Google Scholar 

  29. Li, Z., Mao, X.: Global multiquadric collocation method for groundwater contaminant source identification. Environ. Model. Softw. 26, 1611–1621 (2011)

    Article  Google Scholar 

  30. Liu, G.R., Gu, Y.T.: An Introduction to Meshfree Methods and Their Programming. Springer, Netherlands (2005)

    Google Scholar 

  31. Maier, H.R., Kapelan, Z., Kasprzyk, J., Kollat, J., Matott, L.S., Cunha, M.C., Dandy, G.C., Gibbs, M.S., Keedwell, E., Marchi, A., Ostfeld, A., Savic, D., Solomatine, D.P., Vrugt, J.A., Zecchin, A.C., Minsker, B.S., Barbour, E.J., Kuczera, G., Pasha, F., Castelletti, A., Giuliani, M., Reed, P.M.: Evolutionary algorithms and other metaheuristics in water resources: current status, research challenges and future directions. Environ. Model. Softw. 62, 271–299 (2014)

    Article  Google Scholar 

  32. Majumder, P., Eldho, T.I.: A new groundwater management model by coupling analytic element method and reverse particle tracking with cat swarm optimization. Water Resour. Manag. 1–20 (2016)

  33. McKinney, D.C., Lin, M.-D., et al.: Design methodology for efficient aquifer remediation using pump and treat systems. In: Russell, T. (ed.) Mathematical Modeling in Water Resources, pp 695–702. Elsevier Science Publishers, London (1992)

  34. McKinney, D.C., Lin, M.-D.: Genetic algorithm solution of groundwater management models. Water Resour. Res. 30, 1897–1906 (1994)

    Article  Google Scholar 

  35. Mategaonkar, M., Eldho, T.I.: Groundwater remediation optimization using a point collocation method and particle swarm optimization. Environ. Model. Softw. 32, 37–48 (2012)

    Article  Google Scholar 

  36. Moradi, J.M., Marino, M.A., Afshar, A.: Optimal design and operation of irrigation pumping station. J. Irrig. Drain. Eng. 129, 149–154 (2003)

    Article  Google Scholar 

  37. Moreles, M.A., Vázquez, R., Avila, F.: The differential system method for parameter identification; unconfined aquifer case. Comput. Geosci. 8, 235–253 (2005)

    Article  Google Scholar 

  38. Reddy, N.T., Prakasam, P., Subrahmanyam, G.V., Gowd, P.V., Gurunadha Rao, V.V.S., Gupta, C.P.: Water Balance Studies in Parkal Watershed: Recharge Process and Groundwater Flow Models. Groundwater Department, Andhra Pradesh (1992)

    Google Scholar 

  39. Seeley, T.D.: The Wisdom of the Hive: The Social Physiology of Honey Bee Colonies. Harvard University Press, Cambridge (1995)

    Google Scholar 

  40. Sharma, A.K., Swamee, P.K.: Cost considerations and general principles in the optimal design of water distribution systems. In: 8th Annual Water Distribution Systems Analysis Symposium, pp. 1–15. Cincinnati (2006)

  41. Singh, A.: Groundwater resources management through the applications of simulation modeling: a review. Sci. Total Environ. 499, 414–23 (2014)

    Article  Google Scholar 

  42. Singh, R.M., Datta, B.: Identification of groundwater pollution sources using GA-based linked simulation optimization model. J. Hydrol. Eng. 11, 101–109 (2006)

    Article  Google Scholar 

  43. Swathi, B., Eldho, T.I.: Groundwater flow simulation in confined aquifers using meshless local Petrov-Galerkin (MLPG) method. ISH. J. Hydraul. Eng. 19, 335–348 (2013)

    Google Scholar 

  44. Swathi, B., Eldho, T.I.: Groundwater flow simulation in unconfined aquifers using meshless local Petrov–Galerkin method. Eng. Anal. Bound. Elem. 48, 43–52 (2014)

    Article  Google Scholar 

  45. Swathi, B., Eldho, T.I.: A moving least squares based meshless local petrov-galerkin method for the simulation of contaminant transport in porous media. Eng. Anal. Bound. Elem. 78, 8–19 (2017)

    Article  Google Scholar 

  46. Tartakovsky, A.M., Trask, N., Pan, K., Jones, B., Pan, W., Williams, J.R.: Smoothed particle hydrodynamics and its applications for multiphase flow and reactive transport in porous media. Comput. Geosci. 20, 807–834 (2016)

    Article  Google Scholar 

  47. Wang, M., Zheng, C.: Ground water management optimization using genetic algorithms and simulated annealing: formulation and comparison. J. Am. Water Resour. Assoc. 34, 519–530 (1998)

    Article  Google Scholar 

  48. Willis, R.: A planning model for the management of groundwater quality. Water Resour. Res. 15, 1305–1312 (1979)

    Article  Google Scholar 

  49. Willis, R., Yeh, W.W.-G.: Groundwater Systems Planning and Management. Printice Hall Inc, New Jersey (1987)

    Google Scholar 

  50. Yang, Y., Wu, J., Sun, X., Wu, J., Zheng, C.: A niched Pareto tabu search for multi-objective optimal design of groundwater remediation systems. J. Hydrol. 490, 56–73 (2013)

    Article  Google Scholar 

  51. Zhang, Z., Agarwal, R.K.: Numerical simulation and optimization of CO2 sequestration in saline aquifers for vertical and horizontal well injection. Comput. Geosci. 16, 891–899 (2012)

    Article  Google Scholar 

  52. Zhu, G., Kwong, S.: Gbest-guided artificial bee colony algorithm for numerical function optimization. Appl. Math. Comput. 217, 3166–3173 (2010)

    Google Scholar 

  53. Zhu, T., Atluri, S.N.: A modified collocation method and a penalty formulation for enforcing the essential boundary conditions in the element free Galerkin method. Comput. Mech. 21, 211–222 (1998)

    Article  Google Scholar 

Download references

Acknowledgements

The authors are grateful to Dr. V.V.S. Gurunadha Rao, Ex. Deputy Director, National Geophysical Research Institute (NGRI), Hyderabad, for providing the required field data. The authors are also thankful to the anonymous reviewers and the editor for their constructive comments and suggestions which helped to improve the manuscript.

Author information

Authors and Affiliations

  1. Research Scholar, Department of Civil Engineering, Indian Institute of Technology (IIT) Bombay, Mumbai, Maharashtra, India

    Swathi Boddula

  2. Department of Civil Engineering, IIT Bombay, Powai, Mumbai, Maharashtra, India

    Eldho T. I.

Authors
  1. Swathi Boddula
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Eldho T. I.
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Eldho T. I..

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Boddula, S., T. I., E. Groundwater management using a new coupled model of meshless local Petrov-Galerkin method and modified artificial bee colony algorithm. Comput Geosci 22, 657–675 (2018). https://doi.org/10.1007/s10596-018-9718-8

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10596-018-9718-8

Keywords

Search

Navigation