Developing Four Metaheuristic Algorithms for Multiple-Objective Management of Groundwater

Document Type : Regular Article

Authors

1 Associate Professor, Irrigation & Hydraulics Department, Faculty of Engineering Mansoura University, Mansoura 35516, Egypt

2 Professor, Structural Engineering Department, Faculty of Engineering Mansoura University, Mansoura 35516, Egypt

Abstract

Groundwater is one of the important sources of freshwater and accordingly, there is a need for optimizing its usage. In this paper, four multi-objective metaheuristic algorithms with new evolution strategy are introduced and compared for the optimal management of groundwater namely: Multi-objective genetic algorithms (MOGA), multi-objective memetic algorithms (MOMA), multi-objective particle swarm optimization (MOPSO), and multi-objective shuffled frog leaping algorithm (MOSFLA). The suggested evolution process is based on determining a unique solution of the Pareto solutions called the Pareto-compromise (PC) solution. The advantages of the current development stem from: 1) The new multiple objectives evolution strategy is inspired from the single objective optimization, where fitness calculations depend on tracking the PC solution only through the search history; 2) a comparison among the performance of the four algorithms is introduced.  The development of each algorithm is briefly presented. A comparison study is carried out among the formulation and the results of the four algorithms. The developed four algorithms are tested on two multiple-objective optimization benchmark problems. The four algorithms are then used to optimize two-objective groundwater management problem. The results prove the ability of the developed algorithms to accurately find the Pareto-optimal solutions and thus the potential application on real-life groundwater management problems.

Highlights

Google Scholar

Keywords

Main Subjects

References

[1]     McKinney DC, Lin M-D. Genetic algorithm solution of groundwater management models. Water Resour Res 1994;30:1897–906. doi:10.1029/94WR00554.
[2]     Wang M, Zheng C. GROUND WATER MANAGEMENT OPTIMIZATION USING GENETIC ALGORITHMS AND SIMULATED ANNEALING: FORMULATION AND COMPARISON. J Am Water Resour Assoc 1998;34:519–30. doi:10.1111/j.1752-1688.1998.tb00951.x.
[3]     Gaur S, Ch S, Graillot D, Chahar BR, Kumar DN. Application of Artificial Neural Networks and Particle Swarm Optimization for the Management of Groundwater Resources. Water Resour Manag 2013;27:927–41. doi:10.1007/s11269-012-0226-7.
[4]     Pramada SK, Mohan S, Sreejith PK. Application of genetic algorithm for the groundwater management of a coastal aquifer. ISH J Hydraul Eng 2018;24:124–30. doi:10.1080/09715010.2017.1378597.
[5]     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 2018;22:657–75. doi:10.1007/s10596-018-9718-8.
[6]     Nassery HR, Adinehvand R, Salavitabar A, Barati R. Water Management Using System Dynamics Modeling in Semi-arid Regions. Civ Eng J 2017;3:766–78. doi:10.21859/cej-030913.
[7]     Alizadeh MJ, Shahheydari H, Kavianpour MR, Shamloo H, Barati R. Prediction of longitudinal dispersion coefficient in natural rivers using a cluster-based Bayesian network. Environ Earth Sci 2017;76:86. doi:10.1007/s12665-016-6379-6.
[8]     Barati R. Parameter Estimation of Nonlinear Muskingum Models Using Nelder-Mead Simplex Algorithm. J Hydrol Eng 2011;16:946–54. doi:10.1061/(ASCE)HE.1943-5584.0000379.
[9]     Barati R. Application of excel solver for parameter estimation of the nonlinear Muskingum models. KSCE J Civ Eng 2013;17:1139–48. doi:10.1007/s12205-013-0037-2.
[10]    Haddad OB, Mariño MA. Optimum operation of wells in coastal aquifers. Proc Inst Civ Eng - Water Manag 2011;164:135–46. doi:10.1680/wama.1000037.
[11]    Hosseini K, Nodoushan EJ, Barati R, Shahheydari H. Optimal design of labyrinth spillways using meta-heuristic algorithms. KSCE J Civ Eng 2016;20:468–77. doi:10.1007/s12205-015-0462-5.
[12]    Wu J, Zhu X, Liu J. Using genetic algorithm based simulated annealing penalty function to solve groundwater management model. Sci China Ser E Technol Sci 1999;42:521–9. doi:10.1007/BF02917406.
[13]    Wu J, Zhu X. Using the Shuffled Complex Evolution Global Optimization Method to Solve Groundwater Management Models, 2006, p. 986–95. doi:10.1007/11610113_105.
[14]    Zhu X, Wu J, Wu J. Application of SCE-UA to Optimize the Management Model of Groundwater Resources in Deep Aquifers of the Yangtze Delta. First Int Multi-Symposiums Comput Comput Sci, IEEE; 2006, p. 303–8. doi:10.1109/IMSCCS.2006.192.
[15]    Tamer Ayvaz M. Application of Harmony Search algorithm to the solution of groundwater management models. Adv Water Resour 2009;32:916–24. doi:10.1016/j.advwatres.2009.03.003.
[16]    Gaur S, Chahar BR, Graillot D. Analytic elements method and particle swarm optimization based simulation–optimization model for groundwater management. J Hydrol 2011;402:217–27. doi:10.1016/j.jhydrol.2011.03.016.
[17]    Gaur S, Mimoun D, Graillot D. Advantages of the analytic element method for the solution of groundwater management problems. Hydrol Process 2011;25:3426–36. doi:10.1002/hyp.8071.
[18]    Mategaonkar M, Eldho TI. Groundwater remediation optimization using a point collocation method and particle swarm optimization. Environ Model Softw 2012;32:37–48. doi:10.1016/j.envsoft.2012.01.003.
[19]    El-Ghandour HA, Elsaid A. Groundwater management using a new coupled model of flow analytical solution and particle swarm optimization. Int J Water Resour Environ Eng 2013;5:1–11.
[20]    Park C-H, Aral MM. Multi-objective optimization of pumping rates and well placement in coastal aquifers. J Hydrol 2004;290:80–99. doi:10.1016/j.jhydrol.2003.11.025.
[21]    Abdel-Gawad HA. Multi-objective management of heterogeneous coastal aquifers. Mansoura Eng J 2004;29:C1–14.
[22]    Siegfried T, Bleuler S, Laumanns M, Zitzler E, Kinzelbach W. Multiobjective Groundwater Management Using Evolutionary Algorithms. IEEE Trans Evol Comput 2009;13:229–42. doi:10.1109/TEVC.2008.923391.
[23]    Saafan TA, Moharram SH, Gad MI, KhalafAllah S. A multi-objective optimization approach to groundwater management using genetic algorithm. Int J Water Resour Environ Eng 2011;3:139–49.
[24]    El-Ghandour HA, Elbeltagi E. Optimal Groundwater Management Using Multiobjective Particle Swarm with a New Evolution Strategy. J Hydrol Eng 2014;19:1141–9. doi:10.1061/(ASCE)HE.1943-5584.0000910.
[25]    El-Ghandour HA, Elabd SM. Studying the reliability in multi-objective management of groundwater under uncertainty of hydraulic conductivity values. Mansoura Eng J 2015;40:C58–72.
[26]    Wanakule N, Mays LW, Lasdon LS. Optimal Management of Large-Scale Aquifers: Methodology and Applications. Water Resour Res 1986;22:447–65. doi:10.1029/WR022i004p00447.
[27]    Willis R. A planning model for the management of groundwater quality. Water Resour Res 1979;15:1305–12. doi:10.1029/WR015i006p01305.
[28]    Aguado E, Remson I, Pikul MF, Thomas WA. Optimum pumping to prevent dewatering. J Hydraul Div 1974;100:860–77.
[29]    Andricevic R. A Real-Time Approach to Management and Monitoring of Groundwater Hydraulics. Water Resour Res 1990;26:2747–55. doi:10.1029/WR026i011p02747.
[30]    Gorelick SM, Remson I, Cottle RW. Management model of a groundwater system with a transient pollutant source. Water Resour Res 1979;15:1243–9. doi:10.1029/WR015i005p01243.
[31]    Gorelick SM, Voss CI, Gill PE, Murray W, Saunders MA, Wright MH. Aquifer Reclamation Design: The Use of Contaminant Transport Simulation Combined With Nonlinear Programing. Water Resour Res 1984;20:415–27. doi:10.1029/WR020i004p00415.
[32]    Jones L, Willis R, Yeh WW-G. Optimal control of nonlinear groundwater hydraulics using differential dynamic programming. Water Resour Res 1987;23:2097–106. doi:10.1029/WR023i011p02097.
[33]    Lee S-I, Kitanidis PK. Optimal Estimation and Scheduling in Aquifer Remediation With Incomplete Information. Water Resour Res 1991;27:2203–17. doi:10.1029/91WR01307.
[34]    Mora-Melia D, Iglesias-Rey P, Martínez-Solano F, Muñoz-Velasco P. The Efficiency of Setting Parameters in a Modified Shuffled Frog Leaping Algorithm Applied to Optimizing Water Distribution Networks. Water 2016;8:182. doi:10.3390/w8050182.
[35]    El-Ghandour HA, Elbeltagi E. Comparison of Five Evolutionary Algorithms for Optimization of Water Distribution Networks. J Comput Civ Eng 2018;32:04017066. doi:10.1061/(ASCE)CP.1943-5487.0000717.
[36]    Grierson DE. Pareto multi-criteria decision making. Adv Eng Informatics 2008;22:371–84. doi:10.1016/j.aei.2008.03.001.
[37]    Elbeltagi E, Hegazy T, Grierson D. A new evolutionary strategy for pareto multi-objective optimization. Proc 7th Int Conf Eng Comput Technol Civil-Comp Press Scotl, 2010.
[38]    Elbeltagi E, Hegazy T, Grierson D. Comparison among five evolutionary-based optimization algorithms. Adv Eng Informatics 2005;19:43–53. doi:10.1016/j.aei.2005.01.004.
[39]    Kennedy J, Eberhart R. Particle swarm optimization. Proc IEEE Int Conf Neural Netw IV, 1942–1948, vol. 4, IEEE; 1995, p. 1942–8. doi:10.1109/ICNN.1995.488968.
[40]    Shi Y, Eberhart R. A modified particle swarm optimizer. 1998 IEEE Int Conf Evol Comput Proceedings IEEE World Congr Comput Intell (Cat No98TH8360), IEEE; n.d., p. 69–73. doi:10.1109/ICEC.1998.699146.
[41]    Zhang H, Li H. Multi‐objective particle swarm optimization for construction time‐cost tradeoff problems. Constr Manag Econ 2010;28:75–88. doi:10.1080/01446190903406170.
[42]    Baltar AM, Fontane DG. A generalized multiobjective particle swarm optimization solver for spreadsheet models: application to water quality. Hydrol Days 2006:1–12.
[43]    Elbeltagi E, Hegazy T, Grierson D. A modified shuffled frog-leaping optimization algorithm: applications to project management. Struct Infrastruct Eng 2007;3:53–60. doi:10.1080/15732470500254535.
[44]    Coello CAC, Pulido GT, Lechuga MS. Handling multiple objectives with particle swarm optimization. IEEE Trans Evol Comput 2004;8:256–79. doi:10.1109/TEVC.2004.826067.

Files

Cited by

History

  • Receive Date: 23 April 2018
  • Revise Date: 19 June 2018
  • Accept Date: 20 June 2018

Share

How to cite

Statistics