Abstract
When designing a well field for efficiently extracting groundwater or petroleum, it is common for designers to rely on computational optimization methods to determine the optimal placement of wells. The goal of these methods is to find a well-field solution that maximizes the value of a defined objective function, and to do so while utilizing the least amount of computational effort. To achieve this, researchers have developed algorithms based on a wide range of heuristics. Within groundwater management, popular methods include particle swarm optimization (PSO) and genetic algorithms such as differential evolution (DE). This study seeks to investigate a recently developed method called Extremal Optimization for Well Placement Problems (EO-WPP), and to compare its performance with established methods like PSO and DE. EO-WPP is an optimization method based on the extremal optimization (EO) algorithm. EO optimizes by iteratively identifying and modifying the least effective components of a solution. By following this heuristic, the EO algorithm has the potential to quickly find optimal solutions while requiring minimal computational effort. To test this, the performance of DE, PSO and EO-WPP was compared on four benchmark problems. Two of these are the Rastrigin and the Rosenbrock benchmark functions. These functions were used because of their quick evaluation and their popularity in optimization literature. The third benchmark is a synthetic groundwater model, built to test the methods under the context of groundwater management. The final benchmark is a field problem using the Aberdeen groundwater model in South Dakota. The results reveal that EO-WPP was able to outperform DE and PSO on all tested benchmarks. EO-WPP is an effective and efficient optimization tool for well placement design in groundwater management.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Ahlfeld DP, Barlow PM, Mulligan AE (2005) GWM–A groundwater management process for the US Geological Survey Modular Groundwater Model (MODFLOW-2000). US Department of the Interior, US Geological Survey
Back T, Schwefel HP (1993) An overview of evolutionary algorithms for parameter optimization. Evol Comput 1(1):1–23
Bansal JC, Singh P, Saraswat M, Verma A, Jadon SS, Abraham A (2011) Inertia weight strategies in particle swarm optimization. In: 2011 third world congress on nature and biologically inspired computing. IEEE, pp 633–640
Bayer P, Duran E, Baumann R, Finkel M (2009) Optimized groundwater drawdown in a subsiding urban mining area. J Hydrol 365(1–2):95–104
Boettcher S (2005) Extremal optimization for Sherrington-Kirkpatrick spin glasses. Eur Phys J B Condens Matter Complex Syst 46(4):501–505
Boettcher S, Percus AG (1999) Extremal optimization: methods derived from co-evolution. In: Proceedings of the 1st annual conference on genetic and evolutionary computation, vol 1. Morgan Kaufmann Publishers Inc., pp 825–832
Chen J, Zeng GQ, Zhou W, Du W, Lu KD (2018) Wind speed forecasting using nonlinear-learning ensemble of deep learning time series prediction and extremal optimization. Energy Convers Manag 165:681–695
Das S, Mullick SS, Suganthan PN (2016) Recent advances in differential evolution-an updated survey. Swarm Evolut Comput 27:1–30
Eberhart R, Kennedy J (1995) A new optimizer using particle swarm theory. In: Proceedings of the sixth international symposium on micro machine and human science, 1995. MHS’95. IEEE, pp 39–43
Elçi A, Ayvaz MT (2014) Differential-evolution algorithm based optimization for the site selection of groundwater production wells with the consideration of the vulnerability concept. J Hydrol 511:736–749
Emerick AA, Silva E, Messer B, Almeida LF, Szwarcman D, Pacheco MAC, Vellasco MMBR et al (2009) Well placement optimization using a genetic algorithm with nonlinear constraints. In: SPE reservoir simulation symposium. Society of Petroleum Engineers
Feng Q, Zhang J, Zhang X, Hu A (2012) Optimizing well placement in a coalbed methane reservoir using the particle swarm optimization algorithm. Int J Coal Geol 104:34–45
Fowler KR, Reese JP, Kees CE, Dennis J Jr, Kelley CT, Miller CT, Audet C, Booker AJ, Couture G, Darwin RW et al (2008) Comparison of derivative-free optimization methods for groundwater supply and hydraulic capture community problems. Adv Water Resour 31(5):743–757
Gaur S, Ch S, Graillot D, Chahar BR, Kumar DN (2013) Application of artificial neural networks and particle swarm optimization for the management of groundwater resources. Water Resour Manag 27(3):927–941
Gurarslan G, Karahan H (2015) Solving inverse problems of groundwater-pollution-source identification using a differential evolution algorithm. Hydrol J 23(6):1109–1119
Guyaguler B, Horne RN et al (2001) Uncertainty assessment of well placement optimization. In: SPE annual technical conference and exhibition. Society of Petroleum Engineers
Haddad OB, Tabari MMR, Fallah-Mehdipour E, Mariño M (2013) Groundwater model calibration by meta-heuristic algorithms. Water Resour Manag 27(7):2515–2529
Ho-Huu V, Nguyen-Thoi T, Vo-Duy T, Nguyen-Trang T (2016) An adaptive elitist differential evolution for optimization of truss structures with discrete design variables. Comput Struct 165:59–75
Holland JH (1975) Adaptation in natural and artificial systems: an introductory analysis with applications to biology, control, and artificial intelligence
Humphries TD, Haynes RD, James LA (2014) Simultaneous and sequential approaches to joint optimization of well placement and control. Comput Geosci 18(3–4):433–448
Jamil M, Yang XS (2013) A literature survey of benchmark functions for global optimization problems. arXiv preprint arXiv:1308.4008
Karterakis SM, Karatzas GP, Nikolos IK, Papadopoulou MP (2007) Application of linear programming and differential evolutionary optimization methodologies for the solution of coastal subsurface water management problems subject to environmental criteria. J Hydrol 342(3–4):270–282
Mahinthakumar G, Sayeed M (2005) Hybrid genetic algorithm–local search methods for solving groundwater source identification inverse problems. J Water Resour Plan Manag 131(1):45–57
Mategaonkar M, Eldho T (2012) Groundwater remediation optimization using a point collocation method and particle swarm optimization. Environ Model Softw 32:37–48
Mathur S (2012) Groundwater level forecasting using SVM-PSO. Int J Hydrol Sci Technol 2(2):202–218
Minton JJ (2012) A comparison of common methods for optimal well placement. University of Auckland, research rep
Mühlenbein H, Schomisch M, Born J (1991) The parallel genetic algorithm as function optimizer. Parallel Comput 17(6–7):619–632
Nozohour-leilabady B, Fazelabdolabadi B (2016) On the application of artificial bee colony (abc) algorithm for optimization of well placements in fractured reservoirs; efficiency comparison with the particle swarm optimization (pso) methodology. Petroleum 2(1):79–89
Nwankwor E, Nagar AK, Reid D (2013) Hybrid differential evolution and particle swarm optimization for optimal well placement. Comput Geosci 17(2):249–268
Park CH, Aral MM (2004) Multi-objective optimization of pumping rates and well placement in coastal aquifers. J Hydrol 290(1–2):80–99
Pedersen MEH (2010) Good parameters for differential evolution. Magnus Erik Hvass Pedersen 49
Poli R, Kennedy J, Blackwell T (2007) Particle swarm optimization. Swarm Intell 1(1):33–57
Redoloza F, Li L (2019) A novel method for well placement design in groundwater management: extremal optimization. Adv Water Resour 132(103):405
Reed P, Minsker B, Valocchi AJ (2000) Cost-effective long-term groundwater monitoring design using a genetic algorithm and global mass interpolation. Water Resour Res 36(12):3731–3741
Sarma P, Chen WH et al (2008) Efficient well placement optimization with gradient-based algorithms and adjoint models. In: Intelligent energy conference and exhibition. Society of Petroleum Engineers
Sengupta S, Basak S, Peters R (2018) Particle swarm optimization: a survey of historical and recent developments with hybridization perspectives. Mach Learn Knowl Extr 1(1):157–191
Storn R, Price K (1997) Differential evolution–a simple and efficient heuristic for global optimization over continuous spaces. J Glob Optim 11(4):341–359
Valder JF, Eldridge WG, Davis KW, Medler CJ, Koth KR (2018) Revised groundwater-flow model of the glacial aquifer system north of Aberdeen, South Dakota, through water year 2015. Tech. rep, US Geological Survey
Wang W, Ahlfeld DP (1994) Optimal groundwater remediation with well location as a decision variable: model development. Water Resour Res 30(5):1605–1618
Zeng GQ, Chen J, Dai YX, Li LM, Zheng CW, Chen MR (2015) Design of fractional order pid controller for automatic regulator voltage system based on multi-objective extremal optimization. Neurocomputing 160:173–184
Acknowledgements
The authors acknowledge the financial support of the South Dakota Board of Regents through a Competitive Research Grant. This work is also supported through a grant from the National Science Foundation (OIA-1833069). We are grateful to Dr. Arden Davis for his comments and edits. We would also like to thank the guest editor as well as two anonymous reviewers for their constructive comments, which helped to improve the manuscript substantially.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Redoloza, F., Li, L. A Comparison of Extremal Optimization, Differential Evolution and Particle Swarm Optimization Methods for Well Placement Design in Groundwater Management. Math Geosci 53, 711–735 (2021). https://doi.org/10.1007/s11004-020-09864-3
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11004-020-09864-3