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Pumping Optimization of Coastal Aquifers Assisted by Adaptive Metamodelling Methods and Radial Basis Functions

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The application of metamodelling frameworks is a popular approach to handle the computational cost arising from complex computer simulations and global optimization algorithms in simulation-optimization routines. In this paper, Radial Basis Functions (RBF) are used as metamodels for the computationally expensive variable-density flow and salt transport numerical simulations, in a pumping optimization problem of coastal aquifers. While RBF metamodels have been fairly utilized in many engineering optimization problems, their use is very limited in coastal aquifer management. Two adaptive metamodelling frameworks are employed, that is, the adaptive-recursive approach and the metamodel-embedded evolution strategy. In both frameworks, cubic RBF models are used to approximate the constraint functions imposed on the coastal aquifer pumping optimization problem. The optimal pumping rates are first calculated based on the variable-density and salt transport numerical models of seawater intrusion. The resulting optimal solutions and the computational times are set as benchmark values in order to assess the performance of the metamodelling optimization strategies. Results indicate that the metamodel-embedded evolution framework outperformed in terms of computational efficiency the adaptive-recursive approach while it successfully located the region of the global optimum. Furthermore, with the metamodel-embedded evolution strategy the computational time of the variable-density-based optimization was reduced by 96 %.

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  1. Anderson MP, Woessner WW (2002) Applied groundwater modeling. Academic, San Diego

  2. Ataie-Ashtiani B, Ketabchi H (2011) Elitist continuous ant colony optimization algorithm for optimal management of coastal aquifers. Water Resour Manag 25:165–190

  3. Bhattacharjya RK, Datta B (2005) Optimal management of coastal aquifers using linked simulation optimization approach. Water Resour Manag 19(3):295–320

  4. Christelis V, Mantoglou A (2016) Coastal aquifer management based on the joint use of density-dependent and sharp interface models. Water Resour Manag 30(2):861–876

  5. Christelis V, Kopsiaftis G, Mantoglou A (2012) Coastal aquifer management under drought conditions considering aquifer spatial variability. IAHS-AISH Publ 355:293–297

  6. Dausman A, Langevin C, Bakker M, Schaars F (2010) A comparison between SWI and SEAWAT—The importance of dispersion, inversion and vertical anisotropy. 21st Salt Water Intrusion Meeting, Gov. of Azores, Azores

  7. Dokou Z, Karatzas GP (2012) Saltwater intrusion estimation in a karstified coastal system using density-dependent modeling and comparison with the sharp-interface approach. Hydrol Sci J 57(5):985–999

  8. Efstratiadis A, Koutsoyiannis D (2002) An evolutionary annealing-simplex algorithm for global optimization of water resource systems. Proceeedings of the Fifth International Conference on Hydroinformatics, Cardiff, UK, International Water Association Publishing 2:1423–1428

  9. Efstratiadis A, Nalbantis I, Koutsoyiannis D (2014) Hydrological modelling of temporally-varying catchments: facets of change and the value of information. Hydrol Sci J. doi:10.1080/02626667.2014.982123

  10. Forrester AIJ, Keane AJ (2009) Recent advances in surrogate-based optimization. Prog Aerosp Sci 49:50–79

  11. Forrester AIJ, Sóbester A, Keane AJ (2008) Engineering design via surrogate modelling-A practical guide. Wiley, New York

  12. Graf T, Therrien R (2005) Variable-density groundwater flow and solute transport in porous media containing nonuniform discrete fractures. Adv Water Resour 28:1351–1367

  13. Guo W, Langevin CD (2002) User’s guide to SEAWAT: a computer programm for simulation of three-dimensional variable-density groundwater flow. Report No. US Geol Surv Open file 01–434

  14. Jin Y (2005) A comprehensive survey of fitness approximation in evolutionary computation. Soft Comput 9:3–12

  15. Jin Y (2011) Surrogate-assisted evolutionary computation: recent advances and future challenges. Swarm Evol Comput 1:61–70

  16. Kampolis IC, Karangelos EI, Giannakoglou KC (2004) Gradient-assisted radial basis function networks: theory and applications. Appl Math Modell 28:197–209

  17. Karatzas GP, Dokou Z (2015) Optimal management of saltwater intrusion in the coastal aquifer of Malia, Crete (Greece) using particle swarm optimization. Hydrogeol J. doi:10.1007/s10040-015-1286-6

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

  19. Kourakos G, Mantoglou A (2006) Pumping optimization of coastal aquifers using 3-d density models and approximations with neural networks. XVI international conference on computational methods in water resources, Copehangen

  20. Kourakos G, Mantoglou A (2009) Pumping optimization of coastal aquifers based on evolutionary algorithms and surrogate modular neural network models. Adv Water Resour 32(4):507–521

  21. Mantoglou A (2003) Pumping management of coastal aquifers using analytical models of saltwater intrusion. Water Resour Res. doi:10.1029/2002WR001891

  22. Mantoglou A, Papantoniou M, Giannoulopoulos P (2004) Management of coastal aquifers based on nonlinear optimization and evolutionary algorithms. J Hydrol 297:209–228

  23. Mathworks (2010) MATLAB global optimization toolbox

  24. Mugunthan P, Shoemaker CA, Regis RG (2005) Comparison of function approximation, heuristic and derivative-based methods for automatic calibration of computationally expensive groundwater bioremediation models. Water Resour Res. doi:10.1029/2005WR004134

  25. Papadopoulou MP, Nikolos IK, Karatzas GP (2010) Computational benefits using artificial intelligent methodologies for the solution of an environmental design problem: saltwater intrusion. Water Sci Technol 62(7):1479–1490

  26. Prieto C, Kotronarou A, Destouni G (2006) The influence of temporal hydrological randomness on seawater intrusion in coastal aquifers. J Hydrol 330:285–300

  27. Queipo NV, Haftka RT, Shyy W, Goel T, Vaidyanathan R, Tucker PK (2005) Surrogate-based analysis and optimization. Prog Aerosp Sci 41:1–28

  28. Rao SVN, Sreenivasulu V, Bhallamudi SM, Thandaveswara BS, Sudheer KP (2004) Planning groundwater development in coastal aquifers. Hydrol Sci J. doi:10.1623/hysj.

  29. Razavi S, Tolson BA, Burn DH (2012) Numerical assessment of metamodelling strategies in computationally intensive optimization. Environ Model Softw 34:67–86

  30. Regis RG (2011) Stochastic radial basis function algorithms for large-scale optimization involving expensive black-box objective and constraint functions. Comput Oper Res 38:837–853

  31. Regis RG (2014) Evolutionary programming for high-dimensional constrained expensive black-box optimization using radial basis functions. IEEE Trans Evol Comput 18(3)

  32. Regis RG, Shoemaker CA (2004) Local function approximation in evolutionary algorithms for the optimization of costly functions. IEEE Trans Evol Comput 8(5):490–505

  33. Regis RG, Shoemaker CA (2005) Constrained global optimization of expensive black box functions using radial basis functions. J Global Optim 31:153–171

  34. Regis RG, Shoemaker CA (2007) Improved strategies for radial basis function methods for global optimization. J Global Optim 37:113–135

  35. Rozos E, Efstratiadis A, Nalbantis I, Koutsoyiannis D (2004) Calibration of a semi-distributed model for conjunctive simulation of surface and groundwater flows. Hydrol Sci J 49(5):819–842

  36. Simmons CT (2005) Variable density groundwater flow: from current challenges to future possibilities. Hydrogeol J 13:116–119

  37. Simpson TW, Peplinski JD, Koch PN, Allen JK (2001) Metamodels for computer-based engineering design: survey and recommendations. Eng Comput 17:129–150

  38. Singh A (2012) An overview of the optimization modeling applications. J Hydrol 466–467:167–182

  39. Singh A (2014) Optimization modelling for seawater intrusion management. J Hydrol 508:43–52

  40. Singh A (2015) Managing the environmental problem of seawater intrusion in coastal aquifers through simulation-optimization modeling. Ecol Indic 48:498–504

  41. Sóbester A, Forrester AIJ, Toal DJJ, Tresidder E, Tucker S (2014) Engineering design applications of surrogate-assisted optimization techniques. Optim Eng 15(1):243–265

  42. Sreekanth J, Datta B (2011) Comparative evaluation of Genetic Programming and Neural Network as a potential surrogate models for coastal aquifer management. Water Resour Manag 25:3201–3218

  43. Sreekanth J, Datta B (2015) Review: simulation-optimization models for the management and monitoring of coastal aquifers. Hydrogeol J. doi:10.1007/s10040-015-1272-z

  44. Therrien R, Sudicky EA (1996) Three-dimensional analysis of variably-saturated flow and solute transport in discretely-fractured porous media. J Contam Hydrol 23:1–44

  45. Therrien R, McLaren RG, Sudicky EA, Panday SM (2006) HydroGeoSphere-A three-dimensional numerical model describing fully-integrated subsurface and surface flow and solute transport. Groundwater Simulations Group, University of Waterloo, Canada, draft ed. 2006

  46. Thompson C, Smith L, Maji R (2007) Hydrogeological modelling of submarine groundwater discharge on the continental shelf of Louisiana. J Geophys Res 112, C03014. doi:10.1029/2006JC003557

  47. Voss CI, Souza WR (1987) Variable density flow and solute transport simulations of regional aquifers containing a narrow freshwater-saltwater transition zone. Water Resour Res 23:1851–1866

  48. Werner AD, Bakker M, Post VEA, Vandenbohede A, Lu C, Ataie-Ashtiani B, Simmons CT, Barry DA (2013) Seawater intrusion processes, investigation and management: recent advances and future challenges. Adv Water Resour 51:3–26

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Correspondence to Vasileios Christelis.

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Christelis, V., Mantoglou, A. Pumping Optimization of Coastal Aquifers Assisted by Adaptive Metamodelling Methods and Radial Basis Functions. Water Resour Manage 30, 5845–5859 (2016). https://doi.org/10.1007/s11269-016-1337-3

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  • Coastal aquifers
  • Pumping optimization
  • Metamodels
  • Radial basis functions
  • Global optimization