Management of coastal aquifers based on nonlinear optimization and evolutionary algorithms

Abstract A method of assessing the optimum pumping rates of coastal aquifers based on nonlinear optimization and evolutionary algorithms (EA) is developed. The objective is to maximize the total pumping rate while protecting the wells from sea water intrusion. The formulation of the constraints is based on numerical simulation of the freshwater flow equations. The simulation model is based on the sharp interface and the Ghyben–Herzberg approximation and is applicable to unconfined aquifers and steady-state flow. The single potential formulation of [Water Resour. Res. 12 (1976) 1165] is followed and the governing equations are solved numerically using finite differences. The numerical model can handle aquifers of complex shapes, nonuniform hydraulic conductivity, nonuniform distribution of surface recharge, etc. The constraints are nonlinear with respect to the decision variables resulting in a nonlinear optimization problem. Two optimization methods are investigated, specifically Sequential Quadratic Programming (SQP) and Evolutionary Algorithms (EA). SQP requires less computer time than EA but can get stuck on local optimum solutions. The simulation and optimization methodology is applied to a real unconfined coastal aquifer in the Greek island of Kalymnos for determining the optimal pumping rates while protecting the wells from sea water intrusion.

[1]  J. Bear.  Hydraulics of Groundwater , 1979 .

[2]  H. Essaid.  A multilayered sharp interface model of coupled freshwater and saltwater flow in coastal systems: Model development and application , 1990 .

[3]  H. Yazicigil,et al.  Optimal Management of a Coastal Aquifer in Southern Turkey , 1996 .

[4]  G. O. Essink.  Salt water intrusion in a three-dimensional groundwater system in The Netherlands: a numerical study , 2001 .

[5]  Klaus Schittkowski,et al.  A comparative performance evaluation of 27 nonlinear programming codes , 1983, Computing.

[6]  O. Strack.  A single‐potential solution for regional interface problems in coastal aquifers , 1976 .

[7]  John H. Holland,et al.  Adaptation in Natural and Artificial Systems: An Introductory Analysis with Applications to Biology, Control, and Artificial Intelligence , 1992 .

[8]  C. G. Broyden.  The Convergence of a Class of Double-rank Minimization Algorithms 1. General Considerations , 1970 .

[9]  Philip E. Gill,et al.  Practical optimization , 1981 .

[10]  Shih-Ping Han.  A globally convergent method for nonlinear programming , 1975 .

[11]  William W.-G. Yeh,et al.  MANAGEMENT MODEL FOR CONJUNCTIVE USE OF COASTAL SURFACE WATER AND GROUND WATER , 1998 .

[12]  H. Zimmermann.  Towards global optimization 2: L.C.W. DIXON and G.P. SZEGÖ (eds.) North-Holland, Amsterdam, 1978, viii + 364 pages, US $ 44.50, Dfl. 100,-. , 1979 .

[13]  D. Goldfarb.  A family of variable-metric methods derived by variational means , 1970 .

[14]  P. Gill,et al.  Aquifer Reclamation Design: The Use of Contaminant Transport Simulation Combined With Nonlinear Programing , 1984 .

[15]  M. J. D. Powell,et al.  Variable Metric Methods for Constrained Optimization , 1982, ISMP.

[16]  Arlen W. Harbaugh,et al.  A modular three-dimensional finite-difference ground-water flow model , 1984 .

[17]  S. Gorelick.  A review of distributed parameter groundwater management modeling methods , 1983 .

[18]  Michael A. Saunders,et al.  Procedures for optimization problems with a mixture of bounds and general linear constraints , 1984, ACM Trans. Math. Softw..

[19]  Martin Grötschel,et al.  Mathematical Programming The State of the Art, XIth International Symposium on Mathematical Programming, Bonn, Germany, August 23-27, 1982 , 1983, ISMP.

[20]  K. Schittkowski.  NLPQL: A fortran subroutine solving constrained nonlinear programming problems , 1986 .

[21]  A. Cheng,et al.  Pumping optimization in saltwater‐intruded coastal aquifers , 2000 .

[22]  David E. Goldberg,et al.  Genetic Algorithms in Search Optimization and Machine Learning , 1988 .

[23]  R. Fletcher.  Practical Methods of Optimization , 1988 .

[24]  M. J. D. Powell,et al.  A fast algorithm for nonlinearly constrained optimization calculations , 1978 .

[25]  David B. Fogel,et al.  An introduction to simulated evolutionary optimization , 1994, IEEE Trans. Neural Networks.

[26]  Cass T. Miller,et al.  Optimal design for problems involving flow and transport phenomena in saturated subsurface systems , 2002 .

[27]  Weiqi Wang,et al.  Optimal groundwater remediation with well location as a decision variable: Model development , 1994 .

[28]  Jacob Bensabat,et al.  Optimal management of a regional aquifer under salinization conditions , 2000 .

[29]  P. F. Andersen,et al.  Numerical Modeling of Salt‐Water Intrusion at Hallandale, Florida , 1988 .

[30]  Philip E. Gill,et al.  Numerical Linear Algebra and Optimization , 1991 .

[31]  Manoutchehr Heidari,et al.  Applications of Optimal Hydraulic Control to Ground-Water Systems , 1994 .

[32]  A. Cheng,et al.  Seawater intrusion in coastal aquifers : concepts, methods, and practices , 1999 .

[33]  R. Fletcher,et al.  A New Approach to Variable Metric Algorithms , 1970, Comput. J..

[34]  P. F. Andersen,et al.  Saltwater intrusion in aquifers: Development and testing of a three‐dimensional finite element model , 1987 .

[35]  Bithin Datta,et al.  Development of multiobjective management models for coastal aquifers , 1999 .

[36]  U. Shamir,et al.  Optimal Annual Operation of a Coastal Aquifer , 1984 .

[37]  A. Mantoglou.  Pumping management of coastal aquifers using analytical models of saltwater intrusion , 2003 .

[38]  D. Shanno.  Conditioning of Quasi-Newton Methods for Function Minimization , 1970 .