Dynamic Optimal Groundwater Management with Inclusion of Fixed Costs
Publication: Journal of Water Resources Planning and Management
Volume 128, Issue 1
Abstract
Obtaining optimal solutions for groundwater resources planning problems, while simultaneously considering both fixed costs and time-varying pumping rates, is a challenging task. Application of conventional optimization algorithms such as linear and nonlinear programming is difficult due to the discontinuity of the fixed cost function in the objective function and the combinatorial nature of assigning discrete well locations. Use of conventional discrete algorithms such as integer programming or discrete dynamic programming is hampered by the large computational burden caused by varying pumping rates over time. A novel procedure that integrates a genetic algorithm (GA) with constrained differential dynamic programming (CDDP) calculates optimal solutions for a groundwater resources planning problem while simultaneously considering fixed costs and time-varying pumping rates. The GA determines the number and locations of pumping wells with operating costs then evaluated using CDDP. This study demonstrates that fixed costs associated with installing wells significantly impact the optimal number and locations of wells.
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References
Ahlfeld, D. P., Mulvey, J. M., and Pinder, G. F.(1988b). “Contaminated groundwater remediation design using simulation, optimization, and sensitivity theory, 2: Analysis of a field site.” Water Resour. Res., 24(5), 443–452.
Ahlfeld, D. P., Mulvey, J. M., Pinder, G. F., and Wood, E. F.(1988a). “Contaminated groundwater remediation design using simulation, optimization, and sensitivity theory. 1: Model development.” Water Resour. Res., 24(5), 431–441.
Aguado, E., and Remson, I.(1974). “Ground-water hydraulics in aquifer management.” J. Hydraul. Div., 100(1), 103–118.
Basagaoglu, H., and Marino, M. A.(1999). “Joint management of surface and ground water supplies.” Ground Water, 37(2), 214–222.
Bellman, R. E., and Dreyfus, S. E. (1962). Applied dynamic programming, Princeton University Press, Princeton, N.J.
Chang, S. C. (1986). “A hierarchical, temporal decomposition approach to long horizon optimal control problems,” PhD dissertation, Univ. of Connecticut, Storrs.
Chang, L. C., Shoemaker, C. A., and Liu, P. L. F.(1992). “Optimal time-varying pumping rates for groundwater remediation: Application of a constrained optimal control algorithm.” Water Resour. Res., 28(12), 3157–3171.
Cieniawski, S. E., Eheart, J. W., and Ranjithan, S.(1995). “Using genetic algorithm to solve a multiobjective groundwater monitoring problem.” Water Resour. Res., 31(2), 399–409.
Culver, T. B., and Shoemaker, C. A.(1992). “Dynamic optimal control for groundwater remediation with flexible management periods.” Water Resour. Res., 28(3), 629–641.
Culver, T. B., and Shoemaker, C. A.(1997). “Dynamic optimal ground-water reclamation with treatment capital costs.” J. Water Resour. Plan. Manage., 123(1), 23–29.
DeJong, K. A. (1975). “An analysis of the behavior of a class of genetic adaptive systems.” PhD dissertation, Univ. of Michigan, Ann Arbor.
Goldberg, D. E. (1989). Genetic algorithm in search, optimization, and machine learning, Addison-Wesley, Reading, Mass.
Gorelick, S. M.(1983). “A review of distributed parameter groundwater management modeling methods.” Water Resour. Res., 19(2), 305–319.
Gorelick, S. M., Voss, C. I., Gill, P. E., Murray, W., Saunders, M. A., and Wright, M. H.(1984). “Aquifer reclamation design: The use of contaminant transport simulation combined with nonlinear programming.” Water Resour. Res., 20(4), 415–427.
Jones, L., Willis, R., and Yeh, W. W.-G.(1987). “Optimal control of nonlinear groundwater hydraulics using differential dynamic programming.” Water Resour. Res., 23(11), 2097–2106.
Lin, X., and Yang, Y.(1991). “The optimization of groundwater supply system in SHI JIAZ-HUANG City, China.” Water Sci. Technol., 24(11), 71–76.
McKinney, D. C., and Lin, M. D.(1994). “Genetic algorithm solution of groundwater management models.” Water Resour. Res., 30(6), 1897–1906.
McKinney, D. C., and Lin, M. D.(1995). “Approximate mixed-integer nonlinear programming methods for optimal aquifer remediation design.” Water Resour. Res., 31(3), 731–740.
Molz, F. J., and Bell, L. C.(1977). “Head gradient control in aquifers used for fluid storage.” Water Resour. Res., 13(14), 795–798.
Morshed, J., and Kaluarachchi, J. J.(2000). “Enhancements to genetic algorithm for optimal ground-water management.” J. Hydrologic Eng., 5(1), 67–73.
Murray, D. M., and Yakowitz, S. J.(1979). “Constrained differential dynamic programming and its application to multireservoir control.” Water Resour. Res., 15(5), 1017–1027.
Murtagh, B. A., and Saunders, M. A., (1982). “A projected Lagrangian algorithm and its implementation for sparse nonlinear constraints.” Mathematical programming study 16, North-Holland, Amsterdam, The Netherlands.
Pezeshk, S., Helweg, O. J., and Oliver, K. E. (1994). “Optimal operation of ground-water supply distribution systems,” J. Water Resour. Plng. and Mgmt., 120(5), 573–586.
Philbrick, C. R., and Kitanidis, P. K.(1998). “Optimal conjunctive-use operations and plans,” Water Resour. Res., 34(5), 1307–1316.
Pinder, G. F. (1978). “Galerkin finite element models for aquifer simulation.” Rep. 78-WR-5, Dept. of Civ. Eng., Princeton Univ., Princeton, N.J.
Rosenwald, G. W., and Green, D. W.(1974). “A method for determining the optimum location of wells in a reservoir using mixed-integer programming.” Soc. Pet. Eng. J., 14(1), 44–54.
Taghavi, S. A., Howitt, R. E., and Mariño, M. A.(1994). “Optimal control of ground-water quality management: Nonlinear programming approach,” J. Water Resour. Plan. Manage., 120(6), 962–982.
Takahashi, S., and Peralta, R. C.(1995). “Optimal perennial yield planning for complex nonlinear aquifers: Methods and examples,” Adv. Water Resour., 18(1), 49–62.
Wang, M., and Zheng, C.(1998). “Ground water management optimization using genetic algorithms and simulated annealing: Formulation and comparison.” J. Am. Water Resour. Ass., 34(3), 519–530.
Wardlaw, R., and Sharif, M.(1999). “Evaluation of Genetic Algorithms for Optimal Reservoir System Operation.” J. Water Resour. Plan. Manage., 125(1), 25–33.
Yeh, W. W.-G.(1992). “Systems analysis in ground-water planning and management.” J. Water Resour. Plan. Manage., 118(3), 224–237.
Zheng, C., and Wang, P. P.(1999). “An integrated global and local optimization approach for remediation system design.” Water Resour. Res., 35(1), 137–148.
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Copyright © 2002 American Society of Civil Engineers.
History
Received: Nov 19, 1999
Accepted: Apr 24, 2001
Published online: Jan 1, 2002
Published in print: Jan 2002
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