Applying Dynamic Surrogate Models in Noisy Genetic Algorithms to Optimize Groundwater Remediation Designs
Publication: Journal of Water Resources Planning and Management
Volume 137, Issue 3
Abstract
Computational cost is a critical issue for large-scale water-resource optimization under uncertainty, since time-intensive Monte Carlo simulations are often required to evaluate over multiple parameter realizations. This paper presents an efficient approach for replacing most Monte Carlo simulations with surrogate models within a noisy genetic algorithm (GA). The surrogates are trained to predict the posterior expectations online on the basis of stochastic decision theory, using Monte Carlo simulation results created during the GA run. The surrogates, which in this application are neural networks, are adaptively updated to improve their prediction performance as the search progresses. A Latin hypercube sampling method is used to efficiently sample parameters for the Monte Carlo simulation, and the sampling results are archived so that the estimate of posterior expectation can be iteratively improved in an efficient manner. In addition, the GA is modified to incorporate hypothesis tests in its selection operator to account for sampling noise. The method is applied to a field-scale groundwater remediation design case study, whereas the primary source of uncertainty stems from hydraulic conductivity values in the aquifers. The results show that the method identified more reliable and cost-effective solutions with 86–90% less computational effort than the purely physically based noisy GA approach.
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Acknowledgments
The research was supported by the U.S. Army Research Office under Grant No.: USARODAAD19-001-1-0025. The writers would like to thank Dr. J. Wayland Eheart, Dr. Albert J. Valocchi, and Dr. Dan Roth for helpful comments and suggestions. The writers also thank National Center for Supercomputing Applications (NCSA) for the computational resources.
References
Aly, A. H., and Peralta, R. C. (1999). “Optimal design of aquifer cleanup systems under uncertainty using a neural network and a genetic algorithm.” Water Resour. Res., 35(8), 2523–2532.
Bau, D., and Mayer, A. S. (2006). “Stochastic management of pump-and-treat strategies using surrogate functions.” Adv. Water Resour., 29(12), 1901–1917.
Becker, D., et al. (2006). “Reducing long-term remedial costs by transport modeling optimization.” Ground Water, 44(6), 864–875.
Chan, N. (1993). “Robustness of the multiple realization method for stochastic hydraulic aquifer management.” Water Resour. Res., 29(9), 3159–3167.
Chan, N. (1994). “Partial infeasibility method for chance-constrained aquifer management.” J. Water Resour. Plann. Manage., 120(1), 70–89.
Chan Hilton, A. B., and Culver, T. B. (2005). “Groundwater remediation design under uncertainty using a robust genetic algorithm.” J. Water Resour. Plann. Manage., 131(1), 25–34.
Charnes, A., and Cooper, W. W. (1959). “Chance-constrained programming.” Manage. Sci., 6(1), 73–79.
Fitzpatrick, J. M., and Grefenstette, J. J. (1988). “Genetic algorithms in noisy environments.” Mach. Learn., 3(2–3), 101–120.
Gailey, R. M., and Gorelick, S. M. (1993). “Design of optimal, reliable plume capture schemes: Application to the Gloucester landfill ground-water contamination problem.” Ground Water, 31(1), 107–114.
Goldberg, D. E. (1989). Genetic algorithms in search, optimization and machine learning, Addison-Wesley, New York.
Gopalakrishnan, G., Minsker, B. S., and Goldberg, D. E. (2003). “Optimal sampling in a noisy genetic algorithm for risk-based remediation design.” J. Hydroinf., 5(1), 11–25.
Hastie, T., Tibshirani, R., and Friedman, J. H. (2001). The elements of statistical learning: Data mining, inference, and prediction, Springer, New York.
Hughes, E. J. (2001). “Evolutionary multi-objective ranking with uncertainty and noise.” Proc., 1st Int. Conf. Evolutionary Multi-Criterion Optimization, Zurich, Switzerland, 329–343.
Larsen, R. J., and Marx, M. L. (2001). An introduction to mathematical statistics and its applications, Prentice-Hall, Upper Saddle River, NJ.
McDonald, M. G., and Harbaugh, A. W. (1988). “A modular three-dimensional finite-difference ground-water flow model.” Techniques of Water Resources Investigations 06-A1, U.S. Geological Survey, Reston, VA.
McKay, D. M, Bechman, R. J., and Conover, W. J. (1979). “A comparison of three methods for selecting values of input variables in the analysis of output from a computer code.” Technometrics, 21(2), 239–245.
Miller, B. L., and Goldberg, D. E. (1996). “Optimal sampling for genetic algorithms, in intelligent engineering systems through artificial neural networks.” Smart engineering systems: Neural networks, fuzzy logic, and evolutionary programming, C. H. Dagli et al., eds., Vol. 6, American Society of Mechanical Engineering, New York, 291–297.
Minsker, B. S., et al. (2003). “Final technical report for application of flow and transport optimization codes to groundwater pump and treat systems, environmental security technology certification program (ESTCP).” 〈http://www.frtr.gov/estcp/〉.
Morgan, D. R., Eheart, J. W., and Valocchi, A. J. (1993). “Aquifer remediation design under uncertainty using a new chance constrained programming technique.” Water Resour. Res., 29(3), 551–562.
Neal, R. M. (1996). Bayesian learning for neural networks, Springer-Verlag, New York.
Pleming, J. B., and Manteufel, R. D. (2005). “Replicated Latin hypercube sampling.” 46th AIAA/ASME/ASCE/AHS/ASC Structures, Structural Dynamics and Materials Conf., Austin, TX.
Rogers, L. L., Dowla, F. U., and Johnson, V. M. (1995). “Optimal field-scale groundwater remediation using neural networks and the genetic algorithm.” Environ. Sci. Technol., 29(5), 1145–1155.
Sawyer, C. S., and Lin, Y. (1998). “Mixed-integer chance-constrained models for ground-water remediation.” J. Water Resour. Plann. Manage., 124(5), 285–294.
Singh, A. (2003). “Uncertainty based multi-objective optimization of groundwater remediation design.” M.S. thesis, Univ. of Illinois.
Singh, A., and Minsker, B. S. (2003). “Modeling and characterization of uncertainty for optimization of groundwater remediation at the Umatilla chemical depot.” Proc., ASCE Environmental & Water Resources Institute (EWRI) World Water & Environmental Resources Congress, Philadelphia.
Singh, A., and Minsker, B. S. (2008). “Uncertainty-based multiobjective optimization of groundwater remediation design.” Water Resour. Res., 44, W02404, .
Smalley, J. B., Minsker, B. S., and Goldberg, D. E. (2000). “Risk-based in situ bioremediation design using genetic algorithm.” Water Resour. Res., 36(10), 3043–3051.
Teich, J. (2001). “Pareto-front exploration with uncertain objectives.” Proc., 1st Int. Conf. Evolutionary Multi-Criterion Optimization, Zurich, Switzerland, 314–328.
Tiedeman, C., and Gorelick, S. M. (1993). “Analysis of uncertainty in optimal groundwater contaminant capture design.” Water Resour. Res., 29(7), 2139–2153.
U.S. Army Corps of Engineering (USACE). (1996). “Final remedial design submittal, contaminated groundwater remediation, explosives washout lagoons.” Umatilla Depot Activity, Hermiston, OR.
U.S. Army Corps of Engineering (USACE). (2000). Explosives washout lagoons groundwater model revision (preliminary draft), Umatilla Chemical Depot, Hermiston, OR.
Wagner, B. J., and Gorelick, S. M. (1987). “Optimal groundwater quality management under parameter uncertainty.” Water Resour. Res., 23(7), 1162–1174.
Wagner, B. J., and Gorelick, S. M. (1989). “Reliable aquifer remediation in the presence of spatially variable hydraulic conductivity: from data to design.” Water Resour. Res., 25(10), 2211–2225.
Yan, S. (2006). “Optimizing groundwater remediation designs using dynamic meta-models and genetic algorithms.” Ph.D. thesis, Univ. of Illinois, Urbana, IL.
Yan, S., and Minsker, B. S. (2006). “Optimal groundwater remediation design using an adaptive neural network genetic algorithm.” Water Resour. Res., 42(5), W05407.
Zheng, C., and Wang, P. P. (1999). MT3DMS: Documentation and user’s guide, Rep. to the U.S. Army Corps of Engineers Waterways Experiment Station, 〈http://hydro.geo.ua.edu〉.
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© 2011 American Society of Civil Engineers.
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Received: Jul 21, 2008
Accepted: May 13, 2010
Published online: Jun 25, 2010
Published in print: May 1, 2011
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