Encapsulating the Role of Solution Response Space Roughness on Global Optimal Solution: Application in Identification of Unknown Groundwater Pollution Sources

Om Prakash^1,2*, Bithin Datta^1,2

¹Discipline of Civil and Environmental Engineering, School of Engineering and Physical Sciences, James Cook University, Townsville, Australia; CRC for Contamination Assessment and Remediation of the Environment, Mawson Lakes, Australia.
²Discipline of Civil and Environmental Engineering, School of Engineering and Physical Sciences, James Cook University, Townsville, Australia; CRC for Contamination Assessment and Remediation of the Environment, Mawson Lakes, Australia.

DOI: 10.4236/ojop.2014.33004                

Abstract

A major challenge of any optimization problem is to find the global optimum solution. In a multi-dimensional solution space which is highly non-linear, often the optimization algorithm gets trapped around some local optima. Optimal Identification of unknown groundwater pollution sources poses similar challenges. Optimization based methodology is often applied to identify the unknown source characteristics such as location and flux release history over time, in a polluted aquifer. Optimization based models for identification of these characteristics of unknown ground-water pollution sources rely on comparing the simulated effects of candidate solutions to the observed effects in terms of pollutant concentration at specified sparse spatiotemporal locations. The optimization model minimizes the difference between the observed pollutant concentration measurements and simulated pollutant concentration measurements. This essentially constitutes the objective function of the optimization model. However, the mathematical formulation of the objective function can significantly affect the accuracy of the results by altering the response contour of the solution space. In this study, two separate mathematical formulations of the objective function are compared for accuracy, by incorporating different scenarios of unknown groundwater pollution source identification problem. Simulated Annealing (SA) is used as the solution algorithm for the optimization model. Different mathematical formulations of the objective function for minimizing the difference between the observed and simulated pollutant concentration measurements show different levels of accuracy in source identification results. These evaluation results demonstrate the impact of objective function formulation on the optimal identification, and provide a basis for choosing an appropriate mathematical formulation for unknown pollution source identification in contaminated aquifers.

Keywords

Optimization, Optimal Solution Space, Inverse Problems, Simulated Annealing, Groundwater Pollution, Objective Function Formulation, Pollution Source Identification, Solution Space Roughness

Conflicts of Interest

The authors declare no conflicts of interest.

References

[1]	Mahar, P.S. and Datta, B. (2000) Identification of Pollution Sources in Transient Groundwater System. Water Resources Management, 14, 209-227. http://dx.doi.org/10.1023/A:1026527901213
[2]	Yeh, W.W.-G. (1986) Review of Parameter Identification Procedure in Groundwater Hydrology: The Inverse Problem. Water Resources Research, 22, 95-108. http://dx.doi.org/10.1029/WR022i002p00095
[3]	Gorelick, S.M., Evans, B. and Ramson, I. (1983) Identifying Sources of Groundwater Pollution: An Optimization Approach. Water Resources Research, 19, 779-790. http://dx.doi.org/10.1029/WR019i003p00779
[4]	Datta, B., Beegle, J.E., Kavvas, M.L. and Orlob, G.T. (1989) Development of an Expert-System Embedding Pattern-Recognition Techniques for Pollutionsource Identification. Technical Report: PB-90-185927/XAB, OSTI ID: 6855981. Department of Civil Engineering, California Uniersity, Davis.
[5]	Wagner, B.J. (1992) Simultaneous Parameter Estimation and Contaminant Source Characterization for Coupled Groundwater Flow and Contaminant Transport Modeling. Journal of Hydrology, 135, 275-303. http://dx.doi.org/10.1016/0022-1694(92)90092-A
[6]	Mahar, P.S. and Datta, B. (1997) Optimal Monitoring Network and Ground-Water Pollution Source Identification. Journal of Water Resources Planning and Management, 123, 199-207. http://dx.doi.org/10.1061/(ASCE)0733-9496(1997)123:4(199)
[7]	Mahar, P.S. and Datta, B. (2001) Optimal Identification of Ground-Water Pollution Sources and Parameter Estimation. Journal of Water Resources Planning and Management, 127, 20-29. http://dx.doi.org/10.1061/(ASCE)0733-9496(2001)127:1(20)
[8]	Aral, M.M., Guan, J. and Maslia, M.L. (2001) Identification of Contaminant Source Location and Release History in Aquifers. Journal of Hydrologic Engineering, 6, 225-234. http://dx.doi.org/10.1061/(ASCE)1084-0699(2001)6:3(225)
[9]	Mahinthakumar, G. and Sayeed, M. (2005) Hybrid Genetic Algorithm-Local Search Methods for Solving Groundwater Source Identification Inverse Problems. Journal of Water Resources Planning and Management, 131, 45-57. http://dx.doi.org/10.1061/(ASCE)0733-9496(2005)131:1(45)
[10]	Singh, R.M. and Datta, B. (2006) Identification of Groundwater Pollution Sources Using GA-Based Linked Simulation Optimization Model. Journal of Hydrologic Engineering, 11, 101-109. http://dx.doi.org/10.1061/(ASCE)1084-0699(2006)11:2(101)
[11]	Singh, R.M. and Datta, B. (2004) Groundwater Pollution Source Identification and Simultaneous Parameter Estimation Using Pattern Matching by Artificial Neural Network. Environmental Forensics, 5, 143-159. http://dx.doi.org/10.1080/15275920490495873
[12]	Singh, R.M. and Datta, B. (2007) Artificial Neural Network Modeling for Identification of Unknown Pollution Sources in Groundwater with Partially Missing Concentration Observation Data. Water Resources Management, 21, 557-572. http://dx.doi.org/10.1007/s11269-006-9029-z
[13]	Singh, R.M., Datta, B. and Jain, A. (2004) Identification of Unknown Groundwater Pollution Sources Using Artificial Neural Networks. Journal of Water Resources Planning and Management, 130, 506-514. http://dx.doi.org/10.1061/(ASCE)0733-9496(2004)130:6(506)
[14]	Sun, A.Y., Painter, S.L. and Wittmeyer, G.W. (2006) A Constrained Robust Least Squares Approach for Contaminant Source Release History Identification. Water Resources Research, 42, Published Online. http://dx.doi.org/10.1029/2005WR004312
[15]	Sun, A.Y., Painter, S.L. and Wittmeyer, G.W. (2006) A Robust Approach for Contaminant Source Location and Release History Recovery. Journal of Contaminant Hydrology, 88, 29-44.
[16]	Datta, B., Chakrabarty, D. and Dhar, A. (2009) Optimal Dynamic Monitoring Network Design and Identification of Unknown Groundwater Pollution Sources. Water Resources Management, 23, 2031-2049.
[17]	Datta, B., Chakrabarty, D. and Dhar, A. (2009) Simultaneous Identification of Unknown Groundwater Pollution Sources and Estimation of Aquifer Parameters. Journal of Hydrology, 376, 48-57.
[18]	Datta, B., Chakrabarty, D. and Dhar, A. (2011) Identification of Unknown Groundwater Pollution Sources Using Classical Optimization with Linked Simulation. Journal of Hydro-Environment Research, 5, 25-36. http://dx.doi.org/10.1016/j.jher.2010.08.004
[19]	Jha, M.K. and Datta, B. (2011) Simulated Annealing Based Simulation-Optimization Approach for Identification of Unknown Contaminant Sources in Groundwater Aquifers. Desalination and Water Treatment, 32, 79-85. http://dx.doi.org/10.5004/dwt.2011.2681
[20]	Datta, B., Prakash, O., Campbell, S. and Escalada, G. (2013) Efficient Identification of Unknown Groundwater Pollution Sources Using Linked Simulation-Optimization Incorporating Monitoring Location Impact Factor and Frequency Factor. Water Resources Management, 27, 4959-4976. http://dx.doi.org/10.1007/s11269-013-0451-8
[21]	Chadalavada, S., Datta, B. and Naidu, R. (2011) Optimisation Approach for Pollution Source Identification in Groundwater: An Overview. International Journal of Environment and Waste Management, 8, 40-61. http://dx.doi.org/10.1504/IJEWM.2011.040964
[22]	Amirabdollahian, M. and Datta, B. (2013) Identification of Contaminant Source Characteristics and Monitoring Network Design in Groundwater Aquifers: An Overview. Journal of Environmental Protection, 4, 26-41. http://dx.doi.org/10.4236/jep.2013.45A004
[23]	Harbaugh, A.W., Banta, E.R., Hill, M.C. and McDonald, M.G. (2000) MODFLOW-2000, the US Geological Survey Modular Ground-Water Model. US Geological Survey Open-File Report. 00-92, 121 p.
[24]	Rushton, K.R. and Redshaw, S.C. (1979) Seepage and Groundwater Flow. Wiley, New York.
[25]	Zheng, C. and Wang, P.P. (1999) MT3DMS, A Modular Three-Dimensional Multi-Species Transport Model for Simulation of Advection, Dispersion and Chemical Reactions of Contaminants in Groundwater Systems. US Army Engineer Research and Development Center Contract Report SERDP-99-1, Vicksburg, 202 p.
[26]	Domenico, P.A. and Schwartz, F.W. (1998) Physical and Chemical Hydrogeology. 2nd Edition, John Wiley & Sons, Inc., NewYork.
[27]	Kirkpatrick, S., Gelatt, D.C. and Vecchi, P.M. (1983) Optimization by Simulated Annealing. Science, 220, 671-680. http://dx.doi.org/10.1126/science.220.4598.671
[28]	Metropolis, N., Rosenbluth, A., Rosenbluth, M., Teller, A. and Teller, E. (1953) Equation of State Calculations by Fast Computing Machines. The Journal of Chemical Physics, 21, 1087-1092. http://dx.doi.org/10.1063/1.1699114
[29]	Goffe, W.L. (1996) SIMANN: A Global Optimization Algorithm Using Simulated Annealing. Studied in Nonlinear Dynamics and Econometrics, Berkeley Electronic Press, Berkeley.
[30]	Prakash, O. and Datta, B. (2013) Multiobjective Monitoring Network Design for Efficient Identification of Unknown Groundwater Pollution Sources Incorporating Genetic Programming Based Monitoring. Journal of Hydrologic Engineering, Published Online. http://dx.doi.org/10.1061/(ASCE)HE.1943-5584.0000952