Selecting the optimal design for a soil or groundwater remediation strategy is an enormous challenge for decisionmakers (DMs), due to the number of potential alternatives, the complexity of contaminated subsurface environments, and the need to weigh conflicting objectives such as risk and cost. Simulation/optimization models have been applied to remediation design, but current approaches do not allow for multi-objective optimization. The objective of this research project is to develop, apply, and test new algorithms to solve multi-objective groundwater remediation problems, with the goal of creating a new set of tools for DMs involved in groundwater remediation problems.
Development of an Algorithm for Assessing Tradeoffs Between Cost and Cleanup Performance. A multi-objective optimization algorithm is applied to a groundwater quality management problem involving remediation by pump-and-treat (PAT). The multi-objective optimization framework uses the niched Pareto genetic algorithm (NPGA) and is applied to simultaneously minimize the remedial design cost, and contaminant mass remaining at the end of the remediation horizon. Three test scenarios consider pumping rates for two, five, and fifteen fixed-location wells as the decision variables. A single objective genetic algorithm (SGA) formulation and a random search (RS) also are applied to the three scenarios to compare performances with NPGA. With 15 decision variables, the NPGA is demonstrated to outperform both the SGA algorithm and the RS by generating a better tradeoff curve. For example, for a given cost of $100,000, the NPGA solution found a design with 75 percent less mass remaining than the corresponding RS solution. In the 15-well scenario, the NPGA generated the full span of the Pareto optimal designs, but with 30 percent less computational effort than that required by the SGA. The RS failed to find any Pareto optimal solutions. The optimal population size for the NPGA was approximately 100, and the total computational cost was limited to 2,000 function evaluations. The NPGA was robust with respect to the other algorithm parameters (tournament size and niche radius) when using an optimal population size. The inclusion of niching produced better results in terms of covering the span of the tradeoff curve. As long as some niching was included, the results were insensitive to the value of the parameter controls niching (share > 0).
Incorporation of Uncertainty into Tradeoff Curves. An algorithm has been developed for finding optimal solutions for subsurface remediation design based on minimizing cost, maximizing cleanup performance, and maximizing reliability. The multi-objective optimization algorithm is based on the niched Pareto genetic algorithm. Uncertainty in hydraulic conductivity is determined by finding optimal designs for a series of equally likely hydraulic conductivity values. Reliability is measured by determining the number of designs that meet a cleanup objective for a given cost. The simplified approach taken in this work is to demonstrate the concept of finding tradeoff surfaces based on three conflicting objective functions. In the present work, we chose 100 Monte Carlo samplings. Our analysis of the results indicates that, in order to accurately resolve the reliability in the tails of a log normal distribution with a realistic variance, a considerably greater number of samples would be required. However, thousands of Monte Carlo samplings would present an enormous computational burden, especially for simulations with finer grid resolutions. Furthermore, simulations conducted for domains with spatially distributed hydraulic conductivities could require orders of magnitude and more grid blocks than the 104 used here, and thus even greater computational burdens. More sophisticated approaches to this stochastic optimization problem need to be developed and applied.
Simultaneous Optimization of Plume and Source Remediation. Subsurface remediation usually consists of targeting the source and dissolved plume cleanup separately. A typical approach in optimization is the complete removal of the source prior to plume remediation. However, it is important to recognize the tradeoff between the effort dedicated to source removal and to the cleanup of the groundwater plume emanating from the source. The optimal allocation of source remediation with conventional plume PAT is modeled with the use of multiple simulation processes linked within an optimization framework. The ultimate goal of this work is to provide guidelines for choosing the degree of effort and funds to dedicate to source removal versus plume remediation, based on the conditions at the site (e.g., aquifer heterogeneity, contaminant chemistry, cleanup goals, etc.). The simultaneous optimization of both plume and source technologies was feasible. The inclusion of the source remediation increases in importance as the heterogeneity of the system is increased. The inclusion of biodegradation rates are shown to have little effect on the overall optimization process at rates that would be found in most natural systems. The coupling of the source and plume remediation allows the study of the relationship between the two systems and increases in importance with the heterogeneity increases.
Critical Review of Optimization Methods and Development of Benchmark Problems for Subsurface Remediation. Estimation problems arise routinely in subsurface hydrology for applications that range from water resources management to water quality protection to subsurface restoration. Interest in optimal design of such systems has increased over the last two decades and this area is considered an important and active area of research. In this work, we review the state-of-the-art, assess important challenges that must be resolved to reach a mature level of understanding, and summarize some promising approaches that might help meet some of the challenges. While much has been accomplished to date, we conclude that more work remains before comprehensive, efficient, and robust solution methods are implemented to solve the most challenging applications in subsurface science. We suggest that future directions of research include the application of direct search solution methods, and developments in stochastic and multi-objective optimization. We present a set of comprehensive test problems for use in the research community as a means for benchmarking and comparing optimization approaches.
Pinder GF, Mayer A. Optimization and modeling for remediation and monitoring. In: Environmental Modeling for the Future. DuPont Company, Dover, DE, 2002, pp. 269-302.
Endres K, Mayer AS. Coupling contaminant source and plume optimization. Eos, Transactions of the American Geophysical Union 2001;83:765.
Erickson M, Mayer AS, Horn J. Multi-objective optimal design of groundwater remediation systems: application of the niched Pareto genetic algorithm (NPGA). Advances in Water Resources 2002;25:51-65.
Mayer AS, Kelley T, Miller CT. Optimal design for problems involving flow and transport phenomena in subsurface systems. Advances in Water Resources.
Mayer A, Horn J. Coupling contaminant source and plume optimization. Presented at the Fall Meeting of the American Geophysical Union, San Francisco, CA, December 2001.
Mayer A, Horn J. Designing subsurface remediation systems with mathematical optimization. Presented at the Workshop on Subsurface Flow and Transport Phenomena, Delft Technical University, The Netherlands, October 2000.
Mayer AS, Erickson ME. Development of a multi-objective optimization algorithm for assessing tradeoffs between cost, reliability, and cleanup goals for subsurface remediation. Presented at the 14th International Conference on Computational Methods in Water Resources (CMWR XIV), Delft, The Netherlands, June 23-28, 2002.
Mayer A, Horn J. Optimization of PAT systems by genetic algorithm incorporating a carbon pore diffusion simulator. Presented at the American Society of Civil Engineering Environmental and Water Resources Institute World Water and Environmental Resource Congress, Orlando, FL, May 2001.
Mayer A, Horn J. Optimization of source and plume remediation. Presented at the American Society of Civil Engineering Environmental and Water Resources Institute World Water and Environmental Resource Congress, Roanoke, VA, May 2002.
Mayer A, Horn J. The niched Pareto genetic algorithm 2 applied to the design of groundwater remediation systems. Presented at the 2nd Conference on Evolutionary Multi-Criteria Optimization, Zurich, Switzerland, March 2001.
Mayer A, Horn J. Using multi-objective optimization to construct tradeoff curves for subsurface remediation. Presented at the Society of Industrial and Applied Mathematics Geosciences Meeting, Boulder, CO, June 2001.
Mayer AS, Erickson ME. Development of a multi-objective optimization algorithm for assessing tradeoffs between cost, reliability, and cleanup goals for subsurface remediation. In: Hassanizadeh SM, Schotting RJ, eds. Proceedings of the 14th International Conference on Computational Methods in Water Resources (CMWR XIV), Elsevier Science, 2002, pp. 672-680.
Endres KL, Mayer A, Enfield C. Optimization of source and plume remediation. In: Proceedings of the American Society of Civil and Environmental Engineering and Water Resources Institute World Water and Environmental Resource Congress, American Society of Civil and Environmental Engineering, Washington, DC, 2002, pp. 423-433.
Supplemental Keywords: decisionmaking, environmental remediation, soil, groundwater, subsurface, simulation model, optimization model, pump-and-treat, PAT.