| Affiliation: | 1. Department of Mathematics and Computer Science, Clarkson University, Potsdam, NY 13699-5815, USA;2. School of Computational Sciences, Dirac Science Library, Florida State University, Tallahassee, FL 32306-4120, USA;3. US Army Engineer Research and Development Station, ATTN: CEERD-HF-HG, 3909 Halls Ferry Road, Vicksburg, MS 39180-6133, USA;4. The Boeing Company, P.O. Box 24346, MS 7L 21, Seattle, WA 98124-0346, USA;5. Department of Mathematics, North Carolina State University, Raleigh, NC 27695-8205, USA;6. Department of Environmental Sciences and Engineering, University of North Carolina, Chapel Hill, NC 27599-7400, USA;g Ecole Polytechnique de Montréal – GERAD, C.P. 6079, Succ. Centre-ville, Montréal, Québec, Canada H3C 3A7;h MIT Lincoln Laboratory, 244 Wood Street, Lexington, MA 02420-9108, USA;i Sandia National Laboratories, Livermore, CA 94551-9159, USA |
| Abstract: | Management decisions involving groundwater supply and remediation often rely on optimization techniques to determine an effective strategy. We introduce several derivative-free sampling methods for solving constrained optimization problems that have not yet been considered in this field, and we include a genetic algorithm for completeness. Two well-documented community problems are used for illustration purposes: a groundwater supply problem and a hydraulic capture problem. The community problems were found to be challenging applications due to the objective functions being nonsmooth, nonlinear, and having many local minima. Because the results were found to be sensitive to initial iterates for some methods, guidance is provided in selecting initial iterates for these problems that improve the likelihood of achieving significant reductions in the objective function to be minimized. In addition, we suggest some potentially fruitful areas for future research. |
