@article{fowler_reese_kees_dennis_kelley_miller_audet_booker_couture_darwin_et al._2008, title={Comparison of derivative-free optimization methods for groundwater supply and hydraulic capture community problems}, volume={31}, ISSN={["1872-9657"]}, DOI={10.1016/j.advwatres.2008.01.010}, abstractNote={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.}, number={5}, journal={ADVANCES IN WATER RESOURCES}, author={Fowler, K. R. and Reese, J. P. and Kees, C. E. and Dennis, J. E., Jr. and Kelley, C. T. and Miller, C. T. and Audet, C. and Booker, A. J. and Couture, G. and Darwin, R. W. and et al.}, year={2008}, month={May}, pages={743–757} }
 @article{fowler_kelley_miller_kees_darwin_reese_farthing_reed_2004, title={Solution of a well-field design problem with implicit filtering}, volume={5}, ISSN={["1573-2924"]}, DOI={10.1023/B:OPTE.0000033375.33183.e7}, abstractNote={Problems involving the management of groundwater resources occur routinely, and management decisions based upon optimization approaches offer the potential to save substantial amounts of money. However, this class of application is notoriously difficult to solve due to non-convex objective functions with multiple local minima and both nonlinear models and nonlinear constraints. We solve a subset of community test problems from this application field using MODFLOW, a standard groundwater flow model, and IFFCO, an implicit filtering algorithm that was designed to solve problems similar to those of focus in this work. While sampling methods have received only scant attention in the groundwater optimization literature, we show encouraging results that suggest they are deserving of more widespread consideration for this class of problems. In keeping with our objectives for the community problems, we have packaged the approaches used in this work to facilitate additional work on these problems by others and the application of implicit filtering to other problems in this field. We provide the data for our formulation and solution on the web.}, number={2}, journal={OPTIMIZATION AND ENGINEERING}, author={Fowler, KR and Kelley, CT and Miller, CT and Kees, CE and Darwin, RW and Reese, JP and Farthing, MW and Reed, MSC}, year={2004}, month={Jun}, pages={207–234} }