# A Comparison of Derivative-Free Optimization Methods for Groundwater Supply and Hydraulic Capture Community Problems

### 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.

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Citation
K. R. Fowler, J. P. Reese, C. E. Kees, J. E. Dennis, Jr., C. T. Kelley, C. T. Miller, C. Audet, A. J. Booker, G. Couture, R. W. Darwin, M. W. Farthing, D. E. Finkel, J. M. Gablonsky, G. Gray, T. G. Kolda. A Comparison of Derivative-Free Optimization Methods for Groundwater Supply and Hydraulic Capture Community Problems. Advances in Water Resources, Vol. 31, No. 5, pp. 743-757, 2008. https://doi.org/10.1016/j.advwatres.2008.01.010

### Keywords

Sampling methods, genetic algorithm, local minima, nondifferentiable objective function

### BibTeX

@article{FoReKeDe08,
author = {K. R. Fowler and J. P. Reese and C. E. Kees and J. E. {Dennis, Jr.} and C. T. Kelley and C. T. Miller and C. Audet and A. J. Booker and G. Couture and R. W. Darwin and M. W. Farthing and D. E. Finkel and J. M. Gablonsky and G. Gray and T. G. Kolda},
title = {A Comparison of Derivative-Free Optimization Methods for Groundwater Supply and Hydraulic Capture Community Problems},
journal = {Advances in Water Resources},
volume = {31},
number = {5},
pages = {743--757},
month = {May},
year = {2008},