Abstract
Designing groundwater systems is a challenging problem in industrial engineering, where pumping wells have to be located in an optimal location to minimize the cost of installation and maintenance. Groundwater flows are studied using simulators, which makes difficult to standard optimization methods to find satisfactory results, since approximating the gradient is not accurate and computationally expensive. We tackle the problem using the Mesh Adaptive Basin Hopping approach, which combines a heuristic search step with a derivative-free local optimizer. We apply our method to two design problems in the ground-water supply field; the method is able to outperform the state-of-the-art algorithms, providing better solutions with a tight budget of objective function evaluations.
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References
Abramson, M.A., Audet, C.: Convergence of mesh adaptive direct search to second-order stationary points. SIAM J. Optim. 17(2), 606–619 (2006)
Abramson, M.A., Audet, C., Dennis, J.E., Jr., Le Digabel, S.: Orthomads: a deterministic mads instance with orthogonal directions. SIAM J. Optim. 20(2), 948–966 (2009)
Audet, C., Dennis, J.E., Jr.: Mesh adaptive direct search algorithms for constrained optimization. SIAM J. Optim. 17(1), 188–217 (2006)
Auger, A., Hansen, N.: A restart cma evolution strategy with increasing population size. In: Proceedings of the IEEE Congress on Evolutionary Computation, 2005, vol. 2, pp. 1769–1776. IEEE, Piscataway (2005)
Bertsekas, D.: On the Goldstein-Levitin-Polyak gradient projection method. IEEE Trans. Autom. Control 21(2), 174–184 (2002)
Choi, T.D., Eslinger, O.J., Gilmore, P., Patrick, A., Kelley, C.T., Gablonsky, J.M.: IFFCO: implicit filtering for constrained optimization, version 2. Technical Report, Center for Research in Scientific Computation, North Carolina State University, Raleigh (1999)
Conn, A.R., Scheinberg, K., Vicente, L.N.: Introduction to Derivative-Free Optimization. Society for Industrial Mathematics, Philadelphia (2009)
Deb, K., Pratap, A., Agarwal, S., Meyarivan, T.: A fast and elitist multiobjective genetic algorithm: NSGA-II. IEEE Trans. Evol. Comput. 6(2), 182–197 (2002)
Fowler, K.R., Kelley, C.T., Kees, C.E., Miller, C.T.: A hydraulic capture application for optimal remediation design. Dev. Water Sci. 55, 1149–1157 (2004)
Fowler, K.R., Kelley, C.T., Miller, C.T., Kees, C.E., Darwin, R.W., Reese, J.P., Farthing, M.W., Reed, M.S.C.: Solution of a well-field design problem with implicit filtering. Optim. Eng. 5(2), 207–234 (2004)
Fowler, K.R., Reese, J.P., Kees, C.E., Dennis, J.E., Jr., Kelley, C.T., Miller, C.T., Audet, C., Booker, A.J., Couture, G., Darwin, R.W.: Comparison of derivative-free optimization methods for groundwater supply and hydraulic capture community problems. Adv. Water Resour. 31(5), 743–757 (2008)
Gilmore, P., Kelley, C.T.: An implicit filtering algorithm for optimization of functions with many local minima. SIAM J. Optim. 5, 269 (1995)
Hansen, N., Müller, S.D., Koumoutsakos, P.: Reducing the time complexity of the derandomized evolution strategy with covariance matrix adaptation (cma-es). Evol. Comput. 11(1), 1–18 (2003)
Harbaugh, A.W., McDonald, M.G.: User’s documentation for MODFLOW-96, an update to the US Geological Survey modular finite-difference ground-water flow model. US Department of the Interior, US Geological Survey (1996)
Hemker, T., Fowler, K.R., von Stryk, O.: Derivative-free optimization methods for handling fixed costs in optimal groundwater remediation design. In: Proceedings of the CMWR XVI-Computational Methods in Water Resources, pp. 19–22. Citeseer (2006)
Hemker, T., Fowler, K.R., Farthing, M.W., von Stryk, O.: A mixed-integer simulation-based optimization approach with surrogate functions in water resources management. Optim. Eng. 9(4), 341–360 (2008)
Holland, J.H.: Adaptation in Natural and Artificial Systems: An Introductory Analysis with Applications to Biology, Control, and Artificial Intelligence. The MIT Press, Cambridge (1992)
Lewis, R.M., Torczon, V.: Pattern search algorithms for linearly constrained minimization. SIAM J. Optim. 10(3), 917–941 (2000)
Pardalos, P.M., Schoen, F.: Recent advances and trends in global optimization: deterministic and stochastic methods. In: Proceedings of the Sixth International Conference on Foundations of Computer-Aided Process Design (2004)
Price, K.V.: Differential evolution. In: Handbook of Optimization, pp. 187–214. Springer, New York (2013)
Storn, R., Price., K.: Differential evolution—a simple and efficient heuristic for global optimization over continuous spaces. J. Glob. Optim. 11(4), 341–359 (1997)
Stracquadanio, G., La Ferla, A., De Felice, M., Nicosia, G.: Design of robust space trajectories. In: Research and Development in Intelligent Systems XXVIII, pp. 341–354. Springer, New York (2011)
Stracquadanio, G., Pappalardo, E., Pardalos, P.M.: A mesh adaptive basin hopping method for the design of circular antenna arrays. J. Optim. Theory Appl. 155(3), 1008–1024 (2012)
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Pappalardo, E., Stracquadanio, G. (2014). Designing Groundwater Supply Systems Using the Mesh Adaptive Basin Hopping Algorithm. In: Rassias, T., Floudas, C., Butenko, S. (eds) Optimization in Science and Engineering. Springer, New York, NY. https://doi.org/10.1007/978-1-4939-0808-0_21
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DOI: https://doi.org/10.1007/978-1-4939-0808-0_21
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