Designing Groundwater Supply Systems Using the Mesh Adaptive Basin Hopping Algorithm

  • Elisa Pappalardo
  • Giovanni StracquadanioEmail author


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.


Differential Evolution Unconfined Aquifer Installation Cost Simulator Call Objective Function Evaluation 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


  1. 1.
    Abramson, M.A., Audet, C.: Convergence of mesh adaptive direct search to second-order stationary points. SIAM J. Optim. 17(2), 606–619 (2006)CrossRefzbMATHMathSciNetGoogle Scholar
  2. 2.
    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)CrossRefzbMATHMathSciNetGoogle Scholar
  3. 3.
    Audet, C., Dennis, J.E., Jr.: Mesh adaptive direct search algorithms for constrained optimization. SIAM J. Optim. 17(1), 188–217 (2006)CrossRefzbMATHMathSciNetGoogle Scholar
  4. 4.
    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)Google Scholar
  5. 5.
    Bertsekas, D.: On the Goldstein-Levitin-Polyak gradient projection method. IEEE Trans. Autom. Control 21(2), 174–184 (2002)CrossRefMathSciNetGoogle Scholar
  6. 6.
    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)Google Scholar
  7. 7.
    Conn, A.R., Scheinberg, K., Vicente, L.N.: Introduction to Derivative-Free Optimization. Society for Industrial Mathematics, Philadelphia (2009)CrossRefzbMATHGoogle Scholar
  8. 8.
    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)CrossRefGoogle Scholar
  9. 9.
    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)CrossRefGoogle Scholar
  10. 10.
    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)CrossRefzbMATHMathSciNetGoogle Scholar
  11. 11.
    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)CrossRefGoogle Scholar
  12. 12.
    Gilmore, P., Kelley, C.T.: An implicit filtering algorithm for optimization of functions with many local minima. SIAM J. Optim. 5, 269 (1995)CrossRefzbMATHMathSciNetGoogle Scholar
  13. 13.
    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)CrossRefGoogle Scholar
  14. 14.
    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)Google Scholar
  15. 15.
    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)Google Scholar
  16. 16.
    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)CrossRefzbMATHMathSciNetGoogle Scholar
  17. 17.
    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)Google Scholar
  18. 18.
    Lewis, R.M., Torczon, V.: Pattern search algorithms for linearly constrained minimization. SIAM J. Optim. 10(3), 917–941 (2000)CrossRefzbMATHMathSciNetGoogle Scholar
  19. 19.
    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)Google Scholar
  20. 20.
    Price, K.V.: Differential evolution. In: Handbook of Optimization, pp. 187–214. Springer, New York (2013)Google Scholar
  21. 21.
    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)Google Scholar
  22. 22.
    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)Google Scholar
  23. 23.
    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)CrossRefzbMATHMathSciNetGoogle Scholar

Copyright information

© Springer Science+Business Media New York 2014

Authors and Affiliations

  1. 1.Department of Biomedical EngineeringJohns Hopkins UniversityBaltimoreUSA

Personalised recommendations