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Nonlinear and Mixed Integer Linear Programming

  • Oliver Kolb
  • Antonio Morsi
  • Jens Lang
  • Alexander MartinEmail author
Part of the International Series of Numerical Mathematics book series (ISNM, volume 162)

Abstract

In this chapter we compare continuous nonlinear optimization with mixed integer optimization of water supply networks by means of a meso scaled network instance. We introduce a heuristic approach, which handles discrete decisions arising in water supply network optimization through penalization using nonlinear programming. We combine the continuous nonlinear and the mixed integer approach introduced in Chap. 3 to incorporate the solution quality. Finally, we show results for a real municipal water supply network.

Keywords

Penalty Function Mixed Integer Mixed Integer Linear Programming Filling Level Water Supply Network 
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.

References

  1. 1.
    J. Burgschweiger, B. Gnädig, M.C. Steinbach, Optimization models for operative planning in drinking water networks. Optim. Eng. 10(1), 43–73 (2009) MathSciNetCrossRefGoogle Scholar
  2. 2.
    R.H. Byrd, J. Nocedal, R.A. Waltz, Knitro: An integrated package for nonlinear optimization, in Large-Scale Nonlinear Optimization (2006), pp. 35–59 CrossRefGoogle Scholar
  3. 3.
    Gurobi Optimization, Inc. Gurobi Optimizer Version 4.0. Houston, Texas, USA, 2010. Information available at URL http://www.gurobi.com
  4. 4.
    O. Kolb, Simulation and Optimization of Gas and Water Supply Networks, PhD thesis, Technische Universität Darmstadt, 2011 Google Scholar
  5. 5.
    O. Kolb, P. Domschke, J. Lang, Moving penalty functions for optimal control with PDEs on networks, in Progress in Industrial Mathematics at ECMI 2008 (Springer, Berlin, 2010), pp. 925–931 CrossRefGoogle Scholar
  6. 6.
    P. Spellucci, A new technique for inconsistent QP problems in the SQP method. Math. Methods Oper. Res. 47(3), 355–400 (1998) MathSciNetzbMATHCrossRefGoogle Scholar
  7. 7.
    P. Spellucci, An SQP method for general nonlinear programs using only equality constrained subproblems. Math. Program. 82(3), 413–448 (1998) MathSciNetzbMATHCrossRefGoogle Scholar
  8. 8.
    A. Wächter, L.T. Biegler, On the implementation of a primal-dual interior point filter line search algorithm for large-scale nonlinear programming. Math. Program. 106(1), 25–57 (2006) MathSciNetzbMATHCrossRefGoogle Scholar

Copyright information

© Springer Basel 2012

Authors and Affiliations

  • Oliver Kolb
    • 1
  • Antonio Morsi
    • 2
  • Jens Lang
    • 1
  • Alexander Martin
    • 2
    Email author
  1. 1.Numerical Analysis and Scientific ComputingTechnische Universität DarmstadtDarmstadtGermany
  2. 2.Discrete Optimization (Lehrstuhl für Wirtschaftsmathematik)Friedrich-Alexander-Universität Erlangen-NürnbergErlangenGermany

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