Skip to main content
SpringerLink
Log in

Mixed Integer Models for the Stationary Case of Gas Network Optimization

  • Published:
Mathematical Programming Submit manuscript

Abstract

A gas network basically consists of a set of compressors and valves that are connected by pipes. The problem of gas network optimization deals with the question of how to optimize the flow of the gas and to use the compressors cost-efficiently such that all demands of the gas network are satisfied. This problem leads to a complex mixed integer nonlinear optimization problem. We describe techniques for a piece-wise linear approximation of the nonlinearities in this model resulting in a large mixed integer linear program. We study sub-polyhedra linking these piece-wise linear approximations and show that the number of vertices is computationally tractable yielding exact separation algorithms. Suitable branching strategies complementing the separation algorithms are also presented. Our computational results demonstrate the success of this approach.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Balas, E., Ceria, S., Cornuéjols, G.: A lift-and-project cutting plane algorithm for mixed 0-1 programs. Mathematical Programming 58, 295–324 (1993)

    MATH  MathSciNet  Google Scholar 

  2. Beale, E.M.L.: Branch and bound methods for mathematical programming systems. Annals of Discrete Mathematics 5, 201–219 (1979)

    MATH  MathSciNet  Google Scholar 

  3. Beale, E.M.L., Forrest, J.J.H.: Global optimization using special ordered sets. Mathematical Programming 10, 52–69 (1976)

    Article  MATH  MathSciNet  Google Scholar 

  4. Beale, E.L.M., Tomlin, J.A.: Special facilities in a general mathematical programming system for nonconvex problems using ordered sets of variables. In: Lawrence J. (ed) Proceedings of the fifth international conference on operations research. Tavistock Publications, London, 1970, pp 447–454

  5. Christof, T., Löbel, A.: PORTA: POlyhedron Representation Transformation Algorithm, Version 1.3. Konrad-Zuse-Zentrum für Informationstechnik Berlin, 2000

  6. Dantzig, G.B.: Linear programming and extensions. Princeton University Press, 1963

  7. de Farias, Jr., I.R., Johnson, E.L., Nemhauser, G.L.: A generalized assignment problem woth special ordered sets; a polyhedral approach. Mathematical Programming 89, 187–203 (2000)

    MATH  MathSciNet  Google Scholar 

  8. de Farias, Jr., I.R., Johnson, E.L., Nemhauser, G.L.: Branch-and-Cut for combinatorial optimization problems without auxiliary binary variables. The Knowledge Engineering Review 16, 25–39 (2001)

    MATH  Google Scholar 

  9. Ehrhardt, K., Steinbach, M.: Nonlinear optimization in gas networks. In: Bock, H.G., Kostina, E., Phu, H.X., Ranacher, R. (eds) Modeling simulation and optimization of complex processes. Berlin - Heidelberg - New York, Springer, pp 139-148, 2005

  10. Erdmann, B., Lang, J., Roitzsch, R.: KARDOS User's Guide. Technical Report ZR 02-42, Konrad-Zuse-Zentrum Berlin, 2002

  11. Gopal, V.N.: Techniques to optimize fuel and compressor combination selection. In: American Gas Association Transmission Conference, 1979

  12. ILOG CPLEX Division, 889 Alder Avenue, Suite 200, Incline Village, NV 89451, USA. Using the CPLEX Callable Library, 2002. Information available at http://www.cplex.com

  13. Jenicek, T.: Steady-state optimization of gas transport. In: Proceedings of the 2nd international workshop SIMONE on innovative approaches to modelling and optimal control of large scale pipeline networks, September 1993

  14. Hall, Jr. M.: Combinatorial theory. Blaisdell Publishing Co. Ginn and Co., Waltham, Mass.-Toronto, Ont.-London, 1967

  15. Keha, A.B., de Farias Jr. I.R., Nemhauser, G.L.: Models for representing piecewise linear cost functions. Operations Research Letters 32, 44–48 (2004)

    Article  MATH  MathSciNet  Google Scholar 

  16. Králik, J.: Compressor stations in SIMONE. In: Proceedings of the 2nd International Workshop SIMONE on Innovative Approaches to Modelling and Optimal Control of Large Scale Pipeline Networks, 1993

  17. Lee, J., Wilson, D.: Polyhedral methods for piecewise-linear functions I: the lambda method. Discrete Applied Mathematics 108, 269–285 (2001)

    Article  MATH  MathSciNet  Google Scholar 

  18. Markowitz, H.M., Manne, A.S.: On the solution of discrete programming problems. Econometrica 25, 84–110 (1957)

    MATH  MathSciNet  Google Scholar 

  19. Möller, M.: Mixed integer models for the optimisation of gas networks in the stationary case. PhD thesis, Darmstadt University of Technology, 2004

  20. Nemhauser, G.L., Wolsey, L.A.: Integer and combinatorial optimization. Wiley, 1988

  21. Padberg, M.: Approximating separable nonlinear functions via mixed zero-one programs. Operations Research Letters 27, 1–5 (2000)

    Article  MATH  MathSciNet  Google Scholar 

  22. Pratt, K.F., Wilson, J.G.: Optimization of operation of gas transmission systems. Transactions of the Institute of Measurement and Control 6(4), 261–269 (1984)

    Google Scholar 

  23. Carter, R.: Pipeline optimization: Dynamic programming after 30 years. In: Pipeline simulation interest group,URL:// www.psig.com, 1998

  24. Ruhrgas, A.G.: http://www.ruhrgas.com, 2003

  25. Schrijver, A.: Combinatorial optimization. polyhedra and efficiency (3 volumes). Springer, 2003

  26. Sekirnjak, E.: Mixed integer optimization for gas transmission and distribution systems. INFORMS Meeting, Seattle, October 1998, Lecture notes

  27. Sekirnjak, E.: Transiente technische optimierung (TTO-Prototyp). PSI Berlin, 1999. Technical Report

  28. Smeers, Y., De Wolf, D.: The gas transmission problem solved by an extension of the simplex algorithm. Management Science 46, 1454–1465 (2000)

    Google Scholar 

  29. Tomlin, J.A.: A suggested extension of special ordered sets to non-separable non-convex programming problems. Annals of Discrete Mathematics 11, 359–370 (1981)

    MATH  MathSciNet  Google Scholar 

  30. van Oostvoorn, F.: European gas market developments - oportunities and threats-. In: Supplement to the IAEE/GEE Conference ``Energy Markets What's New?'' pp 29–44, Berlin, 9-10 September 1998

  31. Vostrý, Z.: Transient optimization of gas transport and distribution. In: Proceedings of the 2nd International Workshop SIMONE on Innovative Approaches to Modelling and Optimal Control of Large Scale Pipeline Networks, 1993

  32. Williams, H.P.: Model building in mathematical programming. Wiley, 1990

  33. Wilson, D.: Polyhedral methods for piecewise-linear functions. PhD thesis, University of Kentucky 1998. Thesis only availabe via www.umi.com

  34. Wright, S., Somani, M., Ditzel, C.: Compressor station optimization. In: Pipeline Simulation Interest Group, Denver, Colorado, October 1998

  35. Jiří Záworka.: Project SIMONE - Achievements and running development. Institute of Information Theory and Automation, Czech Republik

  36. Zimmer, H.I.: Calculating optimum pipeline operations. American Gas Association Transmission Conference, 1975

Download references

Author information

Authors and Affiliations

  1. Darmstadt University of Technology, Germany

    Alexander Martin, Markus Möller & Susanne Moritz

Authors
  1. Alexander Martin
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Markus Möller
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Susanne Moritz
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Alexander Martin.

Additional information

Received: April, 2004

Rights and permissions

Reprints and permissions

About this article

Cite this article

Martin, A., Möller, M. & Moritz, S. Mixed Integer Models for the Stationary Case of Gas Network Optimization. Math. Program. 105, 563–582 (2006). https://doi.org/10.1007/s10107-005-0665-5

Download citation

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10107-005-0665-5

Keywords

Search

Navigation