Optimization and Engineering

, Volume 17, Issue 2, pp 437–472 | Cite as

High detail stationary optimization models for gas networks: validation and results

  • Martin Schmidt
  • Marc C. Steinbach
  • Bernhard M. Willert


Due to strict regulatory rules in combination with complex nonlinear physics, major gas network operators in Germany and Europe face hard planning problems that call for optimization. In part 1 of this paper we have developed a suitable model hierarchy for that purpose. Here we consider the more practical aspects of modeling. We validate individual model components against a trusted simulation tool, give a structural overview of the model hierarchy, and use its large variety of approximations to devise robust and efficient solution techniques. An extensive computational study demonstrates the suitability of our models and techniques for previously unsolvable problems in gas network planning.


Gas networks Stationary operation High-detail modeling Model validation Sequential NLP solving 

Mathematics Subject Classification

90B10 90C06 90C30 90C90 



This work has been supported by the German Federal Ministry of Economics and Technology owing to a decision of the German Bundestag. The responsibility for the content of this publication lies with the authors. This research has been performed as part of the Energie Campus Nürnberg and supported by funding through the “Aufbruch Bayern (Bavaria on the move)” initiative of the state of Bavaria. We would also like to thank our industry partner Open Grid Europe GmbH and the project partners in the ForNe consortium. Finally, we thank Björn Geißler and Antonio Morsi for many suggestions for improvement.


  1. Burgschweiger J, Gnädig B, Steinbach MC (2009) Nonlinear programming techniques for operative planning in large drinking water networks. Open Appl Math J 3:14–28MathSciNetCrossRefMATHGoogle Scholar
  2. Byrd RH, Nocedal J, Waltz RA (2006) KNITRO: an integrated package for nonlinear optimization. In: Di Pillo G, Roma M (eds) Large scale nonlinear optimization. Springer, New York, pp 35–59CrossRefGoogle Scholar
  3. Drud AS (1996) CONOPT: a system for large scale nonlinear optimization, reference manual for CONOPT subroutine library. Technical Report, ARKI Consulting and Development A/S, BagsvaerdGoogle Scholar
  4. Elad M (2010) Sparse and redundant representations: from theory to applications in signal and image processing. Springer, New YorkCrossRefMATHGoogle Scholar
  5. Fügenschuh A, Geißler B, Gollmer R, Hayn C, Henrion R, Hiller B, Humpola J, Koch T, Lehmann T, Martin A, Mirkov R, Morsi A, Rövekamp J, Schewe L, Schmidt M, Schultz R, Schwarz R, Schweiger J, Stangl C, Steinbach MC, Willert BM (2014) Mathematical optimization for challenging network planning problems in unbundled liberalized gas markets. Energy Syst 5:449–473CrossRefGoogle Scholar
  6. Gill PE, Murray W, Saunders MA (2002) SNOPT: an SQP algorithm for large-scale constrained optimization. SIAM J Optim 12:979–1006MathSciNetCrossRefMATHGoogle Scholar
  7. Humpola J, Joormann I, Oucherif D, Pfetsch ME, Schewe L, Schmidt M, Schwarz R (2015) GasLib—a library of gas network instances. http://www.optimization-online.org/DB_HTML/2015/11/5216.html
  8. Joormann I, Schmidt M, Steinbach MC, Willert BM (2015) What does “feasible” mean? In: Koch T, Hiller B, Pfetsch ME, Schewe L (eds) Evaluating gas network capacities, chapter 11., SIAM-MOS series on optimization, SIAM, Philadelphia, pp 211–232CrossRefGoogle Scholar
  9. Koch T, Hiller B, Pfetsch ME, Schewe L (eds) (2015) Evaluating gas network capacities, SIAM-MOS series, on optimization, SIAM, PhiladelphiaGoogle Scholar
  10. Králik J, Stiegler P, Vostrý Z, Záworka J (1988) Dynamic modeling of large-scale networks with application to gas distribution, vol 6., studies in automation and control. Elsevier Science Publishers, New YorkGoogle Scholar
  11. LaMaTTO++: a framework for modeling and solving mixed-integer nonlinear programming problems on networks (2015) http://www.mso.math.fau.de/edom/projects/lamatto.html
  12. LIWACOM Informations GmbH and SIMONE Research Group s.r.o. (2004) Gleichungen und Methoden, BenutzerhandbuchGoogle Scholar
  13. LIWACOM Informations GmbH and SIMONE Research Group s.r.o. (2009) SIMONE API Interface documentationGoogle Scholar
  14. Martin A, Geißler B, Hayn C, Hiller B, Humpola J, Koch T, Lehmann T, Morsi A, Pfetsch M, Schewe L, Schmidt M, Schultz R, Schwarz R, Schweiger J, Steinbach MC, Willert BM (2011) Optimierung Technischer Kapazitäten in Gasnetzen. In: Optimierung in der Energiewirtschaft, vol. 2157 of VDI-Berichte, pp 105–114Google Scholar
  15. Murtagh BA, Saunders MA (1993) Minos 5.4 user’s guide. Technical Report SOL 83-20R, Department of Operations Research, Stanford University, StanfordGoogle Scholar
  16. Pfetsch ME, Fügenschuh A, Geißler B, Geißler N, Gollmer R, Hiller B, Humpola J, Koch T, Lehmann T, Martin A, Morsi A, Rövekamp J, Schewe L, Schmidt M, Schultz R, Schwarz R, Schweiger J, Stangl C, Steinbach MC, Vigerske S, Willert BM (2015) Validation of nominations in gas network optimization: models, methods, and solutions. Optim Methods Softw 30:15–53MathSciNetCrossRefMATHGoogle Scholar
  17. Rosenthal RE (2008) GAMS—a user’s guide. GAMS Development CorporationGoogle Scholar
  18. Schmidt M, Steinbach MC, Willert BM (2014) High detail stationary optimization models for gas networks. Optim Eng 16:131–164MathSciNetCrossRefGoogle Scholar
  19. Wächter A, Biegler LT (2006) On the implementation of an interior-point filter line-search algorithm for large-scale nonlinear programming. Math Program 106:25–57MathSciNetCrossRefMATHGoogle Scholar
  20. Yin W, Zhang Y (2008) Extracting salient features from less data via \(\ell _1\)-minimization. SIAG/OPT Views-and-News 19:11–19MathSciNetGoogle Scholar
  21. Záworka J (1993) Project SIMONE—achievements and running development. In: Proceedings of 2nd international workshop SIMONE on innovative approaches to modeling and optimal control of large scale pipeline networks. Prague, pp 1–24Google Scholar

Copyright information

© Springer Science+Business Media New York 2015

Authors and Affiliations

  • Martin Schmidt
    • 1
    • 2
  • Marc C. Steinbach
    • 3
  • Bernhard M. Willert
    • 4
  1. 1.Department MathematikFriedrich-Alexander-Universität Erlangen-NürnbergErlangenGermany
  2. 2.Energie Campus NürnbergNurembergGermany
  3. 3.Institute for Applied MathematicsLeibniz Universiät HannoverHannoverGermany
  4. 4.RonnenbergGermany

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