[go: up one dir, main page]
More Web Proxy on the site http://driver.im/ Skip to main content
Log in

A simulated annealing algorithm for transient optimization in gas networks

  • Original Article
  • Published:
Mathematical Methods of Operations Research Aims and scope Submit manuscript

Abstract

In this paper we present a simulated annealing approach for the gas network optimization problem. A gas network consists of a set of pipes to transport the gas from the sources to the sinks whereby gas pressure gets lost due to friction. Further on there are compressors, which increase gas pressure, and valves. The aim is to minimize fuel gas consumption of the compressors whereas demands of consumers have to be satisfied. The problem of transient (time-dependent) optimization of gas networks results in a highly complex mixed integer nonlinear program. We relax the equations describing the gas dynamic in pipes by adding these constraints combined with appropriate penalty factors to the objective function. A suitable neighborhood structure is developed for the relaxed problem where time steps as well as pressure and flow of the gas are decoupled. Our approach convinces with flexibility and very good computational results.

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

Access this article

Subscribe and save

Springer+ Basic
£29.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or eBook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Price includes VAT (United Kingdom)

Instant access to the full article PDF.

Similar content being viewed by others

References

  • Aarts E, Korst J (1989) Simulated annealing and Boltzmann machines. A stochastic approach to combinatorial optimization and neural computing. Wiley, New York

    MATH  Google Scholar 

  • Aarts EHL, de Bont FMJ, Habers EHA, van Laarhoven PJ (1986) Parallel implementations of the statistical cooling algorithm. Integr VLSI J 4:209–238

    Article  Google Scholar 

  • Bohachevsky IO, Johnson ME, Stein ML (1986) Generalized simulated annealing for function optimization. Technometrics 28(3):209–217

    Article  MATH  Google Scholar 

  • Borraz-Sánchez C, Ríos-Mercado RZ (2005) A hybrid meta-heuristic approach for natural gas pipeline network optimization. In: Blesa MJ, Blum C, Roli A, Sampels M (eds) Hybrid Metaheuristics: Second International Workshop, HM 2005, Barcelona, Spain, August 29–30. Springer, Heidelberg, pp 54–65

  • Carter R (1998) Pipeline optimization: dynamic programming after 30 years. In: Pipeline Simultaion Interest Group, URL: http://www.psig.org

  • Černý V (1985) Thermodynamical approach to the traveling salesman problem: an efficient simulation algorithm. J Optim Theory Appl 45:41–51

    Article  MATH  MathSciNet  Google Scholar 

  • Corana A, Marchesi M, Martini C, Ridella S (1987) Minimizing multimodal functions of continuous variables with the “simulated annealing” algorithm. ACM Trans Math Softw 13:262–280

    Article  MATH  MathSciNet  Google Scholar 

  • Dekkers A, Aarts E (1991) Global optimization and simulated annealing. Math Program 50: 367–393

    Article  MATH  MathSciNet  Google Scholar 

  • Ehrhardt K, Steinbach M (2005) Nonlinear optimization in gas networks. In: Bock HG, Kostina E, Phu HX, Ranacher R (eds) Modeling, simulation and optimization of complex processes. Springer, Berlin, pp 139–148

    Chapter  Google Scholar 

  • Gopal VN (1979) Techniques to optimize fuel and compressor combination selection. In: American Gas Association Transmission Conference

  • Jenicek T (1993) 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

  • Kirkpatrick S, Gelatt CD Jr, Vecchi MP (1983) Optimization by simulated annealing. Science 220:671–680

    Article  MathSciNet  Google Scholar 

  • Králik J (1993) 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, September 1993

  • van Laarhoven PJM, Aarts EHL (1987) Simulated annealing: theory and applications. D. Reidel, Dordrecht

    MATH  Google Scholar 

  • Mahlke D (2005) Der Simulated Annealing Algorithmus zur transienten Optimierung von Gasnetzen. Master’s thesis, Technische Universität Darmstadt

  • Martin A, Möller M, Moritz S (2006) Mixed integer models for the stationary case of gas network optimization. Math Program 105:563–582

    Article  MATH  MathSciNet  Google Scholar 

  • Metropolis N, Rosenbluth AW, Rosenbluth MN, Teller AH, Teller E (1953) Equation of state calculations by fast computing machines. J Chem Phys 21(6):1087–1092

    Article  Google Scholar 

  • Michalewicz Z, Fogel DB (2000) How to solve it: modern heuristics. Springer, Heidelberg

    MATH  Google Scholar 

  • Miki M, Hiroyasu T, Fushimi T (2003) Parallel simulated annealing with adaptive neighborhood determined by GA. IEEE Int Conf Syst Man Cybern 1:26–31

    Google Scholar 

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

  • Moritz S (2007) A mixed integer approach for the transient case of gas network optimization PhD thesis, Darmstadt University of Technology (to appear)

  • Nemhauser GL, Wolsey LA (1988) Integer and combinatorial optimization. Wiley, New York

    MATH  Google Scholar 

  • Nolte A, Schrader R (2000) A note on the finite time behavior of simulated annealing. Math Oper Res 25(3):476–484

    Article  MATH  MathSciNet  Google Scholar 

  • Nowak MP, Westphalen M (2003) A linear model for transient gas flow. Technical Report STF38 S03601, SINTEF Industrial Management, Norway

  • Osman IH, Kelly JP (eds) (1996) Meta-heuristics: theory and applications. Kluwer, Dordrecht

    MATH  Google Scholar 

  • Pratt KF, Wilson JG (1984) Optimization of operation of gas transmission systems. Trans Inst Meas Control 6(4):261–269

    Article  Google Scholar 

  • Reeves CR (ed) (1993) Modern heuristic techniques for combinatorial problems. Halstead Press (Wiley), New York

    MATH  Google Scholar 

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

  • Sekirnjak E (1999) Transiente Technische Optimierung (TTO-Prototyp). PSI Berlin, 1999. Technical Report

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

    Article  Google Scholar 

  • Vostrý Z (1993) 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, September 1993

  • Wah BW, Chen YX (2000) Optimal anytime constrained simulated annealing for constrained global optimization. In: Proceedings Sixth International Conference on Principles and Practice of Constraint Programming, pp 425–440

  • Wah BW, Wang T (1999) Constrained simulated annealing with applications in nonlinear continuous constrained global optimization. In: Proceedings of the 11th IEEE International Conference on Tools with Artificial Intelligence, pp 381–388

  • Westphalen M (2004) Anwendungen der stochastischen Optimierung im Stromhandel und Gastransport. PhD thesis, Universität Duisburg-Essen

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

  • Záworka J (1993) Project SIMONE—Achievements and Running Development. Institute of Information Theory and Automation, Czech Republik

    Google Scholar 

  • Zimmer HI (1975) Calculating optimum pipeline operations. In: American Gas Association Transmission Conference

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Alexander Martin.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Mahlke, D., Martin, A. & Moritz, S. A simulated annealing algorithm for transient optimization in gas networks. Math Meth Oper Res 66, 99–115 (2007). https://doi.org/10.1007/s00186-006-0142-9

Download citation

  • Received:

  • Revised:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00186-006-0142-9

Keywords

Navigation