On PDE Solution in Transient Optimization of Gas Networks

Please always quote using this URN: urn:nbn:de:0297-zib-8215
  • Operative planning in gas distribution networks leads to large-scale mixed-integer optimization problems involving a hyperbolic PDE defined on a graph. We consider the NLP obtained under prescribed combinatorial decisions---or as relaxation in a branch and bound framework, addressing in particular the KKT systems arising in primal-dual interior methods. We propose a custom solution algorithm using sparse local projections, based on the KKT systems' structual properties induced by the discretized gas flow equations in combination with the underlying network topology. The numerical efficiency and accuracy of the algorithm are investigated, and detailed computational comparisons with a control space method and with the multifrontal solver MA27 are provided.

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Metadaten
Author:Marc C. Steinbach
Document Type:ZIB-Report
Tag:Gas network; KKT system factorization; PDE constrained optimization; operative planning; sparse projection method
MSC-Classification:65-XX NUMERICAL ANALYSIS / 65Fxx Numerical linear algebra / 65F50 Sparse matrices
76-XX FLUID MECHANICS (For general continuum mechanics, see 74Axx, or other parts of 74-XX) / 76Dxx Incompressible viscous fluids / 76D55 Flow control and optimization [See also 49Q10, 93C20, 93C95]
90-XX OPERATIONS RESEARCH, MATHEMATICAL PROGRAMMING / 90Cxx Mathematical programming [See also 49Mxx, 65Kxx] / 90C30 Nonlinear programming
90-XX OPERATIONS RESEARCH, MATHEMATICAL PROGRAMMING / 90Cxx Mathematical programming [See also 49Mxx, 65Kxx] / 90C35 Programming involving graphs or networks [See also 90C27]
93-XX SYSTEMS THEORY; CONTROL (For optimal control, see 49-XX) / 93Cxx Control systems / 93C20 Systems governed by partial differential equations
Date of first Publication:2004/11/30
Series (Serial Number):ZIB-Report (04-46)
Published in:Appeared in: J. Comput. Appl. Math. 203 (2), 345-361, 2007