Mixed Integer Models for the Stationary Case of Gas Network Optimization

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....

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Bibliographic Details
Published in:Mathematical programming Vol. 105; no. 2-3; pp. 563 - 582
Main Authors: Martin, Alexander, Möller, Markus, Moritz, Susanne
Format: Journal Article
Language:English
Published: Heidelberg Springer 01.02.2006
Springer Nature B.V
Subjects:
Algorithms
Applied mathematics
Applied sciences
Approximation
Compressors
Consumption
Energy consumption
Exact sciences and technology
Gas flow
Integer programming
Linear programming
Mathematical models
Mathematical problems
Mathematical programming
Network management systems
Operational research and scientific management
Operational research. Management science
Optimization
Partial differential equations
Studies
Variables
United States > US
Piece-wise linear functions
Branch and bound method
Gas optimization
Compressor
Linear programming
Mixed integer programming
Non linear programming
Pipe
Cutting plane method
SOS constraints
Stationary condition
Integer programming
Cutting planes
Gas flow
Linear approximation
Branch-and-Bound
Valve
Mathematical model
Piecewise linearization
ISSN:0025-5610, 1436-4646
Online Access:Get full text
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Summary: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. [PUBLICATION ABSTRACT]
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ISSN:0025-5610
1436-4646
DOI:10.1007/s10107-005-0665-5