The Gas Transmission Problem Solved by an Extension of the Simplex Algorithm

  title={The Gas Transmission Problem Solved by an Extension of the Simplex Algorithm},
  author={Daniel De Wolf and Yves Smeers},
  journal={Management Science},
The problem of distributing gas through a network of pipelines is formulated as a cost minimization subject to nonlinear flow-pressure relations, material balances, and pressure bounds. The solution method is based on piecewise linear approximations of the nonlinear flow-pressure relations. The approximated problem is solved by an extension of the Simplex method. The solution method is tested on real-world data and compared with alternative solution methods. 

Solving the gas transmission problem with consideration of the compressors

Resume In [7], De Wolf and Smeers consider the problem of the gas distribution through a network of pipelines. The problem was formulated as a cost minimization subject to nonlinear flow-pressure

Mathematical properties of formulations of the gas transmission problem

The paper presents the mathematical properties of several formulations for the gas transmission problem that account for the nonlinear flow pressure relations. The form of the nonlinear flow pressure

Nonlinear Optimization in Gas Networks

An optimization model focusing on the governing PDE and other nonlinear aspects is presented together with a suitable discretization for transient optimization in large networks by SQP methods, demonstrating the viability of the approach.

A mixed integer approach for time-dependent gas network optimization

A branch-and-cut algorithm is developed which has the potential to guarantee global optimality of the linearized problem where the nonlinearities are approximated within a given accuracy.

Mixed Integer Models for the Stationary Case of Gas Network Optimization

This work describes techniques for a piece-wise linear approximation of the nonlinearities in this model resulting in a large mixed integer linear program and shows that the number of vertices is computationally tractable yielding exact separation algorithms.

A simulated annealing algorithm for transient optimization in gas networks

A simulated annealing approach for the gas network optimization problem where time steps as well as pressure and flow of the gas are decoupled and a suitable neighborhood structure is developed for the relaxed problem.

Design and Operations of Gas Transmission Networks

A minimum energy principle is used to define stationary flows in the network and the minimization process is extended to the choice of suitable diameters on the reinforcing arcs and add a constraint that limits the monetary cost of investment and of purchase and delivery of gas.

Gas Network Optimization: A comparison of Piecewise Linear Models

This paper compares theoretically and computationally basic and advanced MILP formulations for the gas network optimization in dynamic or in steady-state conditions and proposes a goal programming method to construct a-priori the piecewise linear functions.

A Mathematical Programming Model for Allocation of Natural Gas

This paper presents a methodology for the allocation of natural gas that consists of several objective functions, a set of linear constraints, and aSet of nonlinear constraints that represent the momentum balance necessary for each pipe segment, compressor, or valve.

Optimal Dimensioning of Pipe Networks with Application to Gas Transmission Networks

We develop an algorithm to solve the problem of the optimal dimensioning of a fluid gas or water transmission network when the topology of the network is known. The pipe diameters must be chosen to

Computational aspects of two-segment separable programming

Recursive separable programming algorithms based on local, two-segment approximations are described for the solution of separable convex programs and computational comparisons are provided for a variety of test problems.

A simplex algorithm for piecewise-linear programming III: Computational analysis and applications

The piecewise-linear simplex algorithm is observed to run 2–6 times faster than a comparable linear algorithm, not including any additional expense that might be incurred in setting up the equivalent linear program.

Secant approximation methods for convex optimization

The methods discussed are based on local piecewise-linear secant approximations to continuous convex objective functions. Such approximations are easily constructed and require only function

A simplex algorithm for piecewise-linear programming II: Finiteness, feasibility and degeneracy

The simplex method for linear programming can be extended to permit the minimization of any convex separable piecewise-linear objective, subject to linear constraints, under convenient assumptions.

Solving Piecewise-Linear Programs: Experiments with a Simplex Approach

Tests of CPLP, a piecewise-linear simplex implementation based on the XMP subroutine library, show that it is typically 2 to 3 times faster than a comparable linear bounded-variable simplex code applied to equivalent linear programs.

A simplex algorithm for piecewise-linear programming I: Derivation and proof

A general, computationally practical simplex algorithm for piecewise-linear programming that derives and justifies the essential steps of the algorithm, by extension from the simplex method for linear programming in bounded variables.

An Improved Successive Linear Programming Algorithm

A convergence proof is given for PSLP-the first SLP convergence proof for nonlinearly constrained problems of general form, which is supported by computational performance-in the authors' tests, PSLP is significantly more robust than SLPR, and at least as efficient.

Nonlinear Optimization by Successive Linear Programming

A detailed description of an efficient, reliable SLP algorithm along with a convergence theorem for linearly constrained problems and extensive computational results show that SLP compares favorably with the Generalized Reduced Gradient Code GRG2 and with MINOS/GRG.