DOE PAGES title logo U.S. Department of Energy
Office of Scientific and Technical Information

Title: Convex relaxations for gas expansion planning

Abstract

Expansion of natural gas networks is a critical process involving substantial capital expenditures with complex decision-support requirements. Here, given the non-convex nature of gas transmission constraints, global optimality and infeasibility guarantees can only be offered by global optimisation approaches. Unfortunately, state-of-the-art global optimisation solvers are unable to scale up to real-world size instances. In this study, we present a convex mixed-integer second-order cone relaxation for the gas expansion planning problem under steady-state conditions. The underlying model offers tight lower bounds with high computational efficiency. In addition, the optimal solution of the relaxation can often be used to derive high-quality solutions to the original problem, leading to provably tight optimality gaps and, in some cases, global optimal solutions. The convex relaxation is based on a few key ideas, including the introduction of flux direction variables, exact McCormick relaxations, on/off constraints, and integer cuts. Numerical experiments are conducted on the traditional Belgian gas network, as well as other real larger networks. The results demonstrate both the accuracy and computational speed of the relaxation and its ability to produce high-quality solution

Authors:
 [1];  [1];  [1];  [2];  [2]
  1. Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
  2. NICTA and ANU, Canberra (Australia)
Publication Date:
Research Org.:
Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
Sponsoring Org.:
USDOE
OSTI Identifier:
1296664
Report Number(s):
LA-UR-15-24636
Journal ID: ISSN 1091-9856
Grant/Contract Number:  
AC52-06NA25396
Resource Type:
Accepted Manuscript
Journal Name:
INFORMS Journal on Computing
Additional Journal Information:
Journal Volume: 28; Journal Issue: 4; Journal ID: ISSN 1091-9856
Publisher:
INFORMS
Country of Publication:
United States
Language:
English
Subject:
03 NATURAL GAS; Natural gas network; Expansion planning problem; MINLP problem; convex relaxations; Lower bound

Citation Formats

Borraz-Sanchez, Conrado, Bent, Russell Whitford, Backhaus, Scott N., Hijazi, Hassan, and Van Hentenryck, Pascal. Convex relaxations for gas expansion planning. United States: N. p., 2016. Web. doi:10.1287/ijoc.2016.0697.
Borraz-Sanchez, Conrado, Bent, Russell Whitford, Backhaus, Scott N., Hijazi, Hassan, & Van Hentenryck, Pascal. Convex relaxations for gas expansion planning. United States. https://doi.org/10.1287/ijoc.2016.0697
Borraz-Sanchez, Conrado, Bent, Russell Whitford, Backhaus, Scott N., Hijazi, Hassan, and Van Hentenryck, Pascal. Fri . "Convex relaxations for gas expansion planning". United States. https://doi.org/10.1287/ijoc.2016.0697. https://www.osti.gov/servlets/purl/1296664.
@article{osti_1296664,
title = {Convex relaxations for gas expansion planning},
author = {Borraz-Sanchez, Conrado and Bent, Russell Whitford and Backhaus, Scott N. and Hijazi, Hassan and Van Hentenryck, Pascal},
abstractNote = {Expansion of natural gas networks is a critical process involving substantial capital expenditures with complex decision-support requirements. Here, given the non-convex nature of gas transmission constraints, global optimality and infeasibility guarantees can only be offered by global optimisation approaches. Unfortunately, state-of-the-art global optimisation solvers are unable to scale up to real-world size instances. In this study, we present a convex mixed-integer second-order cone relaxation for the gas expansion planning problem under steady-state conditions. The underlying model offers tight lower bounds with high computational efficiency. In addition, the optimal solution of the relaxation can often be used to derive high-quality solutions to the original problem, leading to provably tight optimality gaps and, in some cases, global optimal solutions. The convex relaxation is based on a few key ideas, including the introduction of flux direction variables, exact McCormick relaxations, on/off constraints, and integer cuts. Numerical experiments are conducted on the traditional Belgian gas network, as well as other real larger networks. The results demonstrate both the accuracy and computational speed of the relaxation and its ability to produce high-quality solution},
doi = {10.1287/ijoc.2016.0697},
journal = {INFORMS Journal on Computing},
number = 4,
volume = 28,
place = {United States},
year = {2016},
month = {1}
}

Works referenced in this record:

SCIP: solving constraint integer programs
journal, January 2009


Optimization of capacity expansion planning for gas transportation networks
journal, September 2009

  • Andre, Jean; Bonnans, Frédéric; Cornibert, Laurent
  • European Journal of Operational Research, Vol. 197, Issue 3
  • DOI: 10.1016/j.ejor.2007.12.045

On capacitated network design cut?set polyhedra
journal, May 2002


Design and Operations of Gas Transmission Networks
journal, February 2012

  • Babonneau, Frédéric; Nesterov, Yurii; Vial, Jean-Philippe
  • Operations Research, Vol. 60, Issue 1
  • DOI: 10.1287/opre.1110.1001

Considerations about equations for steady state flow in natural gas pipelines
journal, January 2007

  • Coelho, Paulo M.; Pinho, Carlos
  • Journal of the Brazilian Society of Mechanical Sciences and Engineering, Vol. 29, Issue 3
  • DOI: 10.1590/S1678-58782007000300005

Security-Constrained Optimal Power and Natural-Gas Flow
journal, July 2014

  • Correa-Posada, Carlos M.; Sanchez-Martin, Pedro
  • IEEE Transactions on Power Systems, Vol. 29, Issue 4
  • DOI: 10.1109/TPWRS.2014.2299714

Optimal Dimensioning of Pipe Networks with Application to Gas Transmission Networks
journal, August 1996


The Gas Transmission Problem Solved by an Extension of the Simplex Algorithm
journal, November 2000


CONOPT—A Large-Scale GRG Code
journal, May 1994


Optimal Design of Gas Transmission Networks
journal, April 1978

  • Edgar, T. F.; Himmelblau, D. M.; Bickel, T. C.
  • Society of Petroleum Engineers Journal, Vol. 18, Issue 02
  • DOI: 10.2118/6034-PA

Optimal Design and Operation of Egyptian Gas-Transmission Pipelines
journal, July 2013

  • Elshiekh, T. M.; A. Khalil, S.; El Mawgoud, Hussien A.
  • Oil and Gas Facilities, Vol. 2, Issue 04
  • DOI: 10.2118/163087-PA

Optimization of pipe networks
journal, May 1991

  • Hansen, Claus Thorp; Madsen, Kaj; Nielsen, Hans Bruun
  • Mathematical Programming, Vol. 52, Issue 1-3
  • DOI: 10.1007/BF01582879

Mixed-integer nonlinear programs featuring “on/off” constraints
journal, August 2011

  • Hijazi, Hassan; Bonami, Pierre; Cornuéjols, Gérard
  • Computational Optimization and Applications, Vol. 52, Issue 2
  • DOI: 10.1007/s10589-011-9424-0

Convex reformulations for solving a nonlinear network design problem
journal, May 2015

  • Humpola, Jesco; Fügenschuh, Armin
  • Computational Optimization and Applications, Vol. 62, Issue 3
  • DOI: 10.1007/s10589-015-9756-2

Valid inequalities for the topology optimization problem in gas network design
journal, February 2015


A primal heuristic for optimizing the topology of gas networks based on dual information
journal, August 2014

  • Humpola, Jesco; Fügenschuh, Armin; Lehmann, Thomas
  • EURO Journal on Computational Optimization, Vol. 3, Issue 1
  • DOI: 10.1007/s13675-014-0029-0

Models for representing piecewise linear cost functions
journal, January 2004


On the Solution of Discrete Programming Problems
journal, January 1957

  • Markowitz, Harry M.; Manne, Alan S.
  • Econometrica, Vol. 25, Issue 1
  • DOI: 10.2307/1907744

Computability of global solutions to factorable nonconvex programs: Part I — Convex underestimating problems
journal, December 1976


A Mathematical Programming Model for Allocation of Natural Gas
journal, October 1979

  • O'Neill, Richard P.; Williard, Mark; Wilkins, Bert
  • Operations Research, Vol. 27, Issue 5
  • DOI: 10.1287/opre.27.5.857

Validation of nominations in gas network optimization: models, methods, and solutions
journal, March 2014

  • Pfetsch, Marc E.; Fügenschuh, Armin; Geißler, Björn
  • Optimization Methods and Software, Vol. 30, Issue 1
  • DOI: 10.1080/10556788.2014.888426

Optimization problems in natural gas transportation systems: A state-of-the-art review
journal, June 2015


The Solution of Large-Scale gas Pipeline Design Problems
journal, January 1982


Unsteady and transient flow of compressible fluids in pipelines—a review of theoretical and some experimental studies
journal, March 1987


Optimization for design and operation of natural gas transmission networks
journal, November 2014


On the implementation of an interior-point filter line-search algorithm for large-scale nonlinear programming
journal, April 2005


Model relaxations for the fuel cost minimization of steady-state gas pipeline networks
journal, January 2000


Works referencing / citing this record:

Optimizing natural gas pipeline transmission with nonuniform elevation: A new initialization approach
journal, September 2019

  • Xue, Mengying; Deng, Tianhu; Max Shen, Zuo‐Jun
  • Naval Research Logistics (NRL), Vol. 66, Issue 7
  • DOI: 10.1002/nav.21866

GasLib—A Library of Gas Network Instances
journal, December 2017

  • Schmidt, Martin; Aßmann, Denis; Burlacu, Robert
  • Data, Vol. 2, Issue 4
  • DOI: 10.3390/data2040040

A multilevel model of the European entry-exit gas market
journal, August 2018

  • Grimm, Veronika; Schewe, Lars; Schmidt, Martin
  • Mathematical Methods of Operations Research, Vol. 89, Issue 2
  • DOI: 10.1007/s00186-018-0647-z

A Multilevel Model of the European Entry-Exit Gas Market
journal, January 2017