A reformulation-enumeration MINLP algorithm for gas network design
Gas networks are used to transport natural gas, which is an important resource for both residential and industrial customers throughout the world. The gas network design problem is generally modelled as a nonconvex mixed-integer nonlinear integer programming problem (MINLP). The challenges of solvin...
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| Published in | Journal of global optimization Vol. 90; no. 4; pp. 931 - 963 |
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| Main Authors | , , |
| Format | Journal Article |
| Language | English |
| Published |
New York
Springer US
01.12.2024
Springer Nature B.V |
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| Abstract | Gas networks are used to transport natural gas, which is an important resource for both residential and industrial customers throughout the world. The gas network design problem is generally modelled as a nonconvex mixed-integer nonlinear integer programming problem (MINLP). The challenges of solving the resulting MINLP arise due to the nonlinearity and nonconvexity. In this paper, we propose a framework to study the “design variant” of the problem in which the variables are the diameter choices of the pipes, the flows, the potentials, and the states of various network components. We utilize a nested loop that includes a two-stage procedure that involves a convex reformulation of the original problem in the inner loop and an efficient enumeration scheme in the outer loop. We conduct experiments on benchmark networks to validate and analyze the performance of our framework. |
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| AbstractList | Gas networks are used to transport natural gas, which is an important resource for both residential and industrial customers throughout the world. The gas network design problem is generally modelled as a nonconvex mixed-integer nonlinear integer programming problem (MINLP). The challenges of solving the resulting MINLP arise due to the nonlinearity and nonconvexity. In this paper, we propose a framework to study the “design variant” of the problem in which the variables are the diameter choices of the pipes, the flows, the potentials, and the states of various network components. We utilize a nested loop that includes a two-stage procedure that involves a convex reformulation of the original problem in the inner loop and an efficient enumeration scheme in the outer loop. We conduct experiments on benchmark networks to validate and analyze the performance of our framework. |
| Author | Sahinidis, Nikolaos V. Li, Yijiang Dey, Santanu S. |
| Author_xml | – sequence: 1 givenname: Yijiang surname: Li fullname: Li, Yijiang organization: School of Industrial and Systems Engineering, Georgia Institute of Technology – sequence: 2 givenname: Santanu S. orcidid: 0000-0003-0294-8287 surname: Dey fullname: Dey, Santanu S. email: santanu.dey@isye.gatech.edu organization: School of Industrial and Systems Engineering, Georgia Institute of Technology – sequence: 3 givenname: Nikolaos V. surname: Sahinidis fullname: Sahinidis, Nikolaos V. organization: School of Industrial and Systems Engineering, Georgia Institute of Technology, School of Chemical and Biomolecular Engineering, Georgia Institute of Technology |
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| Cites_doi | 10.1080/10556788.2018.1556661 10.1007/s10589-019-00085-x 10.1016/j.ejor.2016.01.008 10.1007/s10107-005-0581-8 10.1287/mnsc.24.7.747 10.1007/s11081-015-9300-3 10.1137/110827387 10.1287/mnsc.46.11.1454.12087 10.1137/S1052623493260696 10.1007/11841036_62 10.1016/j.apenergy.2015.03.017 10.1007/s00186-016-0533-5 10.1007/s10107-010-0360-z 10.1080/14786445108561362 10.1007/s11081-011-9141-7 10.1007/s10898-020-00974-0 10.1007/978-3-030-54621-2_873-1 10.1007/s12532-018-0138-5 10.3390/data2040040 10.1287/ijoc.2017.0780 10.1080/10556788.2014.888426 10.1287/opre.1110.1001 10.1287/opre.44.4.596 10.1137/1.9781611973693 10.1287/ijoc.2016.0697 10.1007/s10107-005-0594-3 10.1016/j.compchemeng.2015.07.005 10.1007/s12532-008-0001-1 10.1016/j.ejor.2014.12.039 |
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| Copyright_xml | – notice: The Author(s), under exclusive licence to Springer Science+Business Media, LLC, part of Springer Nature 2024. Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law. |
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| Keywords | Mixed-integer nonlinear program Global optimization Network design |
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| References_xml | – reference: Borraz-SanchezCBentRBackhausSHijaziHHentenryckPVConvex relaxations for gas expansion planningINFORMS J. Comput.201628645656355002710.1287/ijoc.2016.0697 – reference: ZhengQPRebennackSIliadisNAPardalosPPardalosPMRebennackSPereiraMVFIliadisNAOptimization Models in the Natural Gas IndustryHandbook of Power Systems I2010HeidebergySpringer – reference: GeiblerBMorsiAScheweLSchmidtMSolving highly detailed gas transport minlps: block separability and penalty alternating direction methodsINFORMS J. Comput.2018302309323381332010.1287/ijoc.2017.0780 – reference: CherryCSome general theorems for non-linear systems possessing reactancePhilos. Mag.1951427116111774436510.1080/14786445108561362 – reference: BragalliCD’AmbrosioCLeeJLodiATothPAzarYErlebachTAn minlp solution method for a water network problemAlgorithms - ESA 20062006Berlin, HeidelbergSpringer69670710.1007/11841036_62 – reference: Collins, M., Cooper, L., Helgason, R., Kennington, J., LeBlanc, L.: Solving the pipe network analysis problem using optimization techniques. Manag. Sci. 24(7), 747–760 (1977/78) – reference: LiersFMartinAMerkertMMertensNMichaelsDSolving mixed-integer nonlinear optimization problems using simultaneous convexification-a case study for gas networksJ. Glob. Optim.202180307340427019110.1007/s10898-020-00974-0 – reference: WolfDDSmeersYThe gas transmission problem solved by an extension of the simplex algorithmManag. Sci.200046111454146510.1287/mnsc.46.11.1454.12087 – reference: ShionoNSuzukiHOptimal pipe-sizing problem of tree-shaped gas distribution networksEur. J. Oper. Res.20162522550560346672010.1016/j.ejor.2016.01.008 – reference: EIA, U.S.: Natural Gas Explained. https://www.eia.gov/energyexplained/natural-gas/natural-gas-pipelines.php. Accessed 21 Apr 2022 (2021) – reference: KochTHillerBPfetschMEScheweLEvaluating Gas Network Capacities2015Philadelphia, PASociety for Industrial and Applied Mathematics10.1137/1.9781611973693 – reference: KhajaviradASahinidisNVA hybrid LP/NLP paradigm for global optimization relaxationsMath. Program. Comput.201810383421383497110.1007/s12532-018-0138-5 – reference: SchmidtMAssmannDBurlacuRHumpolaJJoormannIKanelakisNKochTOucherifDPfetschMEScheweLSchewarzRSirventMGaslib - a library of gas network instancesData2015244010.3390/data2040040 – reference: ApS, M.: The MOSEK Optimization Toolbox for Python Manual. Version 9.3.10. (2022) – reference: WolfDDSmeersYOptimal dimensioning of pipe networks with application to gas transmission networksOper. Res.199644459660810.1287/opre.44.4.596 – reference: Gurobi Optimization, L.: Gurobi Optimizer Reference Manual (2022) – reference: Humpola, J.: Gas Network Optimization by minlp. PhD Dissertation (2014) – reference: Sahinidis, N.V.: BARON 22.9.1: Global Optimization of Mixed-Integer Nonlinear Programs. User’s Manual (2022) – reference: FrangioniAGentileCPerspective cuts for a class of convex 0–1 mixed integer programsMath. Program.2006106225236220808210.1007/s10107-005-0594-3 – reference: Bragalli, C., D’Ambrosio, C., Lee, J., Lodi, A., Toth, P.: Water network design by minlp. IBM Res. Rep. RC24495 (W0802-056) (2008) – reference: BabonneauFNesterovYVialJ-PDesign and operations of gas transmission networksOper. Res.20126013447291165510.1287/opre.1110.1001 – reference: RoseDSchmidtMSteinbachMCWillertBMComputational optimization of gas compressor stations: Minlp models versus continuous reformulationsMath. Meth. Oper. 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| Snippet | Gas networks are used to transport natural gas, which is an important resource for both residential and industrial customers throughout the world. The gas... |
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| SubjectTerms | Algorithms Approximation Computer Science Construction costs Decomposition Enumeration Experiments Integer programming Mathematics Mathematics and Statistics Mixed integer Natural gas Nested loops Network design Network management systems Nominations Nonlinearity Operations Research/Decision Theory Optimization Real Functions |
| Title | A reformulation-enumeration MINLP algorithm for gas network design |
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