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High-Performance Prototyping of Decomposition Methods in GAMS

Author

Listed:
  • Timo Lohmann

    (Uniper Global Commodities SE, 40221 Düsseldorf, Germany)

  • Michael R. Bussieck

    (GAMS Development Corp., Fairfax, Virginia 22031)

  • Lutz Westermann

    (GAMS Software GmbH, 38102 Braunschweig, Germany)

  • Steffen Rebennack

    (Karlsruhe Institute of Technology, Institute of Operations Research, 76131 Karlsruhe, Germany)

Abstract

Prototyping algorithms in algebraic modeling languages has a long tradition. Despite the convenient prototyping platform that modeling languages offer, they are typically seen as rather inefficient with regard to repeatedly solving mathematical programming problems, a concept on which many algorithms are based. The most prominent examples of such algorithms are decomposition methods, such as the Benders decomposition, column generation, and the Dantzig–Wolfe decomposition. In this work, we discuss the underlying reasons for repeated solve deficiency with regard to speed in detail and provide an insider’s look into the algebraic modeling language GAMS. Further, we present recently added features in GAMS that mitigate some of the efficiency drawbacks inherent to the way modeling languages represent model data and ultimately solve a model. In particular, we demonstrate the grid-enabled gather-update-solve-scatter facility and the GAMS object-oriented application programming interface on a large-scale case study that involves a Benders decomposition–type algorithm for a power-expansion planning problem.

Suggested Citation

  • Timo Lohmann & Michael R. Bussieck & Lutz Westermann & Steffen Rebennack, 2021. "High-Performance Prototyping of Decomposition Methods in GAMS," INFORMS Journal on Computing, INFORMS, vol. 33(1), pages 34-50, January.
    • Handle: RePEc:inm:orijoc:v:33:y:2021:i:1:p:34-50
    DOI: 10.1287/ijoc.2019.0905
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    References listed on IDEAS

    as
    1. Stephen Frank & Steffen Rebennack, 2016. "An introduction to optimal power flow: Theory, formulation, and examples," IISE Transactions, Taylor & Francis Journals, vol. 48(12), pages 1172-1197, December.
    2. Steeger, Gregory & Rebennack, Steffen, 2017. "Dynamic convexification within nested Benders decomposition using Lagrangian relaxation: An application to the strategic bidding problem," European Journal of Operational Research, Elsevier, vol. 257(2), pages 669-686.
    3. P. Massé & R. Gibrat, 1957. "Application of Linear Programming to Investments in the Electric Power Industry," Management Science, INFORMS, vol. 3(2), pages 149-166, January.
    4. Lohmann, Timo & Hering, Amanda S. & Rebennack, Steffen, 2016. "Spatio-temporal hydro forecasting of multireservoir inflows for hydro-thermal scheduling," European Journal of Operational Research, Elsevier, vol. 255(1), pages 243-258.
    5. Jeremy A. Bloom & Michael Caramanis & Leonid Charny, 1984. "Long-Range Generation Planning Using Generalized Benders' Decomposition: Implementation and Experience," Operations Research, INFORMS, vol. 32(2), pages 290-313, April.
    6. Jeremy A. Bloom, 1983. "Solving an Electricity Generating Capacity Expansion Planning Problem by Generalized Benders' Decomposition," Operations Research, INFORMS, vol. 31(1), pages 84-100, February.
    7. Timo Lohmann & Steffen Rebennack, 2017. "Tailored Benders Decomposition for a Long-Term Power Expansion Model with Short-Term Demand Response," Management Science, INFORMS, vol. 63(6), pages 2027-2048, June.
    8. Frederic H. Murphy & Yves Smeers, 2005. "Generation Capacity Expansion in Imperfectly Competitive Restructured Electricity Markets," Operations Research, INFORMS, vol. 53(4), pages 646-661, August.
    9. repec:aen:journl:2005v26-03-a05 is not listed on IDEAS
    10. Fell, Harrison & Linn, Joshua, 2013. "Renewable electricity policies, heterogeneity, and cost effectiveness," Journal of Environmental Economics and Management, Elsevier, vol. 66(3), pages 688-707.
    11. Bushnell, James, 2010. "Building blocks: investment in renewable and non-renewable technologies," ISU General Staff Papers 201005250700001113, Iowa State University, Department of Economics.
    12. Dennis Anderson, 1972. "Models for Determining Least-Cost Investments in Electricity Supply," Bell Journal of Economics, The RAND Corporation, vol. 3(1), pages 267-299, Spring.
    13. Michael R. Bussieck & Michael C. Ferris & Alexander Meeraus, 2009. "Grid-Enabled Optimization with GAMS," INFORMS Journal on Computing, INFORMS, vol. 21(3), pages 349-362, August.
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