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Unit Commitment by Augmented Lagrangian Relaxation: Testing Two Decomposition Approaches

Author

Listed:
  • C. Beltran

    (Universitat Politècnica de Catalunya)

  • F. J. Heredia

    (Universitat Politècnica de Catalunya)

Abstract

One of the main drawbacks of the augmented Lagrangian relaxation method is that the quadratic term introduced by the augmented Lagrangian is not separable. We compare empirically and theoretically two methods designed to cope with the nonseparability of the Lagrangian function: the auxiliary problem principle method and the block coordinated descent method. Also, we use the so-called unit commitment problem to test both methods. The objective of the unit commitment problem is to optimize the electricity production and distribution, considering a short-term planning horizon.

Suggested Citation

  • C. Beltran & F. J. Heredia, 2002. "Unit Commitment by Augmented Lagrangian Relaxation: Testing Two Decomposition Approaches," Journal of Optimization Theory and Applications, Springer, vol. 112(2), pages 295-314, February.
    • Handle: RePEc:spr:joptap:v:112:y:2002:i:2:d:10.1023_a:1013601906224
    DOI: 10.1023/A:1013601906224
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    Cited by:

    1. Qu, Kaiping & Yu, Tao & Huang, Linni & Yang, Bo & Zhang, Xiaoshun, 2018. "Decentralized optimal multi-energy flow of large-scale integrated energy systems in a carbon trading market," Energy, Elsevier, vol. 149(C), pages 779-791.
    2. Wang, Jinwen & Guo, Min & Liu, Yong, 2018. "Hydropower unit commitment with nonlinearity decoupled from mixed integer nonlinear problem," Energy, Elsevier, vol. 150(C), pages 839-846.
    3. Wim Ackooij & Jérôme Malick, 2016. "Decomposition algorithm for large-scale two-stage unit-commitment," Annals of Operations Research, Springer, vol. 238(1), pages 587-613, March.
    4. G. Rius-Sorolla & J. Maheut & Jairo R. Coronado-Hernandez & J. P. Garcia-Sabater, 2020. "Lagrangian relaxation of the generic materials and operations planning model," Central European Journal of Operations Research, Springer;Slovak Society for Operations Research;Hungarian Operational Research Society;Czech Society for Operations Research;Österr. Gesellschaft für Operations Research (ÖGOR);Slovenian Society Informatika - Section for Operational Research;Croatian Operational Research Society, vol. 28(1), pages 105-123, March.
    5. Wim Ackooij, 2014. "Decomposition approaches for block-structured chance-constrained programs with application to hydro-thermal unit commitment," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 80(3), pages 227-253, December.
    6. Wim Ackooij, 2017. "A comparison of four approaches from stochastic programming for large-scale unit-commitment," EURO Journal on Computational Optimization, Springer;EURO - The Association of European Operational Research Societies, vol. 5(1), pages 119-147, March.
    7. Rong, Aiying & Lahdelma, Risto & Luh, Peter B., 2008. "Lagrangian relaxation based algorithm for trigeneration planning with storages," European Journal of Operational Research, Elsevier, vol. 188(1), pages 240-257, July.
    8. Wim Ackooij & Jérôme Malick, 2016. "Decomposition algorithm for large-scale two-stage unit-commitment," Annals of Operations Research, Springer, vol. 238(1), pages 587-613, March.
    9. Luan, Xiaojie & De Schutter, Bart & Meng, Lingyun & Corman, Francesco, 2020. "Decomposition and distributed optimization of real-time traffic management for large-scale railway networks," Transportation Research Part B: Methodological, Elsevier, vol. 141(C), pages 72-97.
    10. Iram Parvez & Jianjian Shen & Ishitaq Hassan & Nannan Zhang, 2021. "Generation of Hydro Energy by Using Data Mining Algorithm for Cascaded Hydropower Plant," Energies, MDPI, vol. 14(2), pages 1-28, January.

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