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Decomposition methods for multi-horizon stochastic programming

Author

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  • Hongyu Zhang

    (Norwegian University of Science and Technology)

  • Ignacio E. Grossmann

    (Carnegie Mellon University)

  • Asgeir Tomasgard

    (Norwegian University of Science and Technology)

Abstract

Multi-horizon stochastic programming includes short-term and long-term uncertainty in investment planning problems more efficiently than traditional multi-stage stochastic programming. In this paper, we exploit the block separable structure of multi-horizon stochastic linear programming, and establish that it can be decomposed by Benders decomposition and Lagrangean decomposition. In addition, we propose parallel Lagrangean decomposition with primal reduction that, (1) solves the scenario subproblems in parallel, (2) reduces the primal problem by keeping one copy for each scenario group at each stage, and (3) solves the reduced primal problem in parallel. We apply the parallel Lagrangean decomposition with primal reduction, Lagrangean decomposition and Benders decomposition to solve a stochastic energy system investment planning problem. The computational results show that: (a) the Lagrangean type decomposition algorithms have better convergence at the first iterations to Benders decomposition, and (b) parallel Lagrangean decomposition with primal reduction is very efficient for solving multi-horizon stochastic programming problems. Based on the computational results, the choice of algorithms for multi-horizon stochastic programming is discussed.

Suggested Citation

  • Hongyu Zhang & Ignacio E. Grossmann & Asgeir Tomasgard, 2024. "Decomposition methods for multi-horizon stochastic programming," Computational Management Science, Springer, vol. 21(1), pages 1-24, June.
    • Handle: RePEc:spr:comgts:v:21:y:2024:i:1:d:10.1007_s10287-024-00509-y
    DOI: 10.1007/s10287-024-00509-y
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    References listed on IDEAS

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    1. Laureano F. Escudero & Juan F. Monge, 2018. "On capacity expansion planning under strategic and operational uncertainties based on stochastic dominance risk averse management," Computational Management Science, Springer, vol. 15(3), pages 479-500, October.
    2. Francesca Maggioni & Elisabetta Allevi & Asgeir Tomasgard, 2020. "Bounds in multi-horizon stochastic programs," Annals of Operations Research, Springer, vol. 292(2), pages 605-625, September.
    3. Michal Kaut & Kjetil Midthun & Adrian Werner & Asgeir Tomasgard & Lars Hellemo & Marte Fodstad, 2014. "Multi-horizon stochastic programming," Computational Management Science, Springer, vol. 11(1), pages 179-193, January.
    4. John R. Birge, 1985. "Decomposition and Partitioning Methods for Multistage Stochastic Linear Programs," Operations Research, INFORMS, vol. 33(5), pages 989-1007, October.
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