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Solving pooling problems with time discretization by LP and SOCP relaxations and rescheduling methods

Author

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  • Masaki Kimizuka

    (Tokyo Institute of Technology)

  • Sunyoung Kim

    (Ewha W. University)

  • Makoto Yamashita

    (Tokyo Institute of Technology)

Abstract

The pooling problem is an important industrial problem in the class of network flow problems for allocating gas flow in pipeline transportation networks. For the pooling problem with time discretization, we propose second order cone programming (SOCP) and linear programming (LP) relaxations and prove that they obtain the same optimal value as the semidefinite programming relaxation. Moreover, a rescheduling method is proposed to efficiently refine the solution obtained by the SOCP or LP relaxation. The efficiency of the SOCP and the LP relaxation and the proposed rescheduling method is illustrated with numerical results on the test instances from the work of Nishi in 2010, some large instances and Foulds 3, 4 and 5 test problems.

Suggested Citation

  • Masaki Kimizuka & Sunyoung Kim & Makoto Yamashita, 2019. "Solving pooling problems with time discretization by LP and SOCP relaxations and rescheduling methods," Journal of Global Optimization, Springer, vol. 75(3), pages 631-654, November.
    • Handle: RePEc:spr:jglopt:v:75:y:2019:i:3:d:10.1007_s10898-019-00795-w
    DOI: 10.1007/s10898-019-00795-w
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    References listed on IDEAS

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    1. Mohammed Alfaki & Dag Haugland, 2013. "Strong formulations for the pooling problem," Journal of Global Optimization, Springer, vol. 56(3), pages 897-916, July.
    2. Akshay Gupte & Shabbir Ahmed & Santanu S. Dey & Myun Seok Cheon, 2017. "Relaxations and discretizations for the pooling problem," Journal of Global Optimization, Springer, vol. 67(3), pages 631-669, March.
    3. Ahmadreza Marandi & Joachim Dahl & Etienne Klerk, 2018. "A numerical evaluation of the bounded degree sum-of-squares hierarchy of Lasserre, Toh, and Yang on the pooling problem," Annals of Operations Research, Springer, vol. 265(1), pages 67-92, June.
    4. Arne Stolbjerg Drud, 1994. "CONOPT—A Large-Scale GRG Code," INFORMS Journal on Computing, INFORMS, vol. 6(2), pages 207-216, May.
    5. Makoto Yamashita & Katsuki Fujisawa & Mituhiro Fukuda & Kazuhiro Kobayashi & Kazuhide Nakata & Maho Nakata, 2012. "Latest Developments in the SDPA Family for Solving Large-Scale SDPs," International Series in Operations Research & Management Science, in: Miguel F. Anjos & Jean B. Lasserre (ed.), Handbook on Semidefinite, Conic and Polynomial Optimization, chapter 0, pages 687-713, Springer.
    6. Marandi, Ahmadreza & Dahl, Joachim & de Klerk, Etienne, 2018. "A numerical evaluation of the bounded degree sum-of-squares hierarchy of Lasserre, Toh, and Yang on the pooling problem," Other publications TiSEM 981f1428-4d42-4d3f-9a7a-7, Tilburg University, School of Economics and Management.
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    Cited by:

    1. Godai Azuma & Mituhiro Fukuda & Sunyoung Kim & Makoto Yamashita, 2023. "Exact SDP relaxations for quadratic programs with bipartite graph structures," Journal of Global Optimization, Springer, vol. 86(3), pages 671-691, July.
    2. Thai Doan Chuong & Xinghuo Yu & Andrew Eberhard & Chaojie Li & Chen Liu, 2024. "Hierarchy relaxations for robust equilibrium constrained polynomial problems and applications to electric vehicle charging scheduling," Journal of Global Optimization, Springer, vol. 90(3), pages 781-811, November.

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