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Relaxations and discretizations for the pooling problem

Author

Listed:
  • Akshay Gupte

    (Clemson University)

  • Shabbir Ahmed

    (Georgia Institute of Technology)

  • Santanu S. Dey

    (Georgia Institute of Technology)

  • Myun Seok Cheon

    (ExxonMobil Research and Engineering Company)

Abstract

The pooling problem is a folklore NP-hard global optimization problem that finds applications in industries such as petrochemical refining, wastewater treatment and mining. This paper assimilates the vast literature on this problem that is dispersed over different areas and gives new insights on prevalent techniques. We also present new ideas for computing dual bounds on the global optimum by solving high-dimensional linear programs. Finally, we propose discretization methods for inner approximating the feasible region and obtaining good primal bounds. Valid inequalities are derived for the discretized models, which are formulated as mixed integer linear programs. The strength of our relaxations and usefulness of our discretizations is empirically validated on random test instances. We report best known primal bounds on some of the large-scale instances.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:jglopt:v:67:y:2017:i:3:d:10.1007_s10898-016-0434-4
    DOI: 10.1007/s10898-016-0434-4
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    References listed on IDEAS

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    1. Christodoulos A. Floudas & Avanish Aggarwal, 1990. "A Decomposition Strategy for Global Optimum Search in the Pooling Problem," INFORMS Journal on Computing, INFORMS, vol. 2(3), pages 225-235, August.
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    9. Santanu S. Dey & Akshay Gupte, 2015. "Analysis of MILP Techniques for the Pooling Problem," Operations Research, INFORMS, vol. 63(2), pages 412-427, April.
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    Cited by:

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    3. Djeumou Fomeni, Franklin, 2018. "A multi-objective optimization approach for the blending problem in the tea industry," International Journal of Production Economics, Elsevier, vol. 205(C), pages 179-192.
    4. Yifu Chen & Christos T. Maravelias, 2022. "Variable Bound Tightening and Valid Constraints for Multiperiod Blending," INFORMS Journal on Computing, INFORMS, vol. 34(4), pages 2073-2090, July.
    5. 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.
    6. Radu Baltean-Lugojan & Ruth Misener, 2018. "Piecewise parametric structure in the pooling problem: from sparse strongly-polynomial solutions to NP-hardness," Journal of Global Optimization, Springer, vol. 71(4), pages 655-690, August.
    7. Xin Cheng & Xiang Li, 2022. "Discretization and global optimization for mixed integer bilinear programming," Journal of Global Optimization, Springer, vol. 84(4), pages 843-867, December.
    8. 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.
    9. Benhamou, Latifa & Giard, Vincent & Khouloud, Mehdi & Fenies, Pierres & Fontane, Frédéric, 2020. "Reverse Blending: An economically efficient approach to the challenge of fertilizer mass customization," International Journal of Production Economics, Elsevier, vol. 226(C).
    10. 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.
    11. Santanu S. Dey & Burak Kocuk & Asteroide Santana, 2020. "Convexifications of rank-one-based substructures in QCQPs and applications to the pooling problem," Journal of Global Optimization, Springer, vol. 77(2), pages 227-272, June.
    12. Xiao Liu & Simge Küçükyavuz & Nilay Noyan, 2017. "Robust multicriteria risk-averse stochastic programming models," Annals of Operations Research, Springer, vol. 259(1), pages 259-294, December.

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