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A strategy to tighten the relaxation of bilinear terms towards petrochemical scheduling problem

Author

Listed:
  • Lifeng Zhang

    (Tsinghua University)

  • Congqin Ge

    (Tsinghua University)

  • Yanfeng Zhang

    (Sichuan University)

  • Wenhui Yang

    (Tsinghua University)

  • Bingzhen Chen

    (Tsinghua University)

  • Zhihong Yuan

    (Tsinghua University)

Abstract

This paper proposes a strategy to improve the relaxation of the normalized multiparametric disaggregation technique. By introducing additional partitions to continuous variables, a bivariate relaxation scheme, piece-wise normalized disaggregation technique (PNMDT) is developed. The proposed approach is first tested over numerical nonlinear programming examples. Based on such a strategy, a global optimization algorithm is then proposed to handle nonconvex optimization problems which involve plentiful bilinear terms. This proposed algorithm is evaluated through solving common scheduling problems in the petrochemical industry, the multi-period blending problem, and the multi-period crude oil scheduling problem. The computational results show that the proposed method can efficiently improve the quality of relaxation and speed up the convergence by reducing the required iterations within the algorithm procedure.

Suggested Citation

  • Lifeng Zhang & Congqin Ge & Yanfeng Zhang & Wenhui Yang & Bingzhen Chen & Zhihong Yuan, 2025. "A strategy to tighten the relaxation of bilinear terms towards petrochemical scheduling problem," Journal of Global Optimization, Springer, vol. 92(3), pages 809-835, July.
    • Handle: RePEc:spr:jglopt:v:92:y:2025:i:3:d:10.1007_s10898-025-01491-8
    DOI: 10.1007/s10898-025-01491-8
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    References listed on IDEAS

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    1. João Teles & Pedro Castro & Henrique Matos, 2013. "Multi-parametric disaggregation technique for global optimization of polynomial programming problems," Journal of Global Optimization, Springer, vol. 55(2), pages 227-251, February.
    2. Pedro Castro & Ignacio Grossmann, 2014. "Optimality-based bound contraction with multiparametric disaggregation for the global optimization of mixed-integer bilinear problems," Journal of Global Optimization, Springer, vol. 59(2), pages 277-306, July.
    3. Teles, João P. & Castro, Pedro M. & Matos, Henrique A., 2013. "Univariate parameterization for global optimization of mixed-integer polynomial problems," European Journal of Operational Research, Elsevier, vol. 229(3), pages 613-625.
    4. Tiago Andrade & Fabricio Oliveira & Silvio Hamacher & Andrew Eberhard, 2019. "Enhancing the normalized multiparametric disaggregation technique for mixed-integer quadratic programming," Journal of Global Optimization, Springer, vol. 73(4), pages 701-722, April.
    5. A. Tsoukalas & A. Mitsos, 2014. "Multivariate McCormick relaxations," Journal of Global Optimization, Springer, vol. 59(2), pages 633-662, July.
    6. Jaromił Najman & Dominik Bongartz & Alexander Mitsos, 2021. "Linearization of McCormick relaxations and hybridization with the auxiliary variable method," Journal of Global Optimization, Springer, vol. 80(4), pages 731-756, August.
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