APOGEE: Global optimization of standard, generalized, and extended pooling problems via linear and logarithmic partitioning schemes. Our recent work globally optimized two classes of large-scale pooling problems: a generalized pooling problem treating the network topology as a decision variable and an extended pooling problem incorporating environmental regulations into constraints. The pooling problems were optimized using a piecewise linear scheme that activates appropriate under- and overestimators with a number of binary decision variables that scales linearly with the number of segments in the piecewise relaxation. Inspired by recent work 0400 and 0390, we introduce a formulation for the piecewise linear relaxation of bilinear functions with a logarithmic number of binary variables and computationally compare the performance of this new formulation to the best-performing piecewise relaxations with a linear number of binary variables. We have unified our work by developing APOGEE, a computational tool that globally optimizes standard, generalized, and extended pooling problems. APOGEE is freely available to the scientific community at helios.princeton.edu/APOGEE/.

References in zbMATH (referenced in 24 articles )

Showing results 1 to 20 of 24.
Sorted by year (citations)

1 2 next

  1. Baltean-Lugojan, Radu; Misener, Ruth: Piecewise parametric structure in the pooling problem: from sparse strongly-polynomial solutions to NP-hardness (2018)
  2. Castillo Castillo, Pedro A.; Castro, Pedro M.; Mahalec, Vladimir: Global optimization of MIQCPs with dynamic piecewise relaxations (2018)
  3. Marandi, Ahmadreza; Dahl, Joachim; de Klerk, Etienne: A numerical evaluation of the bounded degree sum-of-squares hierarchy of Lasserre, Toh, and Yang on the pooling problem (2018)
  4. Gupte, Akshay; Ahmed, Shabbir; Dey, Santanu S.; Cheon, Myun Seok: Relaxations and discretizations for the pooling problem (2017)
  5. Li, Xiang; Tomasgard, Asgeir; Barton, Paul I.: Natural gas production network infrastructure development under uncertainty (2017)
  6. Boland, Natashia; Kalinowski, Thomas; Rigterink, Fabian: New multi-commodity flow formulations for the pooling problem (2016)
  7. Boukouvala, Fani; Misener, Ruth; Floudas, Christodoulos A.: Global optimization advances in mixed-integer nonlinear programming, MINLP, and constrained derivative-free optimization, CDFO (2016)
  8. Castro, Pedro M.: Normalized multiparametric disaggregation: an efficient relaxation for mixed-integer bilinear problems (2016)
  9. Chan, Alice Z.-Y.; Copenhaver, Martin S.; Narayan, Sivaram K.; Stokols, Logan; Theobold, Allison: On structural decompositions of finite frames (2016)
  10. Greco, Salvatore (ed.); Ehrgott, Matthias (ed.); Figueira, José Rui (ed.): Multiple criteria decision analysis. State of the art surveys. In 2 volumes (2016)
  11. Grimstad, Bjarne; Sandnes, Anders: Global optimization with spline constraints: a new branch-and-bound method based on B-splines (2016)
  12. Haugland, Dag: The computational complexity of the pooling problem (2016)
  13. Haugland, Dag; Hendrix, Eligius M. T.: Pooling problems with polynomial-time algorithms (2016)
  14. Hellemo, Lars; Tomasgard, Asgeir: A generalized global optimization formulation of the pooling problem with processing facilities and composite quality constraints (2016)
  15. Dey, Santanu S.; Gupte, Akshay: Analysis of MILP techniques for the pooling problem (2015)
  16. Tseng, Chung-Li; Zhan, Yiduo; Zheng, Qipeng P.; Kumar, Manish: A MILP formulation for generalized geometric programming using piecewise-linear approximations (2015)
  17. Castro, Pedro M.; Grossmann, Ignacio E.: Optimality-based bound contraction with multiparametric disaggregation for the global optimization of mixed-integer bilinear problems (2014)
  18. Misener, Ruth; Floudas, Christodoulos A.: ANTIGONE: algorithms for coNTinuous/Integer global optimization of nonlinear equations (2014)
  19. Kolodziej, Scott; Castro, Pedro M.; Grossmann, Ignacio E.: Global optimization of bilinear programs with a multiparametric disaggregation technique (2013)
  20. Misener, Ruth; Floudas, Christodoulos A.: GLOMIQO: global mixed-integer quadratic optimizer (2013)

1 2 next

Further publications can be found at: http://helios.princeton.edu/APOGEE/publications.html