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 21 articles )

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  1. Gupte, Akshay; Ahmed, Shabbir; Dey, Santanu S.; Cheon, Myun Seok: Relaxations and discretizations for the pooling problem (2017)
  2. Li, Xiang; Tomasgard, Asgeir; Barton, Paul I.: Natural gas production network infrastructure development under uncertainty (2017)
  3. Boland, Natashia; Kalinowski, Thomas; Rigterink, Fabian: New multi-commodity flow formulations for the pooling problem (2016)
  4. Boukouvala, Fani; Misener, Ruth; Floudas, Christodoulos A.: Global optimization advances in mixed-integer nonlinear programming, MINLP, and constrained derivative-free optimization, CDFO (2016)
  5. Castro, Pedro M.: Normalized multiparametric disaggregation: an efficient relaxation for mixed-integer bilinear problems (2016)
  6. Chan, Alice Z.-Y.; Copenhaver, Martin S.; Narayan, Sivaram K.; Stokols, Logan; Theobold, Allison: On structural decompositions of finite frames (2016)
  7. Greco, Salvatore (ed.); Ehrgott, Matthias (ed.); Figueira, José Rui (ed.): Multiple criteria decision analysis. State of the art surveys. In 2 volumes (2016)
  8. Grimstad, Bjarne; Sandnes, Anders: Global optimization with spline constraints: a new branch-and-bound method based on B-splines (2016)
  9. Haugland, Dag: The computational complexity of the pooling problem (2016)
  10. Haugland, Dag; Hendrix, Eligius M. T.: Pooling problems with polynomial-time algorithms (2016)
  11. Hellemo, Lars; Tomasgard, Asgeir: A generalized global optimization formulation of the pooling problem with processing facilities and composite quality constraints (2016)
  12. Dey, Santanu S.; Gupte, Akshay: Analysis of MILP techniques for the pooling problem (2015)
  13. Tseng, Chung-Li; Zhan, Yiduo; Zheng, Qipeng P.; Kumar, Manish: A MILP formulation for generalized geometric programming using piecewise-linear approximations (2015)
  14. Castro, Pedro M.; Grossmann, Ignacio E.: Optimality-based bound contraction with multiparametric disaggregation for the global optimization of mixed-integer bilinear problems (2014)
  15. Misener, Ruth; Floudas, Christodoulos A.: ANTIGONE: algorithms for coNTinuous/Integer global optimization of nonlinear equations (2014)
  16. Kolodziej, Scott; Castro, Pedro M.; Grossmann, Ignacio E.: Global optimization of bilinear programs with a multiparametric disaggregation technique (2013)
  17. Misener, Ruth; Floudas, Christodoulos A.: GLOMIQO: global mixed-integer quadratic optimizer (2013)
  18. Wittmann-Hohlbein, Martina; Pistikopoulos, Efstratios N.: On the global solution of multi-parametric mixed integer linear programming problems (2013)
  19. Lin, Ming-Hua; Tsai, Jung-Fa; Yu, Chian-Son: A review of deterministic optimization methods in engineering and management (2012)
  20. Li, Xiang; Tomasgard, Asgeir; Barton, Paul I.: Decomposition strategy for the stochastic pooling problem (2012)

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