APOGEE

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 16 articles )

Showing results 1 to 16 of 16.
Sorted by year (citations)

  1. Castro, Pedro M.: Normalized multiparametric disaggregation: an efficient relaxation for mixed-integer bilinear problems (2016)
  2. Chan, Alice Z.-Y.; Copenhaver, Martin S.; Narayan, Sivaram K.; Stokols, Logan; Theobold, Allison: On structural decompositions of finite frames (2016)
  3. Greco, Salvatore (ed.); Ehrgott, Matthias (ed.); Figueira, José Rui (ed.): Multiple criteria decision analysis. State of the art surveys. In 2 volumes (2016)
  4. Grimstad, Bjarne; Sandnes, Anders: Global optimization with spline constraints: a new branch-and-bound method based on B-splines (2016)
  5. Haugland, Dag: The computational complexity of the pooling problem (2016)
  6. Haugland, Dag; Hendrix, Eligius M.T.: Pooling problems with polynomial-time algorithms (2016)
  7. Hellemo, Lars; Tomasgard, Asgeir: A generalized global optimization formulation of the pooling problem with processing facilities and composite quality constraints (2016)
  8. Dey, Santanu S.; Gupte, Akshay: Analysis of MILP techniques for the pooling problem (2015)
  9. Castro, Pedro M.; Grossmann, Ignacio E.: Optimality-based bound contraction with multiparametric disaggregation for the global optimization of mixed-integer bilinear problems (2014)
  10. Misener, Ruth; Floudas, Christodoulos A.: ANTIGONE: algorithms for coNTinuous/Integer global optimization of nonlinear equations (2014)
  11. Kolodziej, Scott; Castro, Pedro M.; Grossmann, Ignacio E.: Global optimization of bilinear programs with a multiparametric disaggregation technique (2013)
  12. Misener, Ruth; Floudas, Christodoulos A.: GLOMIQO: global mixed-integer quadratic optimizer (2013)
  13. Wittmann-Hohlbein, Martina; Pistikopoulos, Efstratios N.: On the global solution of multi-parametric mixed integer linear programming problems (2013)
  14. Lin, Ming-Hua; Tsai, Jung-Fa; Yu, Chian-Son: A review of deterministic optimization methods in engineering and management (2012)
  15. Li, Xiang; Tomasgard, Asgeir; Barton, Paul I.: Decomposition strategy for the stochastic pooling problem (2012)
  16. Misener, Ruth; Floudas, Christodoulos A.: Global optimization of mixed-integer quadratically-constrained quadratic programs (MIQCQP) through piecewise-linear and edge-concave relaxations (2012)


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