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 35 articles )

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  1. Sundar, Kaarthik; Nagarajan, Harsha; Linderoth, Jeff; Wang, Site; Bent, Russell: Piecewise polyhedral formulations for a multilinear term (2021)
  2. Chen, Yifu; Maravelias, Christos T.: Preprocessing algorithm and tightening constraints for multiperiod blend scheduling: cost minimization (2020)
  3. Dey, Santanu S.; Kocuk, Burak; Santana, Asteroide: Convexifications of rank-one-based substructures in QCQPs and applications to the pooling problem (2020)
  4. Luedtke, James; D’Ambrosio, Claudia; Linderoth, Jeff; Schweiger, Jonas: Strong convex nonlinear relaxations of the pooling problem (2020)
  5. Huchette, Joey; Vielma, Juan Pablo: A combinatorial approach for small and strong formulations of disjunctive constraints (2019)
  6. Koster, Arie M. C. A.; Kuhnke, Sascha: An adaptive discretization algorithm for the design of water usage and treatment networks (2019)
  7. Li, Can; Grossmann, Ignacio E.: A generalized Benders decomposition-based branch and cut algorithm for two-stage stochastic programs with nonconvex constraints and mixed-binary first and second stage variables (2019)
  8. Nagarajan, Harsha; Lu, Mowen; Wang, Site; Bent, Russell; Sundar, Kaarthik: An adaptive, multivariate partitioning algorithm for global optimization of nonconvex programs (2019)
  9. Baltean-Lugojan, Radu; Misener, Ruth: Piecewise parametric structure in the pooling problem: from sparse strongly-polynomial solutions to NP-hardness (2018)
  10. Castillo Castillo, Pedro A.; Castro, Pedro M.; Mahalec, Vladimir: Global optimization of MIQCPs with dynamic piecewise relaxations (2018)
  11. Kocuk, Burak; Dey, Santanu S.; Sun, X. Andy: Matrix minor reformulation and SOCP-based spatial branch-and-cut method for the AC optimal power flow problem (2018)
  12. 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)
  13. Gupte, Akshay; Ahmed, Shabbir; Dey, Santanu S.; Cheon, Myun Seok: Relaxations and discretizations for the pooling problem (2017)
  14. Li, Xiang; Tomasgard, Asgeir; Barton, Paul I.: Natural gas production network infrastructure development under uncertainty (2017)
  15. Boland, Natashia; Kalinowski, Thomas; Rigterink, Fabian: New multi-commodity flow formulations for the pooling problem (2016)
  16. Boukouvala, Fani; Misener, Ruth; Floudas, Christodoulos A.: Global optimization advances in mixed-integer nonlinear programming, MINLP, and constrained derivative-free optimization, CDFO (2016)
  17. Castro, Pedro M.: Normalized multiparametric disaggregation: an efficient relaxation for mixed-integer bilinear problems (2016)
  18. Chan, Alice Z.-Y.; Copenhaver, Martin S.; Narayan, Sivaram K.; Stokols, Logan; Theobold, Allison: On structural decompositions of finite frames (2016)
  19. Greco, Salvatore (ed.); Ehrgott, Matthias (ed.); Figueira, José Rui (ed.): Multiple criteria decision analysis. State of the art surveys. In 2 volumes (2016)
  20. Grimstad, Bjarne; Sandnes, Anders: Global optimization with spline constraints: a new branch-and-bound method based on B-splines (2016)

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