APOGEE swMATH ID: 8451 Software Authors: Ruth Misener, Jeffrey P. Thompson, Christodoulos A. Floudas Description: 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/. Homepage: http://helios.princeton.edu/APOGEE/ Related Software: GloMIQO; BARON; SCIP; CPLEX; GAMS; ANTIGONE; MINLPLib; LINDO; Bonmin; GitHub; GLOBALLib; MINLP; Gurobi; CONOPT; StdPooling-PolyAlgos; AMPL; LINDOGlobal; Couenne; Ipopt; GloptiPoly Cited in: 39 Publications Further Publications: http://helios.princeton.edu/APOGEE/publications.html all top 5 Cited by 72 Authors 7 Misener, Ruth 6 Floudas, Christodoulos Achilleus 5 Castro, Pedro M. 4 Dey, Santanu Subhas 4 Grossmann, Ignacio E. 3 Li, Xiang 3 Tomasgard, Asgeir 2 Barton, Paul I. 2 Bent, Russell W. 2 Gupte, Akshay 2 Haugland, Dag 2 Kocuk, Burak 2 Linderoth, Jeff T. 2 Nagarajan, Harsha 2 Sundar, Kaarthik 2 Wang, Site 1 Ahmed, Shabbir 1 Baltean-Lugojan, Radu 1 Bernal, David E. 1 Boland, Natashia L. 1 Boukouvala, Fani 1 Castillo Castillo, Pedro A. 1 Chan, Alice Zhuo-Yu 1 Chen, Yifu 1 Cheng, Xin 1 Cheon, Myun-Seok 1 Copenhaver, Martin S. 1 Dahl, Joachim 1 D’Ambrosio, Claudia 1 de Klerk, Etienne 1 Duran, Marco A. 1 Ehrgott, Matthias 1 Figueira, JosĂ© Rui 1 Furman, Kevin C. 1 Greco, Salvatore 1 Grimstad, Bjarne 1 Hellemo, Lars 1 Hendrix, Eligius M. T. 1 Huchette, Joey 1 Kalinowski, Thomas 1 Kolodziej, Scott P. 1 Koster, Arie M. C. A. 1 Kuhnke, Sascha 1 Liang, Yongtu 1 Liao, Qi 1 Lin, Ming-Hua 1 Lu, Mowen 1 Luedtke, James R. 1 Mahalec, Vladimir 1 Marandi, Ahmadreza 1 Maravelias, Christos T. 1 Morton, David P. 1 Narayan, Sivaram K. 1 Newman, Alexandra M. 1 Pistikopoulos, Efstratios N. 1 Rigterink, Fabian 1 Sandnes, Anders 1 Santana, Asteroide 1 Schweiger, Jonas 1 Scioletti, Michael S. 1 Smadbeck, James B. 1 Stokols, Logan F. 1 Sun, Xu Andy 1 Theobold, Allison 1 Tsai, Jung-Fa 1 Tseng, Chung-Li 1 Vielma, Juan Pablo 1 Wittmann-Hohlbein, Martina 1 Yu, Chian-Son 1 Zhan, Yiduo 1 Zheng, Qipeng Phil 1 Zolan, Alexander J. all top 5 Cited in 18 Serials 18 Journal of Global Optimization 4 Optimization and Engineering 2 European Journal of Operational Research 1 Journal of Optimization Theory and Applications 1 Mathematics of Operations Research 1 Operations Research 1 Operations Research Letters 1 Annals of Operations Research 1 Mathematical Programming. Series A. Series B 1 SIAM Journal on Optimization 1 Top 1 Advances in Computational Mathematics 1 INFORMS Journal on Computing 1 Mathematical Problems in Engineering 1 Optimization Methods & Software 1 International Series in Operations Research & Management Science 1 Applied and Computational Mathematics 1 Mathematical Programming Computation all top 5 Cited in 7 Fields 38 Operations research, mathematical programming (90-XX) 3 Numerical analysis (65-XX) 1 General and overarching topics; collections (00-XX) 1 Combinatorics (05-XX) 1 Order, lattices, ordered algebraic structures (06-XX) 1 Linear and multilinear algebra; matrix theory (15-XX) 1 Computer science (68-XX) Citations by Year