APOGEE: Global optimization of standard, generalized, and extended pooling problems via linear and logarithmic partitioning schemes

Abstract 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 (Vielma & Nemhauser, 2010; Vielma, Ahmed, & Nemhauser, 2010b) , 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/ .

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