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

作者：Misener Ruth; Thompson Jeffrey P; Floudas Christodoulos A^*

来源：Computers & Chemical Engineering, 2011, 35(5): 876-892.

DOI：10.1016/j.compchemeng.2011.01.026

• Large-scale optimization
• Global optimization
• MINLP
• Quadratically constrained quadratic programs
• Pooling problem
• EPA Complex Emissions Model

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/.

• 出版日期2011-5-11