Global Optimization of EPA-Extended Pooling Problems
The pooling problem is a challenge seeking to maximize profit subject to feedstock availability, intermediate storage capacity, demand, and product specifications on a network of interconnected nodes. We have extended the pooling problem to incorporate the Environmental Protection Agency (EPA) Title 40 Code of Federal Regulations Part 80.45: Complex Emissions Model into the constraint set so that the final products comply with United States reformulated gasoline standards.
To globally optimize the extended pooling problem, (1) we formulated a mixed-integer nonlinear program (MINLP) representing the EPA Complex Emissions Model and appended this model to a standard pooling problem network, (2) developed a linear relaxation of the MINLP, and (3) integrated these relaxations into a branch-and-bound optimization algorithm. An implementation of our global optimization algorithm, the computational tool APOGEE (Algorithms for Pooling-problem global Optimization in GEneral and Extended Classes), is freely available at helios.princeton.edu/APOGEE/.