Computational Comparison of Piecewise-Linear Relaxations for Pooling Problems

This work discusses alternative relaxation schemes for the pooling problem, a theoretically and practically interesting optimization problem. The problem nonconvexities appear in the form of bilinear terms and can be addressed with the relaxation technique based on the bilinear convex and concave envelopes. We explore ways to improve the relaxation tightness, and thus the efficiency of a global optimization algorithm, by employing a piecewise linearization scheme that partitions the original domain of the variables involved and applies the principles of bilinear relaxation for each one of the resulting subdomains. We employ 15 different piecewise relaxation schemes with mixed-integer representations and conduct a comprehensive computational comparison study over a collection of benchmark pooling problems. For each case, various partitioning variants can be envisioned, cumulatively accounting for a total of 56 700 relaxations. The results demonstrate that some of the schemes are clearly superior to their counterparts and should, therefore, be preferred in the optimization of pooling processes.