(371a) A New Discretization Approach for Solving the Pooling Problem

This work presents a new discretization approach based on disjunctive programming for the pooling problem. The pooling problem has been subject of several studies in the area of process engineering because of its theoretical and practical relevance. It consists in blending materials in intermediate pools to obtain products within given specifications. The pooling problem is a non linear programming problem (NLP), which involves bilinear terms in the quality balances; therefore, it might yield several local optimal solutions. In general, the optimization methodologies used to solve the pooling problem are classified as follows: successive linear programming (SLP), Lagrangian approaches, convex envelopes, reformulation linearization techniques (RLT), branch and bound algorithms, piecewise underestimators and discretization approaches. Recently, Pham et al. (2009) presented a Convex Hull discretization approach that was able to solve the pooling problem to optimal or near optimal solutions. Pham et al. (2009) showed that for single quality problems, an exhaustive enumeration scheme was appropriate yielding most of the cases the optimal solution. Whereas, for multiple quality problems, an implicit enumeration scheme was recommended. In this work we present a discretization approach based on in disjunctive programming that does not require a pre-processing step unlike the implicit enumeration. The advantages of the proposed approach (when compared with a global optimization solver and the implicit enumeration approach) are shown by solving 7 cases of study, corresponding to multiple quality problems. For all the cases of study, near optimal solutions were found within shorter CPU times respect to other algorithms.

Pham, V.; Laird, C.; El-Halwagi, M. Convex hull discretization approach to the global optimization of pooling problems. Industrial and Engineering Chemistry Research. 2009, 48 (4), 1973-1979.