A Convex Hull Discretization Approach to the Global Optimization of Pooling Problems
Viet Pham, Carl D. Laird, and Mahmoud El-Halwagi. Chemical Engineering, Texas A&M University, College Station, TX 77843
The pooling problem is an important optimization problem that is encountered in process operation and scheduling. Because of the presence of bilinear terms, the traditional formulation is nonconvex. Consequently, there is a need to develop computationally-efficient and easy-to-implement global-optimization techniques. In this paper, a new approach is proposed based on three concepts: linearization by discretizing nonlinear variables, pre-processing using implicit enumeration of the discretization to form a convex-hull which limits the size of the search space, and application of integer cuts to ensure compatibility between the original problem and the discretized formulation. The continuous quality variables contributing to the bilinear terms are first discretized. The discretized problem is a mixed integer linear program (MILP) which is globally solvable in a computationally effective manner using branch and bound method. The merits of the proposed approach are illustrated with case studies from literature and comparison with published results.