Tightening Discretization-based MILP Models for the Pooling Problem using Upper Bounds on Bilinear Terms
This work addresses the pooling problem in optimization, offering incremental improvements for computational efficiency in this domain-specific area.
The paper tackled the challenge of solving nonconvex optimization problems like the pooling problem by tightening discretization-based MILP models using upper bounds on bilinear terms, resulting in reduced solution times as demonstrated computationally.
Discretization-based methods have been proposed for solving nonconvex optimization problems with bilinear terms such as the pooling problem. These methods convert the original nonconvex optimization problems into mixed-integer linear programs (MILPs). In this paper we study tightening methods for these MILP models for the pooling problem, and derive valid constraints using upper bounds on bilinear terms. Computational results demonstrate the effectiveness of our methods in terms of reducing solution time.