Tightening Discretization-based MILP Models for the Pooling Problem using Upper Bounds on Bilinear Terms

TL;DR

This paper introduces tightening techniques for MILP models of the pooling problem by leveraging upper bounds on bilinear terms, significantly improving solution efficiency.

Contribution

It proposes novel valid constraints based on upper bounds to tighten discretization-based MILP models for the pooling problem.

Findings

Reduced solution times in computational experiments

Enhanced MILP model accuracy and tightness

Demonstrated effectiveness of the proposed methods

Abstract

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.