Solving the pooling problem at scale with extensible solver GALINI

Abstract: This paper presents a Python library to model pooling problems, a class of network flow problems with many engineering applications. The library automatically generates a mixed-integer quadratically-constrained quadratic optimization problem from a given network structure. The library additionally uses the network structure to build 1) a convex linear relaxation of the non-convex quadratic program and 2) a mixed-integer linear restriction of the problem. We integrate the pooling network library with galini, an open-source extensible global solver for quadratic optimization. We demonstrate galini's extensible characteristics by using the pooling library to develop two galini plug-ins: 1) a cut generator plug-in that adds valid inequalities in the galini cut loop and 2) a primal heuristic plug-in that uses the mixed-integer linear restriction. We test galini on large scale pooling problems and show that, thanks to the good upper bound provided by the mixed-integer linear restriction and the good lower bounds provided by the convex relaxation, we obtain optimality gaps that are competitive with Gurobi 9.1 on the largest problem instances.