Solving the pooling problem at scale with extensible solver GALINI

Francesco Ceccon; Ruth Misener

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arXiv · 2105.01687

Solving the pooling problem at scale with extensible solver GALINI

Francesco Ceccon·Ruth Misener

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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.

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BibTeX RIS

Francesco Ceccon, Ruth Misener. 2021-05-04. Solving the pooling problem at scale with extensible solver GALINI. https://arxiv.org/abs/2105.01687

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