Assessment of a two-step approach for global optimization of mixed-integer polynomial programs using quadratic reformulation

Abstract

This paper revisits the approach of transforming a mixed-integer polynomial program (MIPOP) into a mixed-integer quadratically-constrained program (MIQCP), in the light of recent progress in global solvers for this latter class of models. We automate this transformation in a new reformulation engine called CANON, alongside preprocessing strategies including local search and bounds tightening. We conduct comparative tests on a collection of 137 MIPOPs gathered from test libraries such as MINLPLib. The solver GUROBI gives the best performance on the reformulated MIQCPs and outperforms the generic global solvers BARON and SCIP. The MIQCP reformulation also improves the performance of SCIP compared to direct MIPOP solution, whereas the performance of BARON is comparable on the original MIPOPs and reformulated MIQCPs. Overall, these results establish the effectiveness of quadratic reformulation for MIPOP global optimization and support its integration into global solvers.