Assessment of a two-step approach for global optimization of mixed-integer polynomial programs using quadratic reformulation. (September 2022)

• Record Type: Journal Article
• Authors: Karia, Tanuj; Adjiman, Claire S.; Chachuat, Benoît
• Is Part Of: Computers & chemical engineering. Volume 165(2022)
• Publication Date: 2022-09
• Subjects: Deterministic global optimization -- Mixed-integer nonlinear optimization -- Polynomial optimization -- Quadratically-constrained programming -- Preprocessing -- MINLPLib; Chemical engineering -- Data processing -- Periodicals; 660.0285
• DOI: 10.1016/j.compchemeng.2022.107909
• Languages: English
• ISSNs: 0098-1354

Abstract

Highlights: Comparison of reformulated MIQCPs against original MIPOPs using the solvers GUROBI, BARON and SCIP. Investigation of preprocessing strategies and redundant quadratic constraints on performance of MIQCP reformulation. MIQCP reformulation engine implemented in the C++ library CANON. Reformulated MIQCPs solved significantly faster with GUROBI than original MIPOPs with BARON or SCIP. Several unsolved test instances from MINLPLib successfully solved to global optimality after MIQCP 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.