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.

鉴于后一类模型的全局求解器的最新进展，本文重新审视了将混合整数多项式规划 (MIPOP) 转换为混合整数二次约束规划 (MIQCP) 的方法。我们在一个名为CANON的新重新制定引擎中自动执行此转换，以及包括本地搜索和边界收紧在内的预处理策略。我们对从 MINLPLib 等测试库收集的 137 个 MIPOP 集合进行比较测试。求解器GUROBI在重新制定的 MIQCP 上提供了最佳性能，并且优于通用全局求解器BARON和SCIP。MIQCP 重新制定还提高了SCIP的性能与直接 MIPOP 解决方案相比，BARON的性能在原始 MIPOP 和重新配制的 MIQCP 上具有可比性。总体而言，这些结果确立了 MIPOP 全局优化的二次重构的有效性，并支持将其集成到全局求解器中。