Global Optimization of Mixed-Integer Polynomial Programs via Quadratic Reformulation

Abstract

Mixed-integer polynomial programs (MIPOPs) frequently arise in chemical engineering applications such as pooling, blending and operations planning. Many global optimization solvers rely on mixed-integer linear (MIP) relaxations of MIPOPs and solve them repeatedly as part of a branch-and-bound algorithm using commercial MIP solvers. GUROBI, one of the prominent MIP solvers, recently added the capability to solve mixed-integer quadratically-constrained quadratic programs (MIQCQPs). This paper investigates global optimization of MIPOPs via their reformulation as MIQCQPs followed by their solution to global optimality using GUROBI. The effectiveness of this approach is tested on 60 instances of MIPOPs selected from the library MINLPLib. The performance of the MIQCQP reformulation approach is compared to the state-of-the-art global solvers BARON, ANTIGONE and SCIP in GAMS. For the case of single threading, a reduction of 28% and 42% compared to SCIP and ANTIGONE respectively is observed. This approach, therefore, holds promise for integration into existing global solvers to handle MIPOPs.