Parametric algorithms for global optimization of mixed-integer fractional programming problems in process engineering

In this work, we proposed novel parametric algorithms for solving large-scale mixed-integer linear and nonlinear fractional programming problems, and illustrate their application in process systems engineering. By developing an equivalent parametric formulation of the general mixed-integer fractional program (MIFP), we propose four exact parametric algorithms based on the root-finding methods, including bisection method, Newton´s method, secant method and false position method, respectively, for the global optimization of MIFPs. We also propose an inexact parametric algorithm that can potentially outperform the exact parametric algorithms for some types of MIFPs. Extensive computational studies are performed to demonstrate the efficiency of these parametric algorithms and to compare them with the general-purpose mixed-integer nonlinear programming methods. The applications of the proposed algorithms are illustrated through a case study on process scheduling. Computational results show that the proposed exact and inexact parametric algorithms are more computationally efficient than several general-purpose solvers for solving MIFPs.