Formulating the mixed integer fractional posynomial programming

The mixed integer fractional posynomial programming (MIFPP) problem arises from the summation minimization of several quotient terms appearing in the objective function subject to given constraints. All decision variables of the problem could be binary, integer, and/or continuous with (without) absolute value functions. This paper addresses the problem of providing an optimization approach, which could certainly obtain a solution as close as possible to a global optimum. In order to solve the complex MIFPP problem, several strategies are used including linear programming relaxation, modified goal programming, logarithmic piecewise function (LPF) and so on. In addition, the proposed model solves the undefined problem of the logarithm of zero or negative in the LPF. This significantly improved the utility of LPF in real applications. Finally, an illustrative example is included to demonstrate the solution procedure of the proposed model.