An Algorithm for Optimizing Over the Efficient Set of a Multiple Objective Affine Fractional Problem

Hoang Quang Tuyen

The efficient set of a  multiple objective affine fractional program  is neither convex nor closed. The problem of  minimizing a convex function over this efficient set is a difficult global optimization one. We use a dual formulation of the efficient set to approximate it by weakly efficient sets which are closed.  We proposed a decomposition algorithm for solving the approximation problems.  The proposed method is a branch-and-bound procedure
taking into account affine fractionality of the criterion functions.