Abstract

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.