Solving integer linear fractional semivectorial bilevel programs

Abstract This paper proposes an exact method to solve an integer linear fractional bilevel problem with multiple objectives at the lower level. The proposed algorithm generates the integer optimal bilevel solution, begining by solving the integer linear fractional program of the upper level. Then, the integer optimal solution obtained is tested for optimality of the main problem without going through all the efficient solutions of the lower level problem. If no optimal bilevel solution is obtained, an efficient cut is added to the upper level problem and the next integer optimal solution is determined. The proposed method is based on a classical branch and bound technique for integer decision variables and efficient cuts, which allows may to avoid a large number of non bilevel solutions, thus, shorten the search domain. A numerical example is given and computational experiments reveal satisfying results. Mathematics Subject Classi cation (2020) 90C29 90C10 90C26 90C57