Solving discrete linear fractional bilevel programs with multiple objectives at the upper level

Abstract

<p style='text-indent:20px;'>This paper proposes an exact method to solve an integer linear fractional bilevel problem with multiple objectives at the upper level, designated by <inline-formula><tex-math id="M1">\begin{document}$ IFMOBP $\end{document}</tex-math></inline-formula>. The proposed algorithm generates a set of efficient solutions using a branch and cut algorithm based on a continuous upper level linear fractional problem. Then, the integer optimal solution obtained is tested for optimality of the lower level problem. First, the integer optimal solution of the bilevel problem is sought with a single objective function at each level. After that, an efficient cut is added and new integer solutions are determined. The efficient set is updated each time a candidate bilevel feasible solution non dominated is got and the process ends when there are no unexplored parts of the original domain. The proposed method is based on a dantzig cut to find the next best integer solution of the first objective function of the upper level, an efficient cut to get the set of efficient solutions for the main problem, and the classical branch and bound technique for integer decision variables. After the presentation of the algorithm, a numerical example and computational experiments are provided.</p>