Branch and cut method for solving integer indefinitequadratic bilevel programs with multiple objectives atthe upper level

This paper proposes an exact method to solve an integer indefinite quadratic bilevel problem with multiple objectives at the upper level, where the objective functions at both levels are a product of two linear functions. The suggested algorithm uses a branch and cut algorithm based on a multiobjective integer linear problem obtained by replacing the indefinite quadratic objectives of the upper level by their two linear functions and the classical branch and bound technique for integer decision variables. Then, the integer solutions obtained are tested for optimality of the lower level problem by using a library IBM CPLEX 12.8 for C++ programs. The integer indefinite quadratic bilevel programming problem with single objective at both levels is solved in the first step, based on the dantzig cut. The second phase explorates with the efficient cut to provide the set of efficient solutions without listing the whole integer domain. After the presentation of the algorithm, a numerical example and computational experiments are provided.