Exact solution approach for a class of nonlinear bilevel knapsack problems

We study a class of nonlinear bilevel knapsack problems. The upper-level objective is a nonlinear integer function of both the leader’s and the follower’s decision variables. At the lower level the follower solves a linear binary knapsack problem, where the right-hand side of the knapsack constraint depends on the resource allocated by the leader. After discussing computational complexity issues, we propose an exact solution approach using an equivalent single-level value function reformulation. Extensive computational experiments are performed with quadratic and fractional binary objective functions.