  A novel canonical duality theory (CDT) is presented for solving general
bilevel mixed integer nonlinear optimization governed by linear and quadratic
knapsack problems. It shows that the challenging knapsack problems can be
solved analytically in term of their canonical dual solutions. The existence
and uniqueness of these analytical solutions are proved. NP-Hardness of the
knapsack problems is discussed. A powerful CDT algorithm combined with an
alternative iteration and a volume reduction method is proposed for solving the
NP-hard bilevel knapsack problems. Application is illustrated by a benchmark
problem in optimal topology design. The performance and novelty of the proposed
method are compared with the popular commercial codes.
