Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Canonical Duality Theory and Algorithm for Solving Bilevel Knapsack
  Problems with Applications   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.

24
The categories of this paper are: dg-ga
7
The categories of this paper are: hep-th
26
The categories of this paper are: bayes-an
22
The categories of this paper are: chao-dyn
10
The categories of this paper are: q-bio
27
The categories of this paper are: comp-gas
36
The categories of this paper are: cmp-lg
21
The categories of this paper are: adap-org
28
The categories of this paper are: alg-geom
0
The categories of this paper are: hep-ph
5
The categories of this paper are: gr-qc
29
The categories of this paper are: funct-an
35
The categories of this paper are: mtrl-th
15
The categories of this paper are: nucl-ex
9
The categories of this paper are: nlin
23
The categories of this paper are: solv-int