- Title
- Canonical duality theory and algorithm for solving bilevel knapsack problems with applications
- Creator
- Gao, David
- Date
- 2021
- Type
- Text; Journal article
- Identifier
- http://researchonline.federation.edu.au/vital/access/HandleResolver/1959.17/175581
- Identifier
- vital:15006
- Identifier
-
https://doi.org/10.1109/TSMC.2018.2882792
- Identifier
- ISBN:2168-2216 (ISSN)
- Abstract
- 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 benchmark problems in optimal topology design. The performance and novelty of the proposed method are compared with the popular commercial codes. © 2013 IEEE.
- Publisher
- Institute of Electrical and Electronics Engineers Inc.
- Relation
- IEEE Transactions on Systems, Man, and Cybernetics: Systems Vol. 51, no. 2 (2021), p. 893-904
- Rights
- All metadata describing materials held in, or linked to, the repository is freely available under a CC0 licence
- Rights
- Copyright © 2021 IEEE - All rights reserved.
- Rights
- Open Access
- Subject
- 08 Information and Computing Sciences; 09 Engineering; Bilevel optimization; canonical duality theory (CDT); CDT algorithm; knapsack problems; NP-hardness; Topology design
- Full Text
- Reviewed
- Hits: 2290
- Visitors: 2402
- Downloads: 194
| Thumbnail | File | Description | Size | Format | |||
|---|---|---|---|---|---|---|---|
| View Details Download | SOURCE1 | Published version | 1 MB | Adobe Acrobat PDF | View Details Download |