Abstract
The Multiple-Choice Multi-Dimension Knapsack Problem (MMKP) is a variant of the 0-1 Knapsack Problem, an NP-Hard problem. Hence algorithms for finding the exact solution of MMKP are not suitable for application in real time decision-making applications, like quality adaptation and admission control of an interactive multimedia system. This paper presents two new heuristic algorithms, M-HEU and I-HEU for solving MMKP. Experimental results suggest that M-HEU finds 96% optimal solutions on average with much reduced computational complexity and performs favorably relative to other heuristic algorithms for MMKP. The scalability property of I-HEU makes this heuristic a strong candidate for use in real time applications.
Chapter PDF
Similar content being viewed by others
References
R. Armstrong, D. Kung, P. Sinha and A. Zoltners. A Computational Study of Multiple Choice Knapsack Algorithm. ACM Transaction on Mathematical Software, 9:184–198 (1983).
P. Koleser, A Branch and Bound Algorithm for Knapsack Problem. Management Science, 13:723–735 (1967).
K. Dudziniski and W. Walukiewicz, A Fast Algorithm for the Linear Multiple Choice Knapsack Problem. Operation Research Letters, 3:205–209 (1984).
S. Khan. Quality Adaptation in a Multi-Session Adaptive Multimedia System: Model and Architecture. PhD thesis, Department of Electrical and Computer Engineering, University of Victoria (1998).
S. Khan., K. F. Li and E. G. Manning. The Utility Model for Adaptive Multimedia System. In International Workshop on Multimedia Modeling, pages 111–126 (1997).
M. Magazine, G. Nemhauser and L. Trotter. When the Greedy Solution Solves a Class of Knapsack Problem. Operations Research, 23:207–217 (1975)
M. Magazine and O. Oguz. A Heuristic Algorithm for Multidimensional Zero-One Knapsack Problem. European Journal of Operational Research, 16(3):319–326 (1984).
S. Martello and P. Toth. Algorithms for Knapsack Problems. Annals of Discrete Mathematics, 31:70–79 (1987).
M. Moser, D. P. Jokanovic and N. Shiratori. An Algorithm for the Multidimensional Multiple-Choice Knapsack Problem. IEICE Transactions on Fundamentals of Electronics, 80(3):582–589 (1997).
R. Nauss. The 0-1 Knapsack Problem with Multiple Choice Constraints. European Journal of Operation Research, 2:125–131(1978).
W. H. Press, S. A. Teukolsky, W. T. Vetterling and B. P. Flannery. Numerical Recipes in C: The Art of Scientific Computing. Cambridge University Press, Cambridge, UK, second edition (1992).
W. Shih. A branch and Bound Method for Multiconstraint Knapsack Problem. Journal of the Operational Research Society, 30:369–378 (1979).
Y. Toyoda. A Simplified Algorithm for Obtaining Approximate Solution to Zero-one Programming Problems. Management Science, 21:1417–1427 (1975)
G. F. Luger and W. A. Stubblefield. Artificial Intelligence, Structures and Strategies for Complex Problem Solving, Second edition, The Benjamin/Cummings Publishing Company, Inc., 1993.
R. K. Watson. Applying the Utility Model to IP Networks: Optimal Admission & Upgrade of Service Level Agreements. MASc Thesis, Dept of ECE, University of Victoria, 2001, to appear.
M. Akbar, E. G. Manning, G. C. Shoja, S. Khan, “Heuristics for Solving the Multiple-Choice Multi-Dimension Knapsack Problem”, Technical Report DCS-265-1R, Dept. of CS, UVic, March 2001.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2001 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Akbar, M.M., Manning, E.G., Shoja, G.C., Khan, S. (2001). Heuristic Solutions for the Multiple-Choice Multi-dimension Knapsack Problem. In: Alexandrov, V.N., Dongarra, J.J., Juliano, B.A., Renner, R.S., Tan, C.J.K. (eds) Computational Science - ICCS 2001. ICCS 2001. Lecture Notes in Computer Science, vol 2074. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-45718-6_71
Download citation
DOI: https://doi.org/10.1007/3-540-45718-6_71
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-42233-4
Online ISBN: 978-3-540-45718-3
eBook Packages: Springer Book Archive