Abstract
In [1] Drexl presented a Simulated Annealing (SA) algorithm for multi-constraint 0–1 knapsack problems (MCKP). Drexl studied 57 different MCKP’s which have been published in the literature. In [2], the new optimization heuristic Threshold Accepting (TA) has been introduced. It is demonstrated in [2] that TA yields better results than SA for Traveling Salesman problems. In this paper we give a suited TA algorithm for MCKP’s and report the computational results of test runs for the same set of 57 MCKP’s. Since we were able to use the very same computer as Drexl (an IBM 3090-200 VF), we are able to make quite a fair comparison between the results with SA and TA.
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsPreview
Unable to display preview. Download preview PDF.
References
Drexl, A.: A simulated annealing approach to the mult icons traini zero-one knapsack problem. Z. Computing, 40 (1988) 1–8.
Dueck, G.; Scheuer, T.: Threshold Accepting: A general purpose algorithm appearing superior to simulated annealing. Technical Report 88.10.011, IBM Heidelberg Scientific Center.
Fleisher, J.: Sigmap Newsletter 20 (1976).
Fréville, A.; Plateau, G.: Méthodes heuristiques performantes pour les problèmes en variables 0–1 à plusieurs constraintes en inégalité Publication ANO-91, Université des Sciences et Techniques de Lille (1982).
Fréville, A.; Plateau, G.: Hard 0–1 multiknapsack test problems for size reduction methods. Prepublication informatique 72 Université Paris-Nord (1987).
Kirkpatrick, S.; Gelati, C.D.; Vecchi, M.P. Optimization by simulated annealing. Science, 220 (1983) 671–680.
Metropolis, N.; Rosenbluth, A.; Rosenbluth, M.; Teller, A.; Teller, E.: Equation of state calculation by fast computing machines. Journ. Chem. Phys. 21 (1953) 1087–1092.
Peterson, C.C.: Computational experience with variants of the Balas algorithm applied to the selection of R and D projects. Management Science 13 (1967) 736–750.
Plateau, G.: Reduction de la taille des problèmes linéaires en variables 0–1. Pubi. 71 du Lab. de Calcu de l’Université des Sciences et Techniques de Lille 1 (1976).
Shih, W.: A branch and bound method for the multiconstaint 0–1 knapsack problem. Journ. of the Operational Research Society 30 (1979) 369–378.
Toyoda, Y.: A simplified algorithm for obtaining approximate solutions to 0–1 programming problems. Management Science 21 (1975) 1417–1427.
Weingartner, H.M.; Ness, D.N.: Methods for the solution of the multidimensional 0–1 knapsack problem. Operations Research 15 (1967) 83–103.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1991 B.G. Teubner Stuttgart and Kluwer Academic Publishers
About this chapter
Cite this chapter
Dueck, G., Wirsching, J. (1991). Threshold Accepting Algorithms For 0–1 Knapsack Problems. In: Wacker, H., Zulehner, W. (eds) Proceedings of the Fourth European Conference on Mathematics in Industry. European Consortium for Mathematics in Industry, vol 6. Springer, Dordrecht. https://doi.org/10.1007/978-94-009-0703-4_28
Download citation
DOI: https://doi.org/10.1007/978-94-009-0703-4_28
Publisher Name: Springer, Dordrecht
Print ISBN: 978-94-010-6802-4
Online ISBN: 978-94-009-0703-4
eBook Packages: Springer Book Archive