Abstract
When designing evolutionary algorithms (EAs) for the multidimensional knapsack problem, it is important to consider that the optima lie on the boundary B of the feasible region of the search space. Previously published EAs are reviewed, focusing on how they take this into account. We present new initialization routines and compare several repair and optimization methods, which help to concentrate the search on B. Our experiments identify the best EAs directly exploring B.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
Similar content being viewed by others
References
Chu, P.C., Beasley, J.E.: A Genetic Algorithm for the Multidimensional Knapsack Problem. Journal of Heuristics 4(1), 63–86 (1998)
Chu, P.C.: A Genetic Algorithm Approach for Combinatorial Optimisation Problems. PhD Thesis, The Management School, Imperial College of Science, Technology and Medicine, London (1997)
Corno, F., Sonza Reorda, M., Squillero, G.: The Selfish Gene Algorithm: a new Evolutionary Optimization Strategy. In: Proceedings of the 13th Annual ACM Symposium on Applied Computing (1998)
Eiben, A.E., Bäck, T., Schoenauer, M., Schwefel, H.-P. (eds.): PPSN 1998. LNCS, vol. 1498. Springer, Heidelberg (1998)
Gordon, V., Böhm, A., Whitley, D.: A Note on the Performance of Genetic Algorithms on Zero-One Knapsack Problems. Technical Report CS-93-108, Department of Computer Science, Colorado State University (1993)
Garey, M.R., Johnson, D.S.: Computers and Intractability: A Guide to the Theory of NP-Completeness. W. H. Freeman, San Francisco (1979)
Gottlieb, J.: Evolutionary Algorithms for Multidimensional Knapsack Problems: the Relevance of the Boundary of the Feasible Region. In: Proceedings of the Genetic and Evolutionary Computation Conference, p. 787 (1999)
Gottlieb, J., Raidl, G.R.: Characterizing Locality in Decoder-Based EAs for the Multidimensional Knapsack Problem. In: Proceedings of Artificial Evolution (1999)
Gordon, V., Whitley, D.: Serial and Parallel Genetic Algorithms as Function Optimizers. In: Forrest, S. (ed.) Proceedings of the Fifth International Conference on Genetic Algorithms, pp. 177–183. Morgan Kaufmann, San Francisco (1993)
Hinterding, R.: Mapping, Order-independent Genes and the Knapsack Problem. In: Proceedings of the 1st IEEE International Conference on Evolutionary Computation, pp. 13–17 (1994)
Hoff, A., Løkketangen, A., Mittet, I.: Genetic Algorithms for 0/1 Multidimensional Knapsack Problems. In: Proceedings Norsk Informatikk Konferanse (1996)
Holland, J.H.: Adaptation in Natural and Artificial Systems. University of Michigan Press, Ann Arbor (1975)
Khuri, S., Batarekh, A.: Heuristics for the Integer Knapsack Problem. In: Proceedings of the 10th International Computer Science Conference, Santiago, Chile, pp. 161–172 (1990)
Khuri, S., Bäck, T., Heitkötter, J.: An Evolutionary Approach to Combinatorial Optimization Problems. In: Cizmar, D. (ed.) Proceedings of the 22nd Annual ACM Computer Science Conference, pp. 66–73. ACM Press, New York (1994)
Khuri, S., Bäck, T., Heitkötter, J.: The Zero/One Multiple Knapsack Problem and Genetic Algorithms. In: Deaton, E., Oppenheim, D., Urban, J., Berghel, H. (eds.) Proceedings of the ACM Symposium on Applied Computation, pp. 188–193. ACM Press, New York (1994)
Lin, F.-T., Kao, C.-Y., Hsu, C.-C.: Applying the Genetic Approach to Simulated Annealing in Solving Some NP-Hard Problems. IEEE Transactions on Systems, Man, and Cybernetics 23(6), 1752–1767 (1993)
Løkketangen, A.: A Comparison of a Genetic Algorithm and a Tabu Search Method for 0/1 Multidimensional Knapsack Problems. In: Proceedings of the Nordic Operations Research Conference (1995)
Michalewicz, Z., Arabas, J.: Genetic Algorithms for the 0/1 Knapsack Problem. In: Raś, Z.W., Zemankova, M. (eds.) ISMIS 1994. LNCS, vol. 869, pp. 134–143. Springer, Heidelberg (1994)
Mayer, H.A.: ptGAs - Genetic Algorithms Evolving Noncoding Segments by Means of Promoter/Terminator Sequences. Evolutionary Computation 6(4), 361–386 (1998)
Michalewicz, Z.: Heuristic Methods for Evolutionary Computation Techniques. Journal of Heuristics 1(2), 177–206 (1995)
Martello, S., Toth, P.: Knapsack Problems. John Wiley & Sons, Chichester (1990)
Olsen, A.L.: Penalty functions and the knapsack problem. In: Proceedings of the 1st IEEE International Conference on Evolutionary Computation, pp. 554–558 (1994)
Raidl, G.R.: An Improved Genetic Algorithm for the Multiconstrained 0-1 Knapsack Problem. In: Proceedings of the 5th IEEE International Conference on Evolutionary Computation, pp. 207–211 (1998)
Raidl, G.R.: Weight-Codings in a Genetic Algorithm for the Multiconstraint Knapsack Problem. In: Proceedings of the Congress on Evolutionary Computation, pp. 596–603 (1999)
Richardson, J.T., Palmer, M.R., Liepins, G., Hilliard, M.: Some Guidelines for Genetic Algorithms with Penalty Functions. In: Schaffer, J.D. (ed.) Proceedings of the Third International Conference on Genetic Algorithms, pp. 191–197. Morgan Kaufmann, San Francisco (1989)
Rudolph, G., Sprave, J.: A Cellular Genetic Algorithm with Self- Adjusting Acceptance Threshold. In: Proceedings of the 1st IEE/IEEE International Conference on Genetic Algorithms in Engineering Systems: Innovations and Applications, pp. 365–372. IEE, London (1995)
Rudolph, G., Sprave, J.: Significance of Locality and Selection Pressure in the Grand Deluge Evolutionary Algorithm. In: Ebeling, W., Rechenberg, I., Voigt, H.-M., Schwefel, H.-P. (eds.) PPSN 1996. LNCS, vol. 1141, pp. 686–695. Springer, Heidelberg (1996)
Thiel, J., Voss, S.: Some Experiences on Solving Multiconstraint Zero- One Knapsack Problems with Genetic Algorithms. INFOR. 32(4), 226–242 (1994)
Yang, R.: Line-Breeding Schemes for Combinatorial Optimization. In: [EBSS 1998], pp. 448–457
Zitzler, E., Thiele, L.: Multiobjective Optimization Using Evolutionary Algorithms – A Comparative Case Study. In: [EBSS 1998], pp. 292–301
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2000 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Gottlieb, J. (2000). On the Effectivity of Evolutionary Algorithms for the Multidimensional Knapsack Problem. In: Fonlupt, C., Hao, JK., Lutton, E., Schoenauer, M., Ronald, E. (eds) Artificial Evolution. AE 1999. Lecture Notes in Computer Science, vol 1829. Springer, Berlin, Heidelberg. https://doi.org/10.1007/10721187_2
Download citation
DOI: https://doi.org/10.1007/10721187_2
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-67846-5
Online ISBN: 978-3-540-44908-9
eBook Packages: Springer Book Archive