Abstract
A hybridization of an evolutionary algorithm (EA) with the branch and bound method (B&B) is presented in this paper. Both techniques cooperate by exchanging information, namely lower bounds in the case of the EA, and partial promising solutions in the case of the B&B. The multidimensional knapsack problem has been chosen as a benchmark. To be precise, the algorithms have been tested on large problems instances from the OR-library. As it will be shown, the hybrid approach can provide high quality results, better than those obtained by the EA and the B&B on their own.
Preview
Unable to display preview. Download preview PDF.
Similar content being viewed by others
References
Lawler, E., Wood, D.: Branch and bounds methods: A survey. Operations Research 4, 669–719 (1966)
Bäck, T.: Evolutionary Algorithms in Theory and Practice. Oxford University Press, New York (1996)
Bäck, T., Fogel, D., Michalewicz, Z.: Handbook of Evolutionary Computation. Oxford University Press, New York (1997)
Davis, L.: Handbook of Genetic Algorithms. Van Nostrand Reinhold, New York (1991)
Wolpert, D., Macready, W.: No free lunch theorems for optimization. IEEE Transactions on Evolutionary Computation 1, 67–82 (1997)
Culberson, J.: On the futility of blind search: An algorithmic view of no free lunch. Evolutionary Computation 6, 109–128 (1998)
Garey, M., Johnson, D.: Computers and Intractability: A Guide to the Theory of NP-Completeness. Freeman and Co, San Francisco (1979)
Salkin, H., Mathur, K.: Foundations of Integer Programming. North-Holland, Amsterdam (1989)
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 1994 ACM Symposium on Applied Computation, pp. 188–193. ACM Press, New York (1994)
Cotta, C., Troya, J.: A hybrid genetic algorithm for the 0-1 multiple knapsack problem. In Smith, G., Steele, N., Albrecht, R., eds.: Artificial Neural Nets and Genetic Algorithms 3, Wien New York, Springer-Verlag (1998) 251–255
Chu, P.C., Beasley, J.E.: A genetic algorithm for the multidimensional knapsack problem. Journal of Heuristics 4, 63–86 (1998)
Gottlieb, J.: Permutation-based evolutionary algorithms for multidimensional knapsack problems. In: Carroll, J., Damiani, E., Haddad, H., Oppenheim, D. (eds.) ACM Symposium on Applied Computing 2000, pp. 408–414. ACM Press, New York (2000)
Raidl, G., Gottlieb, J.: Empirical analysis of locality, heritability and heuristic bias in evolutionary algorithms: A case study for the multidimensional knapsack problem. Technical Report TR 186–1–04–05, Institute of Computer Graphics and Algorithms, Vienna University of Technology (2004)
Cotta, C., Aldana, J.F., Nebro, A.J., Troya, J.M.: Hybridizing genetic algorithms with branch and bound techniques for the resolution of the TSP. In: Pearson, D.W., Steele, N.C., Albrecht, R.F. (eds.) Artificial Neural Nets and Genetic Algorithms 2, Wien, New York, pp. 277–280. Springer, Heidelberg (1995)
Volgenant, A., Jonker, R.: A branch and bound algorithm for the symmetric traveling salesman problem based on the 1-tree relaxation. European Journal of Operational Research 9, 83–88 (1982)
Nagard, A., Heragu, S.S., Haddock, J.: A combined branch and bound and genetic algorithm based for a flowshop scheduling algorithm. Annals of Operation Research 63, 397–414 (1996)
French, A., Robinson, A., Wilson, J.: Using a hybrid genetic-algorithm/branch and bound approach to solve feasibility and optimization integer programming problems. Journal of Heuristics 7, 551–564 (2001)
Cotta, C., Troya, J.: Embedding branch and bound within evolutionary algorithms. Applied Intelligence 18, 137–153 (2003)
Beasley, J.: Or-library: distributing test problems by electronic mail. Journal of the Operational Research Society 41, 1069–1072 (1990)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2005 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Gallardo, J.E., Cotta, C., Fernández, A.J. (2005). Solving the Multidimensional Knapsack Problem Using an Evolutionary Algorithm Hybridized with Branch and Bound. In: Mira, J., Álvarez, J.R. (eds) Artificial Intelligence and Knowledge Engineering Applications: A Bioinspired Approach. IWINAC 2005. Lecture Notes in Computer Science, vol 3562. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11499305_3
Download citation
DOI: https://doi.org/10.1007/11499305_3
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-26319-7
Online ISBN: 978-3-540-31673-2
eBook Packages: Computer ScienceComputer Science (R0)