Solving the Multidimensional Knapsack Problem Using an Evolutionary Algorithm Hybridized with Branch and Bound

  • José E. Gallardo
  • Carlos Cotta
  • Antonio J. Fernández
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3562)


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.


Genetic Algorithm Evolutionary Algorithm Search Tree Hybrid Algorithm Knapsack Problem 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Lawler, E., Wood, D.: Branch and bounds methods: A survey. Operations Research 4, 669–719 (1966)MathSciNetGoogle Scholar
  2. 2.
    Bäck, T.: Evolutionary Algorithms in Theory and Practice. Oxford University Press, New York (1996)zbMATHGoogle Scholar
  3. 3.
    Bäck, T., Fogel, D., Michalewicz, Z.: Handbook of Evolutionary Computation. Oxford University Press, New York (1997)zbMATHCrossRefGoogle Scholar
  4. 4.
    Davis, L.: Handbook of Genetic Algorithms. Van Nostrand Reinhold, New York (1991)Google Scholar
  5. 5.
    Wolpert, D., Macready, W.: No free lunch theorems for optimization. IEEE Transactions on Evolutionary Computation 1, 67–82 (1997)CrossRefGoogle Scholar
  6. 6.
    Culberson, J.: On the futility of blind search: An algorithmic view of no free lunch. Evolutionary Computation 6, 109–128 (1998)CrossRefGoogle Scholar
  7. 7.
    Garey, M., Johnson, D.: Computers and Intractability: A Guide to the Theory of NP-Completeness. Freeman and Co, San Francisco (1979)zbMATHGoogle Scholar
  8. 8.
    Salkin, H., Mathur, K.: Foundations of Integer Programming. North-Holland, Amsterdam (1989)zbMATHGoogle Scholar
  9. 9.
    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)CrossRefGoogle Scholar
  10. 10.
    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) 251–255Google Scholar
  11. 11.
    Chu, P.C., Beasley, J.E.: A genetic algorithm for the multidimensional knapsack problem. Journal of Heuristics 4, 63–86 (1998)zbMATHCrossRefGoogle Scholar
  12. 12.
    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)CrossRefGoogle Scholar
  13. 13.
    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)Google Scholar
  14. 14.
    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)Google Scholar
  15. 15.
    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)zbMATHCrossRefMathSciNetGoogle Scholar
  16. 16.
    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)CrossRefGoogle Scholar
  17. 17.
    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)zbMATHCrossRefGoogle Scholar
  18. 18.
    Cotta, C., Troya, J.: Embedding branch and bound within evolutionary algorithms. Applied Intelligence 18, 137–153 (2003)zbMATHCrossRefGoogle Scholar
  19. 19.
    Beasley, J.: Or-library: distributing test problems by electronic mail. Journal of the Operational Research Society 41, 1069–1072 (1990)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2005

Authors and Affiliations

  • José E. Gallardo
    • 1
  • Carlos Cotta
    • 1
  • Antonio J. Fernández
    • 1
  1. 1.Dept. Lenguajes y Ciencias de la Computación, ETSI InformáticaUniversity of MálagaMálagaSpain

Personalised recommendations