Advertisement

A New Grouping Genetic Algorithm for the Quadratic Multiple Knapsack Problem

  • Alok Singh
  • Anurag Singh Baghel
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4446)

Abstract

The quadratic multiple knapsack problem is an extension of the well known 0/1 multiple knapsack problem. In the quadratic multiple knapsack problem, profit values are associated not only with individual objects but also with pairs of objects. Profit value associated with a pair of objects is added to the overall profit if both objects of the pair belong to the same knapsack. Being an extension of the 0/1 multiple knapsack problem, this problem is also NP-Hard. In this paper, we have proposed a new steady-state grouping genetic algorithm for the quadratic multiple knapsack problem and compared our results with two recently proposed methods – a genetic algorithm and a stochastic hill climber. The results show the effectiveness of our approach.

Keywords

Combinatorial optimization grouping genetic algorithm  knapsack problem quadratic multiple knapsack problem.  

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Garey, M.R., Johnson, D.S.: Computers and Intractability: A Guide to the Theory of NP-Completeness. W.H. Freeman, San Francisco (1979)zbMATHGoogle Scholar
  2. 2.
    Khuri, S., Bäck, T., Heitkötter, J.: The Zero/One Multiple Knapsack Problem and Genetic Algorithms. In: Proceedings of the 1994 ACM Symposium on Applied Computing, pp. 188–193. ACM Press, New York (1994)CrossRefGoogle Scholar
  3. 3.
    Cotta, C., Troya, J.M.: A Hybrid Genetic Algorithm for the 0-1 Multiple Knapsack Problem. In: Artificial Neural Networks and Genetic algorithms, vol. 3, pp. 250–254. Springer, Berlin (1998)Google Scholar
  4. 4.
    Yoon, Y., Kim, Y.H., Moon, B.R.: An Evolutionary Lagrangian Method for the 0/1 Multiple Knapsack Problem. In: Proceedings of the GECCO-2005, pp. 629–635. ACM Press, New York (2005)CrossRefGoogle Scholar
  5. 5.
    Hiley, A., Julstrom, B.A.: The Quadratic Multiple Knapsack Problem and Three Heuristic Approaches to it. In: Proceedings of the GECCO-2006, pp. 547–552. ACM Press, New York (2006)CrossRefGoogle Scholar
  6. 6.
    Falkenauer, E.: New Representations and Operators for GAs Applied to Grouping Problems. Evolutionary Computation 2, 123–144 (1992)Google Scholar
  7. 7.
    Falkenauer, E.: Genetic Algorithms and Grouping Problems. John Wiley & Sons, Chicester (1998)Google Scholar
  8. 8.
    Davis, L.: Handbook of Genetic Algorithms. Van Nostrand Reinhold, New York (1991)Google Scholar
  9. 9.
    Singh, A., Gupta, A.K.: Two Heuristics for the One-Dimensional Bin-Packing Problem. To appear in OR-Spectrum (2007)Google Scholar

Copyright information

© Springer Berlin Heidelberg 2007

Authors and Affiliations

  • Alok Singh
    • 1
  • Anurag Singh Baghel
    • 2
  1. 1.J. K. Institute of Applied Physics and Technology, Faculty of Science, University of Allahabad, Allahabad – 211002, UPIndia
  2. 2.Department of Electronics and Communication, Banasthali Vidyapith Jaipur Campus, Sarojini Marg, Jaipur – 302001, RajasthanIndia

Personalised recommendations