Advertisement

The PROBE Metaheuristic and Its Application to the Multiconstraint Knapsack Problem

  • Mousbah Barake
  • Pierre Chardaire
  • Geoff P. McKeown
Part of the Applied Optimization book series (APOP, volume 86)

Abstract

A new metaheuristic technique called PROBE is presented. The application of PROBE to the multiconstraint knapsack problem is described. Experimental results obtained using the resulting algorithm are compared with the results obtained by Chu and Beasley using a Genetic Algorithm.

Keywords

Metaheuristic PROBE OCTANE Multiconstraint knapsack problem Genetic algorithm. 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Bibliography

  1. R. Aboudi and K. Jörnsten. Tabu search for general zero-one integer programs using the pivot and complement heuristic. ORSA J. Computing, 6: 82–93, 1994.zbMATHCrossRefGoogle Scholar
  2. D. Avis and K. Fukada. A pivoting algorithm for convex hulls and vertex enumerationof arrangements and polyhedra. In Proceedings of the 7th ACM Symposium on Computational Geometry, pages 98–104. ACM, 1991.Google Scholar
  3. E. Balas. Integer programming and convex analysis: Intersection cuts from outer polars. Mathematical Programming, 2: 330–382, 1972.MathSciNetCrossRefGoogle Scholar
  4. E. Balas, S. Ceria, M. Dawande, F. Margot, and G. Pataki. OCTANE: a new heuristic for zero-one programs. Operations Research, 49: 207–225, 2001.MathSciNetzbMATHCrossRefGoogle Scholar
  5. E. Balas and C. H. Martin. Pivot and complement — A heuristic for zero-one programming. Management Science, 26: 86–96, 1980.MathSciNetzbMATHCrossRefGoogle Scholar
  6. J.E. Beasley. OR-Library: Distributing test problems by electronic mail. Journal of the Operational Research Society,41:1069–1072, 1990.http://mscmga.ms.ic.ac.uk/info.html.Google Scholar
  7. P. Chardaire, G. P. McKeown, and J. A. Maki. GRASP algorithms with path relinking and PROBE for the graph bisection problem. Manuscript, 2003a.Google Scholar
  8. R Chardaire, G. P. McKeown, and J. A. Maki. GRASP algorithms with path re-linking and PROBE for the multiconstraint knapsack problem. Manuscript, 2003b.Google Scholar
  9. R Chardaire, G.P. McKeown, and J. A. Maki. Application of GRASP to the 0–1 multiple knapsack problem. In E. J. W. Boers, editor, Applications of Evolutionary Computing, pages 30–39. Springer-Verlag LNCS 2037, 2001.Google Scholar
  10. P. C. Chu and J. E. Beasley. A genetic algorithm for the multidimensional knapsack problem. Journal of Heuristics, 4 (1): 63–86, 1998.zbMATHCrossRefGoogle Scholar
  11. C. Cotta and J. M. Troya. A hybrid genetic algorithm for the 0–1 multiple knapsack problem. In G. D. Smith, N. C. Steele, and R. F. Albrecht, editors, Artificial neural nets and genetic algorithms 3, pages 251–255. Springer-Verlag, 1998.Google Scholar
  12. B. Gavish and H. Pirkul. Efficient algorithms for solving multiconstraint zero-one knapsack problems to optimality. Mathematical Programming, 31: 78–105, 1985.MathSciNetzbMATHCrossRefGoogle Scholar
  13. F. Glover. Surrogate constraint duality in mathematical programming. Operations Research, 23 (3): 434–453, 1975.MathSciNetzbMATHCrossRefGoogle Scholar
  14. H. J. Greenberg and W.P. Pierskalla. Surrogate mathematical programming. Operations Research, 18: 924–939, 1970.MathSciNetzbMATHCrossRefGoogle Scholar
  15. S. Martello and P. Toth. Knapsack Problems: Algorithms and Computer Implementations. Wiley, 1990.Google Scholar
  16. Z. Michalwicz. Genetic Algorithms + Data Structures = Evolution Programs. Springer-Verlag, 1996.Google Scholar
  17. H. Pirkul. A heuristic solution procedure for the multiconstraint zero-one knapsack problem. Naval Research Logistics, 34: 161–172, 1987.zbMATHCrossRefGoogle Scholar
  18. G.R. Raidi. An improved genetic algorithm for the multiconstrained 0–1 knapsack problem. In Proceedings of the 5th IEEE International Conference on Evolutionary Computation, pages 207–211. IEEE, 1998.Google Scholar
  19. W. Shih. A branch and bound method for the multiconstraint zero-one knapsack problem. J. of the Operational Research Society, 30: 369–378, 1979.zbMATHGoogle Scholar

Copyright information

© Springer Science+Business Media New York 2003

Authors and Affiliations

  • Mousbah Barake
    • 1
  • Pierre Chardaire
    • 2
  • Geoff P. McKeown
    • 2
  1. 1.ColchesterUK
  2. 2.School of Information SystemsUniversity of East AngliaNorwichUK

Personalised recommendations