About this Journal Submit a Manuscript Table of Contents
Discrete Dynamics in Nature and Society
Volume 2013 (2013), Article ID 474852, 10 pages
http://dx.doi.org/10.1155/2013/474852
Research Article

A Memetic Lagrangian Heuristic for the 0-1 Multidimensional Knapsack Problem

1Future IT R&D Laboratory, LG Electronics Umyeon R&D Campus, 38 Baumoe-ro, Seocho-gu, Seoul 137-724, Republic of Korea
2Department of Computer Science and Engineering, Kwangwoon University, 20 Kwangwoon-ro, Nowon-gu, Seoul 139-701, Republic of Korea

Received 9 January 2013; Accepted 23 April 2013

Academic Editor: Xiaohui Liu

Copyright © 2013 Yourim Yoon and Yong-Hyuk Kim. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Linked References

  1. M. R. Garey and D. S. Johnson, Computers and Intractability: A Guide to the Theory of NP-Completeness, W. H. Freeman and Company, San Francisco, Calif, USA, 1979. View at MathSciNet
  2. R. Mansini and M. G. Speranza, “CORAL: an exact algorithm for the multidimensional knapsack problem,” INFORMS Journal on Computing, vol. 24, no. 3, pp. 399–415, 2012. View at Publisher · View at Google Scholar · View at MathSciNet
  3. S. Martello and P. Toth, “An exact algorithm for the two-constraint 0-1 knapsack problem,” Operations Research, vol. 51, no. 5, pp. 826–835, 2003. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  4. S. Boussier, M. Vasquez, Y. Vimont, S. Hanafi, and P. Michelon, “A multi-level search strategy for the 0-1 multidimensional knapsack problem,” Discrete Applied Mathematics, vol. 158, no. 2, pp. 97–109, 2010. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  5. V. Boyer, M. Elkihel, and D. El Baz, “Heuristics for the 0-1 multidimensional knapsack problem,” European Journal of Operational Research, vol. 199, no. 3, pp. 658–664, 2009. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  6. P. C. Chu and J. E. Beasley, “A genetic algorithm for the multidimensional Knapsack problem,” Journal of Heuristics, vol. 4, no. 1, pp. 63–86, 1998. View at Scopus
  7. F. Della Croce and A. Grosso, “Improved core problem based heuristics for the 0-1 multi-dimensional knapsack problem,” Computers & Operations Research, vol. 39, no. 1, pp. 27–31, 2012. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  8. K. Fleszar and K. S. Hindi, “Fast, effective heuristics for the 0-1 multi-dimensional knapsack problem,” Computers & Operations Research, vol. 36, no. 5, pp. 1602–1607, 2009. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  9. S. Hanafi and C. Wilbaut, “Improved convergent heuristics for the 0-1 multidimensional knapsack problem,” Annals of Operations Research, vol. 183, no. 1, pp. 125–142, 2011. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  10. M. J. Magazine and O. Oguz, “A heuristic algorithm for the multidimensional zero-one knapsack problem,” European Journal of Operational Research, vol. 16, no. 3, pp. 319–326, 1984. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  11. M. Vasquez and Y. Vimont, “Improved results on the 0-1 multidimensional knapsack problem,” European Journal of Operational Research, vol. 165, no. 1, pp. 70–81, 2005. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  12. Y. Vimont, S. Boussier, and M. Vasquez, “Reduced costs propagation in an efficient implicit enumeration for the 01 multidimensional knapsack problem,” Journal of Combinatorial Optimization, vol. 15, no. 2, pp. 165–178, 2008. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  13. Y. Yoon, Y.-H. Kim, and B.-R. Moon, “A theoretical and empirical investigation on the Lagrangian capacities of the 0-1 multidimensional knapsack problem,” European Journal of Operational Research, vol. 218, no. 2, pp. 366–376, 2012. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  14. C. Cotta and J. M. Troya, “A hybrid genetic algorithm for the 0-1 multiple knapsack problem,” in Artificial Neural Networks and Genetic Algorithms, G. D. Smith, N. C. Steele, and R. F. Albrecht, Eds., vol. 3, pp. 251–255, Springer, New york, NY, USA, 1997.
  15. J. Gottlieb, Evolutionary algorithms for constrained optimization problems [Ph.D. thesis], Department of Computer Science, Technical University of Clausthal, Clausthal, Germany, 1999.
  16. S. Khuri, T. Bäck, and J. Heitkötter, “The zero/one multiple knapsack problem and genetic algorithmspages,” in Proceedings of the ACM Symposium on Applied Computing, pp. 188–193, ACM Press, 1994.
  17. G. R. Raidl, “Improved genetic algorithm for the multiconstrained 0-1 knapsack problem,” in Proceedings of the IEEE International Conference on Evolutionary Computation (ICEC '98), pp. 207–211, May 1998. View at Scopus
  18. J. Thiel and S. Voss, “Some experiences on solving multiconstraint zero-one knapsack problems with genetic algorithms,” INFOR, vol. 32, no. 4, pp. 226–242, 1994.
  19. Y. Yoon, Y.-H. Kim, and B.-R. Moon, “An evolutionary Lagrangian method for the 0-1 multiple knapsack problem,” in Proceedings of the Genetic and Evolutionary Computation Conference (GECCO '05), pp. 629–635, June 2005. View at Scopus
  20. A. Fréville, “The multidimensional 0-1 knapsack problem: an overview,” European Journal of Operational Research, vol. 155, no. 1, pp. 1–21, 2004. View at Publisher · View at Google Scholar · View at MathSciNet
  21. A. Fréville and S. Hanafi, “The multidimensional 0-1 knapsack problem-bounds and computational aspects,” Annals of Operations Research, vol. 139, no. 1, pp. 195–227, 2005. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  22. H. Kellerer, U. Pferschy, and D. Pisinger, Knapsack Problems, Springer, Berlin, Germany, 2004. View at MathSciNet
  23. G. R. Raidl, “Weight-codings in a genetic algorithm for the multiconstraint knapsack problem,” in Proceedings of the Congress on Evolutionary Computation, vol. 1, pp. 596–603, 1999.
  24. M. L. Fisher, “The Lagrangian relaxation method for solving integer programming problems,” Management Science, vol. 27, no. 1, pp. 1–18, 1981. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  25. K. D. Boese, A. B. Kahng, and S. Muddu, “A new adaptive multi-start technique for combinatorial global optimizations,” Operations Research Letters, vol. 16, no. 2, pp. 101–113, 1994. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  26. T. Jones and S. Forrest, “Fitness distance correlation as a measure of problem difficulty for genetic algorithms,” in Proceedings of the 6th International Conference on Genetic Algorithms, pp. 184–192, 1995.
  27. Y.-H. Kim and B.-R. Moon, “Investigation of the fitness landscapes in graph bipartitioning: an empirical study,” Journal of Heuristics, vol. 10, no. 2, pp. 111–133, 2004. View at Publisher · View at Google Scholar · View at Scopus
  28. J. Puchinger, G. R. Raidl, and U. Pferschy, “The multidimensional knapsack problem: structure and algorithms,” INFORMS Journal on Computing, vol. 22, no. 2, pp. 250–265, 2010. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  29. J. E. Beasley, “Obtaining test problems via Internet,” Journal of Global Optimization, vol. 8, no. 4, pp. 429–433, 1996. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  30. Y. Yoon, Y.-H. Kim, A. Moraglio, and B.-R. Moon, “A theoretical and empirical study on unbiased boundary-extended crossover for real-valued representation,” Information Sciences, vol. 183, no. 1, pp. 48–65, 2012. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet