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Discrete Dynamics in Nature and Society
Volume 2013 (2013), Article ID 474852, 10 pages
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.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
- 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.
- J. Gottlieb, Evolutionary algorithms for constrained optimization problems [Ph.D. thesis], Department of Computer Science, Technical University of Clausthal, Clausthal, Germany, 1999.
- 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.
- 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.
- 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.
- 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.
- A. Fréville, “The multidimensional 0-1 knapsack problem: an overview,” European Journal of Operational Research, vol. 155, no. 1, pp. 1–21, 2004.
- 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.
- H. Kellerer, U. Pferschy, and D. Pisinger, Knapsack Problems, Springer, Berlin, Germany, 2004.
- 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.
- M. L. Fisher, “The Lagrangian relaxation method for solving integer programming problems,” Management Science, vol. 27, no. 1, pp. 1–18, 1981.
- 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.
- 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.
- 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.
- 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.
- J. E. Beasley, “Obtaining test problems via Internet,” Journal of Global Optimization, vol. 8, no. 4, pp. 429–433, 1996.
- 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.