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A dynamic programming based reduction procedure for the multidimensional 0-1 knapsack problem

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  • Balev, Stefan
  • Yanev, Nicola
  • Freville, Arnaud
  • Andonov, Rumen

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  • Balev, Stefan & Yanev, Nicola & Freville, Arnaud & Andonov, Rumen, 2008. "A dynamic programming based reduction procedure for the multidimensional 0-1 knapsack problem," European Journal of Operational Research, Elsevier, vol. 186(1), pages 63-76, April.
    • Handle: RePEc:eee:ejores:v:186:y:2008:i:1:p:63-76
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    References listed on IDEAS

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    1. Frieze, A. M. & Clarke, M. R. B., 1984. "Approximation algorithms for the m-dimensional 0-1 knapsack problem: Worst-case and probabilistic analyses," European Journal of Operational Research, Elsevier, vol. 15(1), pages 100-109, January.
    2. Freville, A. & Plateau, G., 1986. "Heuristics and reduction methods for multiple constraints 0-1 linear programming problems," European Journal of Operational Research, Elsevier, vol. 24(2), pages 206-215, February.
    3. P. C. Gilmore & R. E. Gomory, 1966. "The Theory and Computation of Knapsack Functions," Operations Research, INFORMS, vol. 14(6), pages 1045-1074, December.
    4. A. Victor Cabot, 1970. "An Enumeration Algorithm for Knapsack Problems," Operations Research, INFORMS, vol. 18(2), pages 306-311, April.
    5. Soyster, A. L. & Lev, B. & Slivka, W., 1978. "Zero-one programming with many variables and few constraints," European Journal of Operational Research, Elsevier, vol. 2(3), pages 195-201, May.
    6. Richard Bellman, 1957. "On a Dynamic Programming Approach to the Caterer Problem--I," Management Science, INFORMS, vol. 3(3), pages 270-278, April.
    7. Shizuo Senju & Yoshiaki Toyoda, 1968. "An Approach to Linear Programming with 0-1 Variables," Management Science, INFORMS, vol. 15(4), pages 196-207, December.
    8. Hanafi, Said & Freville, Arnaud, 1998. "An efficient tabu search approach for the 0-1 multidimensional knapsack problem," European Journal of Operational Research, Elsevier, vol. 106(2-3), pages 659-675, April.
    9. A. M. Geoffrion, 1969. "An Improved Implicit Enumeration Approach for Integer Programming," Operations Research, INFORMS, vol. 17(3), pages 437-454, June.
    10. Egon Balas, 1967. "Discrete Programming by the Filter Method," Operations Research, INFORMS, vol. 15(5), pages 915-957, October.
    11. M. W. P. Savelsbergh, 1994. "Preprocessing and Probing Techniques for Mixed Integer Programming Problems," INFORMS Journal on Computing, INFORMS, vol. 6(4), pages 445-454, November.
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    Cited by:

    1. Diaz, Juan Esteban & Handl, Julia & Xu, Dong-Ling, 2018. "Integrating meta-heuristics, simulation and exact techniques for production planning of a failure-prone manufacturing system," European Journal of Operational Research, Elsevier, vol. 266(3), pages 976-989.
    2. Sabah Bushaj & İ. Esra Büyüktahtakın, 2024. "A K-means Supported Reinforcement Learning Framework to Multi-dimensional Knapsack," Journal of Global Optimization, Springer, vol. 89(3), pages 655-685, July.
    3. Cao, Chengxuan & Gao, Ziyou & Li, Keping, 2012. "Capacity allocation problem with random demands for the rail container carrier," European Journal of Operational Research, Elsevier, vol. 217(1), pages 214-221.
    4. Zahra Beheshti & Siti Shamsuddin & Siti Yuhaniz, 2013. "Binary Accelerated Particle Swarm Algorithm (BAPSA) for discrete optimization problems," Journal of Global Optimization, Springer, vol. 57(2), pages 549-573, October.
    5. Chiranjit Changdar & Rajat Kumar Pal & Ghanshaym Singha Mahapatra & Abhinandan Khan, 2020. "A genetic algorithm based approach to solve multi-resource multi-objective knapsack problem for vegetable wholesalers in fuzzy environment," Operational Research, Springer, vol. 20(3), pages 1321-1352, September.
    6. Liu, Yipeng & Koehler, Gary J., 2010. "Using modifications to Grover's Search algorithm for quantum global optimization," European Journal of Operational Research, Elsevier, vol. 207(2), pages 620-632, December.
    7. Yoon, Yourim & Kim, Yong-Hyuk & Moon, Byung-Ro, 2012. "A theoretical and empirical investigation on the Lagrangian capacities of the 0-1 multidimensional knapsack problem," European Journal of Operational Research, Elsevier, vol. 218(2), pages 366-376.
    8. Jakob Puchinger & Günther R. Raidl & Ulrich Pferschy, 2010. "The Multidimensional Knapsack Problem: Structure and Algorithms," INFORMS Journal on Computing, INFORMS, vol. 22(2), pages 250-265, May.

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