IDEAS home Printed from https://ideas.repec.org/a/eee/ejores/v155y2004i1p1-21.html
   My bibliography  Save this article

The multidimensional 0-1 knapsack problem: An overview

Author

Listed:
  • Freville, Arnaud

Abstract

No abstract is available for this item.

Suggested Citation

  • Freville, Arnaud, 2004. "The multidimensional 0-1 knapsack problem: An overview," European Journal of Operational Research, Elsevier, vol. 155(1), pages 1-21, May.
    • Handle: RePEc:eee:ejores:v:155:y:2004:i:1:p:1-21
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0377-2217(03)00274-1
    Download Restriction: Full text for ScienceDirect subscribers only
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. James H. Lorie & Leonard J. Savage, 1955. "Three Problems in Rationing Capital," The Journal of Business, University of Chicago Press, vol. 28, pages 229-229.
    2. 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.
    3. 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.
    4. Michael J. Magazine & Maw-Sheng Chern, 1984. "A Note on Approximation Schemes for Multidimensional Knapsack Problems," Mathematics of Operations Research, INFORMS, vol. 9(2), pages 244-247, May.
    5. Magazine, M. J. & Oguz, Osman, 1981. "A fully polynomial approximation algorithm for the 0-1 knapsack problem," European Journal of Operational Research, Elsevier, vol. 8(3), pages 270-273, November.
    6. 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.
    7. Fred Glover, 1989. "Tabu Search---Part I," INFORMS Journal on Computing, INFORMS, vol. 1(3), pages 190-206, August.
    8. Egon Balas & Clarence H. Martin, 1980. "Pivot and Complement--A Heuristic for 0-1 Programming," Management Science, INFORMS, vol. 26(1), pages 86-96, January.
    9. Sanjiv Sarin & Mark H. Karwan & Ronald L. Rardin, 1987. "A new surrogate dual multiplier search procedure," Naval Research Logistics (NRL), John Wiley & Sons, vol. 34(3), pages 431-450, June.
    10. Bruce H. Faaland & Frederick S. Hillier, 1979. "Interior Path Methods for Heuristic Integer Programming Procedures," Operations Research, INFORMS, vol. 27(6), pages 1069-1087, December.
    11. Roberto Battiti & Giampietro Tecchiolli, 1994. "The Reactive Tabu Search," INFORMS Journal on Computing, INFORMS, vol. 6(2), pages 126-140, May.
    12. M. E. Dyer & A. M. Frieze, 1989. "Probabilistic Analysis of the Multidimensional Knapsack Problem," Mathematics of Operations Research, INFORMS, vol. 14(1), pages 162-176, February.
    13. Barcia, Paulo & Holm, Soren, 1988. "A revised bound improvement sequence algorithm," European Journal of Operational Research, Elsevier, vol. 36(2), pages 202-206, August.
    14. Raymond R. Hill & Charles H. Reilly, 2000. "The Effects of Coefficient Correlation Structure in Two-Dimensional Knapsack Problems on Solution Procedure Performance," Management Science, INFORMS, vol. 46(2), pages 302-317, February.
    15. Pisinger, David, 1995. "An expanding-core algorithm for the exact 0-1 knapsack problem," European Journal of Operational Research, Elsevier, vol. 87(1), pages 175-187, November.
    16. ,, 1999. "Problems And Solutions," Econometric Theory, Cambridge University Press, vol. 15(3), pages 427-432, June.
    17. Michael Held & Richard M. Karp, 1970. "The Traveling-Salesman Problem and Minimum Spanning Trees," Operations Research, INFORMS, vol. 18(6), pages 1138-1162, December.
    18. P. C. Gilmore & R. E. Gomory, 1966. "The Theory and Computation of Knapsack Functions," Operations Research, INFORMS, vol. 14(6), pages 1045-1074, December.
    19. Kwak, Wikil & Shi, Yong & Lee, Heeseok & Lee, Cheng F., 1996. "Capital Budgeting with Multiple Criteria and Multiple Decision Makers," Review of Quantitative Finance and Accounting, Springer, vol. 7(1), pages 97-112, July.
    20. Magazine, M. J. & Oguz, Osman, 1984. "A heuristic algorithm for the multidimensional zero-one knapsack problem," European Journal of Operational Research, Elsevier, vol. 16(3), pages 319-326, June.
    21. Marshall L. Fisher, 1980. "Worst-Case Analysis of Heuristic Algorithms," Management Science, INFORMS, vol. 26(1), pages 1-17, January.
    22. A. M. Geoffrion, 1969. "An Improved Implicit Enumeration Approach for Integer Programming," Operations Research, INFORMS, vol. 17(3), pages 437-454, June.
    23. Laguna, Manuel & Kelly, James P. & Gonzalez-Velarde, JoseLuis & Glover, Fred, 1995. "Tabu search for the multilevel generalized assignment problem," European Journal of Operational Research, Elsevier, vol. 82(1), pages 176-189, April.
    24. Stelios H. Zanakis, 1977. "Heuristic 0-1 Linear Programming: An Experimental Comparison of Three Methods," Management Science, INFORMS, vol. 24(1), pages 91-104, September.
    25. Lokketangen, Arne & Glover, Fred, 1998. "Solving zero-one mixed integer programming problems using tabu search," European Journal of Operational Research, Elsevier, vol. 106(2-3), pages 624-658, April.
    26. ,, 1999. "Problems And Solutions," Econometric Theory, Cambridge University Press, vol. 15(4), pages 629-637, August.
    27. Clifford C. Petersen, 1967. "Computational Experience with Variants of the Balas Algorithm Applied to the Selection of R&D Projects," Management Science, INFORMS, vol. 13(9), pages 736-750, May.
    28. Freville, Arnaud & Plateau, Gerard, 1993. "An exact search for the solution of the surrogate dual of the 0-1 bidimensional knapsack problem," European Journal of Operational Research, Elsevier, vol. 68(3), pages 413-421, August.
    29. ,, 1999. "Problems And Solutions," Econometric Theory, Cambridge University Press, vol. 15(5), pages 777-788, October.
    30. Yoshiaki Toyoda, 1975. "A Simplified Algorithm for Obtaining Approximate Solutions to Zero-One Programming Problems," Management Science, INFORMS, vol. 21(12), pages 1417-1427, August.
    31. Szkatula, Krzysztof, 1994. "The growth of multi-constraint random knapsacks with various right-hand sides of the constraints," European Journal of Operational Research, Elsevier, vol. 73(1), pages 199-204, February.
    32. ,, 1999. "Problems And Solutions," Econometric Theory, Cambridge University Press, vol. 15(1), pages 151-160, February.
    33. David Pisinger, 2000. "A Minimal Algorithm for the Bounded Knapsack Problem," INFORMS Journal on Computing, INFORMS, vol. 12(1), pages 75-82, February.
    34. Ellis L. Johnson & George L. Nemhauser & Martin W.P. Savelsbergh, 2000. "Progress in Linear Programming-Based Algorithms for Integer Programming: An Exposition," INFORMS Journal on Computing, INFORMS, vol. 12(1), pages 2-23, February.
    35. Egon Balas, 1967. "Discrete Programming by the Filter Method," Operations Research, INFORMS, vol. 15(5), pages 915-957, October.
    36. G. L. Nemhauser & Z. Ullmann, 1969. "Discrete Dynamic Programming and Capital Allocation," Management Science, INFORMS, vol. 15(9), pages 494-505, May.
    37. A. Victor Cabot, 1970. "An Enumeration Algorithm for Knapsack Problems," Operations Research, INFORMS, vol. 18(2), pages 306-311, April.
    38. Charles E. Gearing & William W. Swart & Turgut Var, 1973. "Determining the Optimal Investment Policy for the Tourism Sector of a Developing Country," Management Science, INFORMS, vol. 20(4-Part-I), pages 487-497, December.
    39. Richard Loulou & Eleftherios Michaelides, 1979. "New Greedy-Like Heuristics for the Multidimensional 0-1 Knapsack Problem," Operations Research, INFORMS, vol. 27(6), pages 1101-1114, December.
    40. Silvano Martello & Paolo Toth, 1988. "A New Algorithm for the 0-1 Knapsack Problem," Management Science, INFORMS, vol. 34(5), pages 633-644, May.
    41. Schilling, Kenneth E., 1990. "The growth of m-constraint random knapsacks," European Journal of Operational Research, Elsevier, vol. 46(1), pages 109-112, May.
    42. Frederick S. Hillier, 1969. "Efficient Heuristic Procedures for Integer Linear Programming with an Interior," Operations Research, INFORMS, vol. 17(4), pages 600-637, August.
    43. Kurt Spielberg, 1969. "Algorithms for the Simple Plant-Location Problem with Some Side Conditions," Operations Research, INFORMS, vol. 17(1), pages 85-111, February.
    44. Kurt Spielberg, 1969. "Plant Location with Generalized Search Origin," Management Science, INFORMS, vol. 16(3), pages 165-178, November.
    45. 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.
    46. Hugh Everett, 1963. "Generalized Lagrange Multiplier Method for Solving Problems of Optimum Allocation of Resources," Operations Research, INFORMS, vol. 11(3), pages 399-417, June.
    47. Seymour Kaplan, 1966. "Solution of the Lorie-Savage and Similar Integer Programming Problems by the Generalized Lagrange Multiplier Method," Operations Research, INFORMS, vol. 14(6), pages 1130-1136, December.
    48. Helga Meier & Nicos Christofides & Gerry Salkin, 2001. "Capital Budgeting Under Uncertainty---An Integrated Approach Using Contingent Claims Analysis and Integer Programming," Operations Research, INFORMS, vol. 49(2), pages 196-206, April.
    49. WOLSEY, Laurence A., 1980. "Heuristic analysis, linear programming and branch and bound," LIDAM Reprints CORE 407, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    50. 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.
    51. Mark H. Karwan & Ronald L. Rardin, 1984. "Surrogate Dual Multiplier Search Procedures in Integer Programming," Operations Research, INFORMS, vol. 32(1), pages 52-69, February.
    52. Eugene L. Lawler, 1979. "Fast Approximation Algorithms for Knapsack Problems," Mathematics of Operations Research, INFORMS, vol. 4(4), pages 339-356, November.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Otto, Alena & Li, Xiyu, 2020. "Product sequencing in multiple-piece-flow assembly lines," Omega, Elsevier, vol. 91(C).
    2. Nils Boysen & Simon Emde & Malte Fliedner, 2016. "The basic train makeup problem in shunting yards," OR Spectrum: Quantitative Approaches in Management, Springer;Gesellschaft für Operations Research e.V., vol. 38(1), pages 207-233, January.
    3. Paola Cappanera & Marco Trubian, 2005. "A Local-Search-Based Heuristic for the Demand-Constrained Multidimensional Knapsack Problem," INFORMS Journal on Computing, INFORMS, vol. 17(1), pages 82-98, February.
    4. Bahram Alidaee & Vijay P. Ramalingam & Haibo Wang & Bryan Kethley, 2018. "Computational experiment of critical event tabu search for the general integer multidimensional knapsack problem," Annals of Operations Research, Springer, vol. 269(1), pages 3-19, October.
    5. Wu, Jigang & Srikanthan, Thambipillai & Yan, Chengbin, 2008. "Algorithmic aspects for power-efficient hardware/software partitioning," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 79(4), pages 1204-1215.
    6. Bas, Esra, 2011. "An investment plan for preventing child injuries using risk priority number of failure mode and effects analysis methodology and a multi-objective, multi-dimensional mixed 0-1 knapsack model," Reliability Engineering and System Safety, Elsevier, vol. 96(7), pages 748-756.
    7. Yuji Nakagawa & Ross J. W. James & César Rego & Chanaka Edirisinghe, 2014. "Entropy-Based Optimization of Nonlinear Separable Discrete Decision Models," Management Science, INFORMS, vol. 60(3), pages 695-707, March.
    8. Boyer, V. & Elkihel, M. & El Baz, D., 2009. "Heuristics for the 0-1 multidimensional knapsack problem," European Journal of Operational Research, Elsevier, vol. 199(3), pages 658-664, December.
    9. Yalçın Akçay & Haijun Li & Susan Xu, 2007. "Greedy algorithm for the general multidimensional knapsack problem," Annals of Operations Research, Springer, vol. 150(1), pages 17-29, March.
    10. João Claro & Jorge Sousa, 2010. "A multiobjective metaheuristic for a mean-risk static stochastic knapsack problem," Computational Optimization and Applications, Springer, vol. 46(3), pages 427-450, July.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Arnaud Fréville & SaÏd Hanafi, 2005. "The Multidimensional 0-1 Knapsack Problem—Bounds and Computational Aspects," Annals of Operations Research, Springer, vol. 139(1), pages 195-227, October.
    2. 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.
    3. Dimitris Bertsimas & Ramazan Demir, 2002. "An Approximate Dynamic Programming Approach to Multidimensional Knapsack Problems," Management Science, INFORMS, vol. 48(4), pages 550-565, April.
    4. 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.
    5. 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.
    6. Paola Cappanera & Marco Trubian, 2005. "A Local-Search-Based Heuristic for the Demand-Constrained Multidimensional Knapsack Problem," INFORMS Journal on Computing, INFORMS, vol. 17(1), pages 82-98, February.
    7. Raymond R. Hill & Charles H. Reilly, 2000. "The Effects of Coefficient Correlation Structure in Two-Dimensional Knapsack Problems on Solution Procedure Performance," Management Science, INFORMS, vol. 46(2), pages 302-317, February.
    8. Yalçın Akçay & Haijun Li & Susan Xu, 2007. "Greedy algorithm for the general multidimensional knapsack problem," Annals of Operations Research, Springer, vol. 150(1), pages 17-29, March.
    9. Wilbaut, Christophe & Salhi, Saïd & Hanafi, Saïd, 2009. "An iterative variable-based fixation heuristic for the 0-1 multidimensional knapsack problem," European Journal of Operational Research, Elsevier, vol. 199(2), pages 339-348, December.
    10. 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.
    11. Syam Menon & Ali Amiri, 2004. "Scheduling Banner Advertisements on the Web," INFORMS Journal on Computing, INFORMS, vol. 16(1), pages 95-105, February.
    12. Krzysztof S. Targiel & Maciej Nowak & Tadeusz Trzaskalik, 2018. "Scheduling non-critical activities using multicriteria approach," Central European Journal of Operations Research, Springer;Slovak Society for Operations Research;Hungarian Operational Research Society;Czech Society for Operations Research;Österr. Gesellschaft für Operations Research (ÖGOR);Slovenian Society Informatika - Section for Operational Research;Croatian Operational Research Society, vol. 26(3), pages 585-598, September.
    13. Okitonyumbe Y.F., Joseph & Ulungu, Berthold E.-L., 2013. "Nouvelle caractérisation des solutions efficaces des problèmes d’optimisation combinatoire multi-objectif [New characterization of efficient solution in multi-objective combinatorial optimization]," MPRA Paper 66123, University Library of Munich, Germany.
    14. Amit Kumar & Anila Gupta, 2013. "Mehar’s methods for fuzzy assignment problems with restrictions," Fuzzy Information and Engineering, Springer, vol. 5(1), pages 27-44, March.
    15. Monica Motta & Caterina Sartori, 2020. "Normality and Nondegeneracy of the Maximum Principle in Optimal Impulsive Control Under State Constraints," Journal of Optimization Theory and Applications, Springer, vol. 185(1), pages 44-71, April.
    16. Chenchen Wu & Dachuan Xu & Donglei Du & Wenqing Xu, 2016. "An approximation algorithm for the balanced Max-3-Uncut problem using complex semidefinite programming rounding," Journal of Combinatorial Optimization, Springer, vol. 32(4), pages 1017-1035, November.
    17. Uzma Ashraf & Hassan Ali & Muhammad Nawaz Chaudry & Irfan Ashraf & Adila Batool & Zafeer Saqib, 2016. "Predicting the Potential Distribution of Olea ferruginea in Pakistan incorporating Climate Change by Using Maxent Model," Sustainability, MDPI, vol. 8(8), pages 1-11, July.
    18. World Bank, 2003. "Argentina : Reforming Policies and Institutions for Efficiency and Equity of Public Expenditures," World Bank Publications - Reports 14637, The World Bank Group.
    19. Brown, Jeffrey R., 2001. "Private pensions, mortality risk, and the decision to annuitize," Journal of Public Economics, Elsevier, vol. 82(1), pages 29-62, October.
    20. Mark Christensen, 2007. "What We Might Know (But Aren't Sure) About Public-Sector Accrual Accounting," Australian Accounting Review, CPA Australia, vol. 17(41), pages 51-65, March.

    More about this item

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:ejores:v:155:y:2004:i:1:p:1-21. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/locate/eor .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.