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The Theory and Computation of Knapsack Functions

Citations

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  1. Hifi, Mhand & Paschos, Vangelis Th. & Zissimopoulos, Vassilis, 2004. "A simulated annealing approach for the circular cutting problem," European Journal of Operational Research, Elsevier, vol. 159(2), pages 430-448, December.
  2. Silva, Elsa & Oliveira, José Fernando & Silveira, Tiago & Mundim, Leandro & Carravilla, Maria Antónia, 2023. "The Floating-Cuts model: a general and flexible mixed-integer programming model for non-guillotine and guillotine rectangular cutting problems," Omega, Elsevier, vol. 114(C).
  3. François Vanderbeck, 2001. "A Nested Decomposition Approach to a Three-Stage, Two-Dimensional Cutting-Stock Problem," Management Science, INFORMS, vol. 47(6), pages 864-879, June.
  4. Y-J Seong & Y-G G & M-K Kang & C-W Kang, 2004. "An improved branch and bound algorithm for a strongly correlated unbounded knapsack problem," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 55(5), pages 547-552, May.
  5. Manuel Laguna, 1998. "Applying Robust Optimization to Capacity Expansion of One Location in Telecommunications with Demand Uncertainty," Management Science, INFORMS, vol. 44(11-Part-2), pages 101-110, November.
  6. Mhand Hifi & Catherine Roucairol, 2001. "Approximate and Exact Algorithms for Constrained (Un) Weighted Two-dimensional Two-staged Cutting Stock Problems," Journal of Combinatorial Optimization, Springer, vol. 5(4), pages 465-494, December.
  7. Sbihi, Abdelkader, 2010. "A cooperative local search-based algorithm for the Multiple-Scenario Max-Min Knapsack Problem," European Journal of Operational Research, Elsevier, vol. 202(2), pages 339-346, April.
  8. Dimitris Bertsimas & Ramazan Demir, 2002. "An Approximate Dynamic Programming Approach to Multidimensional Knapsack Problems," Management Science, INFORMS, vol. 48(4), pages 550-565, April.
  9. Steiner, Erich & McKinnon, Ken, 2000. "Dynamic programming using the Fritz-John conditions," European Journal of Operational Research, Elsevier, vol. 123(1), pages 145-153, May.
  10. Ben Messaoud, Said & Chu, Chengbin & Espinouse, Marie-Laure, 2008. "Characterization and modelling of guillotine constraints," European Journal of Operational Research, Elsevier, vol. 191(1), pages 112-126, November.
  11. M Hifi & M Michrafy, 2006. "A reactive local search-based algorithm for the disjunctively constrained knapsack problem," Journal of the Operational Research Society, Palgrave Macmillan;The OR Society, vol. 57(6), pages 718-726, June.
  12. de Armas, Jesica & Miranda, Gara & León, Coromoto, 2012. "Improving the efficiency of a best-first bottom-up approach for the Constrained 2D Cutting Problem," European Journal of Operational Research, Elsevier, vol. 219(2), pages 201-213.
  13. Andonov, R. & Poirriez, V. & Rajopadhye, S., 2000. "Unbounded knapsack problem: Dynamic programming revisited," European Journal of Operational Research, Elsevier, vol. 123(2), pages 394-407, June.
  14. 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.
  15. 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.
  16. Deane, Jason & Agarwal, Anurag, 2012. "Scheduling online advertisements to maximize revenue under variable display frequency," Omega, Elsevier, vol. 40(5), pages 562-570.
  17. Russo, Mauro & Sforza, Antonio & Sterle, Claudio, 2013. "An improvement of the knapsack function based algorithm of Gilmore and Gomory for the unconstrained two-dimensional guillotine cutting problem," International Journal of Production Economics, Elsevier, vol. 145(2), pages 451-462.
  18. Yanhong Feng & Hongmei Wang & Zhaoquan Cai & Mingliang Li & Xi Li, 2023. "Hybrid Learning Moth Search Algorithm for Solving Multidimensional Knapsack Problems," Mathematics, MDPI, vol. 11(8), pages 1-28, April.
  19. Suliman, Saad M. A., 2001. "Pattern generating procedure for the cutting stock problem," International Journal of Production Economics, Elsevier, vol. 74(1-3), pages 293-301, December.
  20. Song, X. & Chu, C.B. & Nie, Y.Y. & Bennell, J.A., 2006. "An iterative sequential heuristic procedure to a real-life 1.5-dimensional cutting stock problem," European Journal of Operational Research, Elsevier, vol. 175(3), pages 1870-1889, December.
  21. Becker, Henrique & Buriol, Luciana S., 2019. "An empirical analysis of exact algorithms for the unbounded knapsack problem," European Journal of Operational Research, Elsevier, vol. 277(1), pages 84-99.
  22. Wang, Danni & Xiao, Fan & Zhou, Lei & Liang, Zhe, 2020. "Two-dimensional skiving and cutting stock problem with setup cost based on column-and-row generation," European Journal of Operational Research, Elsevier, vol. 286(2), pages 547-563.
  23. Chen, C. S. & Lee, S. M. & Shen, Q. S., 1995. "An analytical model for the container loading problem," European Journal of Operational Research, Elsevier, vol. 80(1), pages 68-76, January.
  24. Suliman, S.M.A., 2006. "A sequential heuristic procedure for the two-dimensional cutting-stock problem," International Journal of Production Economics, Elsevier, vol. 99(1-2), pages 177-185, February.
  25. 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.
  26. David Pisinger, 2000. "A Minimal Algorithm for the Bounded Knapsack Problem," INFORMS Journal on Computing, INFORMS, vol. 12(1), pages 75-82, February.
  27. Igor Kierkosz & Maciej Łuczak, 2019. "A one-pass heuristic for nesting problems," Operations Research and Decisions, Wroclaw University of Science and Technology, Faculty of Management, vol. 29(1), pages 37-60.
  28. Onur Tavaslıoğlu & Oleg A. Prokopyev & Andrew J. Schaefer, 2019. "Solving Stochastic and Bilevel Mixed-Integer Programs via a Generalized Value Function," Operations Research, INFORMS, vol. 67(6), pages 1659-1677, November.
  29. Mhand Hifi & Slim Sadfi, 2002. "The Knapsack Sharing Problem: An Exact Algorithm," Journal of Combinatorial Optimization, Springer, vol. 6(1), pages 35-54, March.
  30. Fayard, Didier & Zissimopoulos, Vassilis, 1995. "An approximation algorithm for solving unconstrained two-dimensional knapsack problems," European Journal of Operational Research, Elsevier, vol. 84(3), pages 618-632, August.
  31. Vinay Dharmadhikari, 1975. "Decision-Stage Method: Convergence Proof, Special Application, and Computation Experience," NBER Working Papers 0094, National Bureau of Economic Research, Inc.
  32. 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.
  33. Raka Jovanovic & Stefan Voß, 2024. "Matheuristic fixed set search applied to the multidimensional knapsack problem and the knapsack problem with forfeit sets," OR Spectrum: Quantitative Approaches in Management, Springer;Gesellschaft für Operations Research e.V., vol. 46(4), pages 1329-1365, December.
  34. Kunikazu Yoda & András Prékopa, 2016. "Convexity and Solutions of Stochastic Multidimensional 0-1 Knapsack Problems with Probabilistic Constraints," Mathematics of Operations Research, INFORMS, vol. 41(2), pages 715-731, May.
  35. Mhand Hifi & Hedi Mhalla & Slim Sadfi, 2005. "Sensitivity of the Optimum to Perturbations of the Profit or Weight of an Item in the Binary Knapsack Problem," Journal of Combinatorial Optimization, Springer, vol. 10(3), pages 239-260, November.
  36. Freville, Arnaud, 2004. "The multidimensional 0-1 knapsack problem: An overview," European Journal of Operational Research, Elsevier, vol. 155(1), pages 1-21, May.
  37. Song, X. & Chu, C.B. & Lewis, R. & Nie, Y.Y. & Thompson, J., 2010. "A worst case analysis of a dynamic programming-based heuristic algorithm for 2D unconstrained guillotine cutting," European Journal of Operational Research, Elsevier, vol. 202(2), pages 368-378, April.
  38. Vera Neidlein & Andrèa C. G. Vianna & Marcos N. Arenales & Gerhard Wäscher, 2008. "The Two-Dimensional, Rectangular, Guillotineable-Layout Cutting Problem with a Single Defect," FEMM Working Papers 08035, Otto-von-Guericke University Magdeburg, Faculty of Economics and Management.
  39. Lamanna, Leonardo & Mansini, Renata & Zanotti, Roberto, 2022. "A two-phase kernel search variant for the multidimensional multiple-choice knapsack problem," European Journal of Operational Research, Elsevier, vol. 297(1), pages 53-65.
  40. Hoto, Robinson & Arenales, Marcos & Maculan, Nelson, 2007. "The one dimensional Compartmentalised Knapsack Problem: A case study," European Journal of Operational Research, Elsevier, vol. 183(3), pages 1183-1195, December.
  41. Oliver Bastert & Benjamin Hummel & Sven de Vries, 2010. "A Generalized Wedelin Heuristic for Integer Programming," INFORMS Journal on Computing, INFORMS, vol. 22(1), pages 93-107, February.
  42. Reinaldo Morabito & Vitória Pureza, 2010. "A heuristic approach based on dynamic programming and and/or-graph search for the constrained two-dimensional guillotine cutting problem," Annals of Operations Research, Springer, vol. 179(1), pages 297-315, September.
  43. Gomory, Ralph, 2016. "Origin and early evolution of corner polyhedra," European Journal of Operational Research, Elsevier, vol. 253(3), pages 543-556.
  44. Marco A. Boschetti & Vittorio Maniezzo & Francesco Strappaveccia, 2016. "Using GPU Computing for Solving the Two-Dimensional Guillotine Cutting Problem," INFORMS Journal on Computing, INFORMS, vol. 28(3), pages 540-552, August.
  45. Wei, Lijun & Lim, Andrew, 2015. "A bidirectional building approach for the 2D constrained guillotine knapsack packing problem," European Journal of Operational Research, Elsevier, vol. 242(1), pages 63-71.
  46. Mohammad Sabbagh & Richard Soland, 2009. "An improved partial enumeration algorithm for integer programming problems," Annals of Operations Research, Springer, vol. 166(1), pages 147-161, February.
  47. Hifi, Mhand, 1997. "The DH/KD algorithm: a hybrid approach for unconstrained two-dimensional cutting problems," European Journal of Operational Research, Elsevier, vol. 97(1), pages 41-52, February.
  48. Nicolas Fröhlich & Stefan Ruzika, 2022. "Interdicting facilities in tree networks," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 30(1), pages 95-118, April.
  49. Setzer, Thomas & Blanc, Sebastian M., 2020. "Empirical orthogonal constraint generation for Multidimensional 0/1 Knapsack Problems," European Journal of Operational Research, Elsevier, vol. 282(1), pages 58-70.
  50. Celia Glass & Jeroen Oostrum, 2010. "Bun splitting: a practical cutting stock problem," Annals of Operations Research, Springer, vol. 179(1), pages 15-33, September.
  51. 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.
  52. Chia‐Shin Chung & Ming S. Hung & Walter O. Rom, 1988. "A hard knapsack problem," Naval Research Logistics (NRL), John Wiley & Sons, vol. 35(1), pages 85-98, February.
  53. Mhand Hifi, 2004. "Dynamic Programming and Hill-Climbing Techniques for Constrained Two-Dimensional Cutting Stock Problems," Journal of Combinatorial Optimization, Springer, vol. 8(1), pages 65-84, March.
  54. 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.
  55. Wilbaut, Christophe & Todosijevic, Raca & Hanafi, Saïd & Fréville, Arnaud, 2023. "Heuristic and exact reduction procedures to solve the discounted 0–1 knapsack problem," European Journal of Operational Research, Elsevier, vol. 304(3), pages 901-911.
  56. Huang, Ping H. & Lawley, Mark & Morin, Thomas, 2011. "Tight bounds for periodicity theorems on the unbounded Knapsack problem," European Journal of Operational Research, Elsevier, vol. 215(2), pages 319-324, December.
  57. Sławomir Bąk & Jacek Błażewicz & Grzegorz Pawlak & Maciej Płaza & Edmund K. Burke & Graham Kendall, 2011. "A Parallel Branch-and-Bound Approach to the Rectangular Guillotine Strip Cutting Problem," INFORMS Journal on Computing, INFORMS, vol. 23(1), pages 15-25, February.
  58. Parada Daza, Victor & Gomes de Alvarenga, Arlindo & de Diego, Jose, 1995. "Exact solutions for constrained two-dimensional cutting problems," European Journal of Operational Research, Elsevier, vol. 84(3), pages 633-644, August.
  59. Yuen, Boon J., 1995. "Improved heuristics for sequencing cutting patterns," European Journal of Operational Research, Elsevier, vol. 87(1), pages 57-64, November.
  60. Ralph E. Gomory, 2002. "Early Integer Programming," Operations Research, INFORMS, vol. 50(1), pages 78-81, February.
  61. Joni L. Jones & Gary J. Koehler, 2005. "A Heuristic for Winner Determination in Rule-Based Combinatorial Auctions," INFORMS Journal on Computing, INFORMS, vol. 17(4), pages 475-489, November.
  62. Hifi, Mhand & M'Hallah, Rym, 2006. "Strip generation algorithms for constrained two-dimensional two-staged cutting problems," European Journal of Operational Research, Elsevier, vol. 172(2), pages 515-527, July.
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