(1966), “The theory and computation of knapsack functions”, Operations Research, 14, 1045–1074. (1980), “A Reduction Algorithm for Knapsack Problems”, Methods of Operations Research, 36, 49–60. (1957), Dynamic programming, Princeton Univ. ![]() (1980): “An Algorithm for Large Zero-One Knapsack Problems”, Operations Research, 28, 1130–1154.īellman, R.E. This process is experimental and the keywords may be updated as the learning algorithm improves.īalas, E., Zemel, E. These keywords were added by machine and not by the authors. Computational experiments are presented, showing that the presented algorithm out-performs all previously published algorithms for BKP. ![]() Compared to other algorithms for BKP, the presented algorithm uses tighter reductions and enumerates considerably less item types. Sorting and reduction is done by need, resulting in very little effort for the preprocessing. To avoid these problems, a specialized algorithm is proposed which solves an expanding core problem through dynamic programming, such that the number of enumerated item types is minimal. However this paper demonstrates, that the transformation introduces many similar weighted items, resulting in very hard instances of the 0–1 Knapsack Problem. The currently most efficient algorithm for BKP transforms the data instance to an equivalent 0–1 Knapsack Problem, which is solved efficiently through a specialized algorithm. ![]() The Bounded Knapsack Problem (BKP) is a generalization of the 0–1 Knapsack Problem where a bounded amount of each item type is available.
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