A new algorithm for the 0-1 knapsack problem
Management Science
Knapsack problems: algorithms and computer implementations
Knapsack problems: algorithms and computer implementations
Mathematical Programming: Series A and B
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STOC '98 Proceedings of the thirtieth annual ACM symposium on Theory of computing
A Polynomial Linear Search Algorithm for the n-Dimensional Knapsack Problem
Journal of the ACM (JACM)
Linear time algorithms for knapsack problems with bounded weights
Journal of Algorithms
Dynamic Programming and Strong Bounds for the 0-1 Knapsack Problem
Management Science
Core Problems in Knapsack Algorithms
Operations Research
Dynamic Programming
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Proceedings of the 9th annual conference on Genetic and evolutionary computation
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FAW '08 Proceedings of the 2nd annual international workshop on Frontiers in Algorithmics
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The accuracy of search heuristics: an empirical study on knapsack problems
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A heuristic approach for allocation of data to RFID tags: A data allocation knapsack problem (DAKP)
Computers and Operations Research
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Proceedings of the 13th annual conference on Genetic and evolutionary computation
Minimal Equivalent Binary Knapsack Inequalities
INFORMS Journal on Computing
A novel quantum inspired cuckoo search for knapsack problems
International Journal of Bio-Inspired Computation
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A two state reduction based dynamic programming algorithm for the bi-objective 0-1 knapsack problem
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International Journal of Bio-Inspired Computation
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Journal of Artificial Intelligence Research
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Journal of Computational and Applied Mathematics
Exact solution of the robust knapsack problem
Computers and Operations Research
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ACM Transactions on Software Engineering and Methodology (TOSEM)
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The knapsack problem is believed to be one of the "easier" NP-hard problems. Not only can it be solved in pseudo-polynomial time, but also decades of algorithmic improvements have made it possible to solve nearly all standard instances from the literature. The purpose of this paper is to give an overview of all recent exact solution approaches, and to show that the knapsack problem still is hard to solve for these algorithms for a variety of new test problems. These problems are constructed either by using standard benchmark instances with larger coefficients, or by introducing new classes of instances for which most upper bounds perform badly. The first group of problems challenge the dynamic programming algorithms while the other group of problems are focused towards branch-and-bound algorithms. Numerous computational experiments with all recent state-of-the-art codes are used to show that (KP) is still difficult to solve for a wide number of problems. One could say that the previous benchmark tests were limited to a few highly structured instances, which do not show the full characteristics of knapsack problems.