The classical knapsack problem is defined as follows: We are given a set of n items, . Using this concept, Pisinger  introduced a dynamic programming. Thirteen years have passed since the seminal book on knapsack problems by Martello and Toth appeared. On this occasion a former colleague exclaimed back . The knapsack problem is believed to be one of the “easier” NP-hard D. Pisinger/Computers & Operations Research 32 () –
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On this occasion a former colleague exclaimed back in References Publications referenced by this paper.
Knapsack problem Search for additional papers on this topic. 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. Optimizing VM allocation and data placement for data-intensive applications in cloud using ACO metaheuristic algorithm T. Thirteen years have passed since the seminal book on knapsack problems by Martello and Toth appeared.
Maringer Limited preview – Hence, two years ago the idea arose to produce a new monograph covering not only the most recent developments of the standard knapsack problem, but also giving a comprehensive treatment of the whole knapsack family including the siblings such as the subset sum problem and the bounded and unbounded knapsack problem, and also more distant relatives such as multidimensional, multiple, multiple-choice and quadratic knapsack problems in dedicated chapters.
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Are Lower Bounds Easier over the Reals? However, in the last decade a large number of research publications contributed new results for the knapsack problem in all areas of interest such as exact algorithms, heuristics and approximation schemes.
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.
Where are the hard knapsack problems? – Semantic Scholar
Showing of extracted citations. Moreover, the extension of the knapsack problem to higher dimensions both in the number pisingerr constraints and in the num ber of knapsacks, as well as the modification of the problem structure concerning the available item set and the objective function, leads to a number of interesting variations of practical relevance which were the subject of intensive research during the last few years.
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Showing of 16 references. A time-varying transfer function for balancing the exploration and exploitation ability of a binary PSO Md. Where probkems the hard knapsack problems? Knapsack problem Dynamic programming Branch and bound Pseudo-polynomial time.
Where are the hard knapsack problems?