Knapsack problem

Known as: Unbounded knapsack problem, Binary knapsack problem, BKP 
The knapsack problem or rucksack problem is a problem in combinatorial optimization: Given a set of items, each with a weight and a value, determine… (More)
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1967-2017
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Approximation algorithmBaby-step giant-stepBacktrackingBin packing problem
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Dynamic programmingOperations research

Related mentions per year

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1936-2019
19401960198020002020
Knapsack problem
Approximation algorithm
Genetic algorithm
Optimization problem
Computational complexity theory
Computer science

Papers overview

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Highly Cited
2005
Highly Cited
2005
Improved results on the 0-1 multidimensional knapsack problem
Geometric Constraint and Cutting planes have been successfully used to solve the 0–1 multidimensional knapsack problem. Our… (More)
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Highly Cited
2004
Highly Cited
2004
Approximating the stochastic knapsack problem: the benefit of adaptivity
We consider a stochastic variant of the NP-hard 0/1 knapsack problem in which item values are deterministic and item sizes are… (More)
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Highly Cited
1999
Highly Cited
1999
The 0-1 Knapsack problem with a single continuous variable
Constraints arising in practice often contain many 0-1 variables and one or a small number of continuous variables. Existing… (More)
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Highly Cited
1998
Highly Cited
1998
A Genetic Algorithm for the Multidimensional Knapsack Problem
In this paper we present a heuristic based upon genetic algorithms for the multidimensional knapsack problem. A heuristic… (More)
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Highly Cited
1994
Highly Cited
1994
The zero/one multiple knapsack problem and genetic algorithms
A genetic algorithm, GENEsYs, is applied to an NP-complele problem, the 0/1 multiple knapsack problem. The partitioning of the… (More)
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Highly Cited
1993
Highly Cited
1993
A PTAS for the Multiple Knapsack Problem
item in the big bin and obtains a profit of 1 while OPT = 2. This also shows that ordering bins in non-increasing capacities does… (More)
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Highly Cited
1989
Highly Cited
1989
The stochastic knapsack problem
Considered is a knapsack with integer volume Fand which is capable of holding K different classes of objects. An object from… (More)
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Highly Cited
1975
Highly Cited
1975
Fast Approximation Algorithms for the Knapsack and Sum of Subset Problems
Given a positive integer M and n pairs of positive integers (p~, cD, , (p. , c.), maximize the s u m ~ ~p~ subject to the cons t… (More)
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Highly Cited
1975
Highly Cited
1975
Approximate Algorithms for the 0/1 Knapsack Problem
A serms of increasingly accurate algorithms to obtain approximate solutions to the 0/1 one-dlmensmnal knapsack problem :s… (More)
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Highly Cited
1974
Highly Cited
1974
Computing Partitions with Applications to the Knapsack Problem
Given <italic>r</italic> numbers <italic>s</italic><subscrpt>1</subscrpt>, ···, <italic>s<subscrpt>r</subscrpt></italic… (More)
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