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The multidimensional 0–1 knapsack problem: An overview
European Journal of Operational Research, 2004zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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A New Algorithm for the 0-1 Knapsack Problem
Management Science, 1988We present a new algorithm for the optimal solution of the 0-1 Knapsack problem, which is particularly effective for large-size problems. The algorithm is based on determination of an appropriate small subset of items and the solution of the corresponding “core problem”: from this we derive a heuristic solution for the original problem which, with ...
Silvano Martello, Paolo Toth
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A Minimal Algorithm for the 0-1 Knapsack Problem
Operations Research, 1997Several types of large-sized 0-1 Knapsack Problems (KP) may be easily solved, but in such cases most of the computational effort is used for sorting and reduction. In order to avoid this problem it has been proposed to solve the so-called core of the problem: a Knapsack Problem defined on a small subset of the variables. The exact core cannot, however,
David Pisinger
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2021
In this chapter, we design conventional and syntactical circuits for the 0/1 knapsack problem, describe two cost functions for the syntactical circuit, evaluate the number of operations and the time required by the algorithms for the optimization and counting, discuss an example, and show experimental results.
Michal Mankowski, Mikhail Moshkov
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In this chapter, we design conventional and syntactical circuits for the 0/1 knapsack problem, describe two cost functions for the syntactical circuit, evaluate the number of operations and the time required by the algorithms for the optimization and counting, discuss an example, and show experimental results.
Michal Mankowski, Mikhail Moshkov
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The Collapsing 0–1 Knapsack Problem
Mathematical Programming, 1978The "Collapsing 0---1 Knapsack Problem" is a type of non-linear knapsack problem in which the knapsack size is a non-increasing function of the number of items included. An algorithm is developed and computational results included.
Posner, Marc E., Guignard, Monique
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Multivariable Branching: A 0-1 Knapsack Problem Case Study
INFORMS Journal on Computing, 2021We explore the benefits of multivariable branching schemes for linear-programming-based branch-and-bound algorithms for the 0-1 knapsack problem—that is, the benefits of branching on sets of variables rather than on a single variable (the current default in integer-programming solvers).
Yu Yang +2 more
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Matroidal relaxations for 0–1 knapsack problems
Operations Research Letters, 1993zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Amado, Lígia, Barcia, Paulo
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Adjacency of the 0–1 knapsack problem
Computers & Operations Research, 1992zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Geist, Daniel, Rodin, Ervin Y.
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An algorithm for 0‐1 multiple‐knapsack problems
Naval Research Logistics Quarterly, 1978AbstractThe 0‐1 multiple‐knapsack problem is an extension of the well‐known 0‐1 knapsack problem. It is a problem of assigning m objects, each having a value and a weight, to n knapsacks in such a way that the total weight in each knapsack is less than its capacity limit and the total value in the knapsacks is maximized.A branch‐and‐bound algorithm for
Hung, Ming S., Fisk, John C.
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Linear programming for the 0–1 quadratic knapsack problem
European Journal of Operational Research, 1996zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Billionnet, Alain, Calmels, Frédéric
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