The knapsack problem is one of the most studied problems in combinatorial optimization, with many real-life applications. For this reason, many special cases and generalizations have been examined.[1][2]
Common to all versions are a set of n items, with each item having an associated profit pj and weight wj. The binary decision variable xj is used to select the item. The objective is to pick some of the items, with maximal total profit, while obeying that the maximum total weight of the chosen items must not exceed W. Generally, these coefficients are scaled to become integers, and they are almost always assumed to be positive.
The knapsack problem in its most basic form:
maximize
subject to
^Martello, Silvano and Toth, Paolo (1990). Knapsack Problems: Algorithms and Computer Implementations. John Wiley & Sons. ISBN 978-0471924203.{{cite book}}: CS1 maint: multiple names: authors list (link)
^Cite error: The named reference KP-KPP was invoked but never defined (see the help page).
and 22 Related for: List of knapsack problems information
The knapsackproblem is one of the most studied problems in combinatorial optimization, with many real-life applications. For this reason, many special...
The knapsackproblem is the following problem in combinatorial optimization: Given a set of items, each with a weight and a value, determine which items...
case of the knapsackproblem and of the multiple subset sum problem. The run-time complexity of SSP depends on two parameters: n - the number of input...
the knapsackproblem. The problem can be formulated as an integer linear programming problem. A paper machine can produce an unlimited number of master...
optimization problems are the travelling salesman problem ("TSP"), the minimum spanning tree problem ("MST"), and the knapsackproblem. In many such problems, such...
to the problem in practice. There are algorithms for many NP-complete problems, such as the knapsackproblem, the traveling salesman problem, and the...
including a number of bin packing algorithms and test data. Martello, Silvano; Toth, Paolo (1990), "Bin-packing problem" (PDF), KnapsackProblems: Algorithms...
distributed multiple- variant of the knapsackproblem is as follows: given a set of items of varying volume and a set ofknapsacksof varying capacity, assign...
practical value for many hard problems. One of the examples of an approximate algorithm is the Knapsackproblem, where there is a set of given items. Its goal...
measures the quality of the represented solution. The fitness function is always problem-dependent. For instance, in the knapsackproblem one wants to maximize...
most convenient technique for parsing, for the knapsackproblem and other combinatorial optimization problems. It is also the program execution strategy used...
approximation is not always exact. A related problem is the partition problem, a variant of the knapsackproblem from operations research. Some weights are...
zag was listed on the Blue Mountains local government heritage register on 27 December 1991; while the adjacent Knapsack Viaduct was listed on the New...
for solving large knapsackproblems and which are used in almost every efficient algorithm for this type ofproblem. Other areas of Zemel's research include...
significant contributions in the areas ofknapsack and assignment problems, packing problems, and vehicle routing. As of 2023, he published 160 peer-reviewed...
Short integer solution (SIS) and ring-SIS problems are two average-case problems that are used in lattice-based cryptography constructions. Lattice-based...
tree problem (AWlCTP) Multiple knapsackproblem (MKP) Maximum independent set problem (MIS) Ant colony optimization (ACO) based optimization of 45 nm...
Rascal Does Not Dream of a Knapsack Kid, a third film adapting volume nine, premiered in December 2023. An anime adaptation of the University Student...
solve the problem in reasonable times in most cases. Similarly, algorithms can solve the NP-complete knapsackproblem over a wide range of sizes in less...
Judge–advisor system Knapsackproblem Land allocation decision support system Listof concept- and mind-mapping software Morphological analysis (problem-solving)...
Global Information
