Everything about Continuous knapsack problem
Algorithmic problem in computer science
In theoretical computer science, the continuous knapsack problem is an algorithmic problem in combinatorial optimization in which the goal is to fill a container fractional amounts of different materials chosen to maximize the value of the selected materials. It is a variation of the classic knapsack problem, in which the items to be placed in the container are indivisible; however, the continuous knapsack problem may be solved in polynomial time whereas the classic knapsack problem is NP-hard. It is a classic example of how a seemingly small change in the formulation of a problem can have a large impact on its computational complexity. Wikipedia →
🧭 Start here: a 6-step reading path
- Read the overview: Continuous knapsack problemA 5-minute orientation
- Skim a recent paper: The robust bilevel continuous knapsack problem with uncertain coefficients in the follower’s objectiveInfluential work since 2022
- Pick up a classic book: MetaheuristicsThe most-reprinted book on the subject
- Read the landmark paper: The 0-1 Knapsack problem with a single continuous variableCited 83 times
- Go sideways: Knapsack problemA closely related topic
- Go sideways: Linear programming relaxationA closely related topic
📖 Definitions
No dictionary entry for this exact phrase.
🗂️ The subject at a glance
🏆 Landmark papers (most cited)
The 0-1 Knapsack problem with a single continuous variable
Breakpoint searching algorithms for the continuous quadratic knapsack problem
On the continuous quadratic knapsack problem
A Newton’s method for the continuous quadratic knapsack problem
Variable Fixing Algorithms for the Continuous Quadratic Knapsack Problem
Iterative semi-continuous relaxation heuristics for the multiple-choice multidimensional knapsack problem
On Linear-Time Algorithms for the Continuous Quadratic Knapsack Problem
On a nonseparable convex maximization problem with continuous knapsack constraints
🆕 Influential since 2022
The robust bilevel continuous knapsack problem with uncertain coefficients in the follower’s objective
The Stochastic Bilevel Continuous Knapsack Problem with Uncertain Follower’s Objective
A combinatorial algorithm for inverse continuous quadratic knapsack problem
Variable fixing method by weighted average for the continuous quadratic knapsack problem
Continuous linear knapsack problems revisited
📚 Books worth reading
MetaheuristicsMauricio G. C. Resende, Jorge Pinho de Sousa · 2004
Recent Trends in Applied Artificial IntelligenceMoonis Ali · 2013
Ranked by number of editions on Open Library, a rough measure of how lasting a book is.
🔗 Related topics
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- Quadratic knapsack problem The quadratic knapsack problem (QKP), first introduced in 19th century, is an extension of knapsack problem that allows for quadratic terms in the objective…
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