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What (who) is manually operated knapsack - definition
![multiple constrained problem]] could consider both the weight and volume of the boxes. <br />(Solution: if any number of each box is available, then three yellow boxes and three grey boxes; if only the shown boxes are available, then all except for the green box.)](https://commons.wikimedia.org/wiki/Special:FilePath/Knapsack.svg?width=200 "multiple constrained problem]] could consider both the weight and volume of the boxes. <br />(Solution: if any number of each box is available, then three yellow boxes and three grey boxes; if only the shown boxes are available, then all except for the green box.)")
![A ROV's suction device about to capture a specimen of the deep sea octopus ''[[Cirroteuthis muelleri]]''](https://commons.wikimedia.org/wiki/Special:FilePath/Cirroteuthis muelleri.jpg?width=200 "A ROV's suction device about to capture a specimen of the deep sea octopus ''[[Cirroteuthis muelleri]]''")
![A [[Royal Navy]] ROV (''Cutlet'') first used in the 1950s to retrieve practice torpedoes and mines](https://commons.wikimedia.org/wiki/Special:FilePath/Cutletrov.jpg?width=200 "A [[Royal Navy]] ROV (''Cutlet'') first used in the 1950s to retrieve practice torpedoes and mines")
![NOAAS ''Okeanos Explorer'']]](https://commons.wikimedia.org/wiki/Special:FilePath/Deep Discoverer (51816198671).jpg?width=200 "NOAAS ''Okeanos Explorer'']]")
![Image taken by a ROV of [[krill]] feeding on [[ice algae]] in [[Antarctica]].](https://commons.wikimedia.org/wiki/Special:FilePath/Krillicekils.jpg?width=200 "Image taken by a ROV of [[krill]] feeding on [[ice algae]] in [[Antarctica]].")
![oceanographic]] research vessel.](https://commons.wikimedia.org/wiki/Special:FilePath/ROV Hercules 2005.JPG?width=200 "oceanographic]] research vessel.")
, retrieves a mine neutralization vehicle (MNV) after the device conducted an underwater water mine survey.jpg?width=200 "AN/SLQ-48 Mine Neutralization Vehicle")
Wikipedia
The knapsack problem is the following problem in combinatorial optimization:
- Given a set of items, each with a weight and a value, determine which items to include in the collection so that the total weight is less than or equal to a given limit and the total value is as large as possible.
It derives its name from the problem faced by someone who is constrained by a fixed-size knapsack and must fill it with the most valuable items. The problem often arises in resource allocation where the decision-makers have to choose from a set of non-divisible projects or tasks under a fixed budget or time constraint, respectively.
The knapsack problem has been studied for more than a century, with early works dating as far back as 1897. The name "knapsack problem" dates back to the early works of the mathematician Tobias Dantzig (1884–1956), and refers to the commonplace problem of packing the most valuable or useful items without overloading the luggage.
