The knapsack problem is a problem in combinatorial optimization: Given a set of items, each with a weight and a value, determine the number of each item to include in a 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.
Basic solutions to the knapsack problems with a high enough given number of items can take a very long time to compute. This is where genetic algorithms come into play. These algorithms produce random generation, where crossover and mutations of solutions take place, and then using a fitness function passes on the best solutions to next generation (in nature this is known as natural selection) to repeat the same on the new population till the time we hit the number of generation limit or achieve the fitness score expected from it.