![]() A number of specialized algorithms are developed. This has motivated some researchers to develop specialized algorithms for particular hard problems.This thesis considers a number of hard Knapsack Problems with a single constraint. For example, subset sum and strongly correlated data types. However, a number of hard knapsack instances have been identified. For some types of data instances, very efficient algorithms have been found. The classical 0-1Knapsack Problem arises when there is one knapsack and one item of each type.Knapsack Problems have been intensively studied over the past forty years because of their direct application to problems arising in industry (for example, cargo loading, cutting stock, and budget control) and also for their contribution to the solution methods for integer programming problems.Several exact algorithms based on branch and bound and dynamic programming have been proposed to solve the Knapsack Problems. The specific problem that arises depends on the number of knapsacks (single or multiple) to be filled and on the number of available items of each type (bounded or unbounded). ![]() Problems in this class are typically concerned with selecting from a set of given items, each with a specified weight and value, a subset of items whose weight sum does not exceed a prescribed capacity and whose value is maximum. ![]() The Knapsack Problems are among the simplest integer programs which are NP-hard.
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