Abstract
Abstract This paper presents an efficient algorithm for the general (as opposed to the binary) knapsack problem. The algorithm generates tight bounds on the variables from the LP relaxation of the problem which give the optimal values of most of the variables very quickly. A branch-and-bound procedure is then employed to solve the remaining reduced problem. Extensive computatonal tests have confirmed the efficiency of this approach for a wide variety of problems with as many as 5000 variables.
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