Dynamic programming algorithms, efficient solution of the LP-relaxation and approximation schemes for the Penalized Knapsack Problem

Abstract

We consider the 0–1 Penalized Knapsack Problem (PKP). Each item has a profit, a weight and a penalty and the goal is to maximize the sum of the profits minus the greatest penalty value of the items included in a solution. We propose an exact approach relying on a procedure which narrows the relevant range of penalties, on the identification of a core… (More)

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