Reduction strategies for the Cardinality Constrained Knapsack problem

Abstract

In the paper the Cardinality Constrained Knapsack Problem is considered. It is a variant of the Continuous Knapsack Problem in which no more than a specified number of variables are allowed to have positive values. This problem arises when a limited resource is allocated among competing activities, and an upper bound is imposed on the number of activities that can be selected in a solution. The Cardinality Constrained Knapsack Problem is NP-hard. We analyze the structural properties of its optimal solutions and propose procedure allowing to reduce the size of the original problem.