An algorithm for determining the K-best solutions of the one-dimensional Knapsack problem

Abstract

In this work we present an enumerative scheme for determining the K-best solutions (K > 1) of the one dimensional knapsack problem. If n is the total number of different items and b is the knapsack's capacity, the computational complexity of the proposed scheme is bounded by O(Knb) with memory requirements bounded by O(nb). The algorithm was implemented in a workstation and computational tests for varying values of the parameters were performed.