Determining the K-best solutions of knapsack problems

It is well‐known that knapsack problems arise as subproblems of a number of large‐scale integer optimization problems. In order to solve these large problems, it is necessary to solve the subproblems efficiently, and for many of them it can be useful to determine the K‐best solutions. In this paper, a branch‐and‐bound method for the unbounded knapsack problem described in the literature is extended to determine the K‐best solutions of unbounded and bounded knapsack problems. We show that the proposed extension determines exactly the K‐best solutions and we solve important classical instances using high values of K.