An efficient algorithm for the collapsing knapsack problem

The collapsing knapsack problem (CKP) is a type of nonlinear knapsack problem in which the knapsack size is a non-increasing function of the number of items included. This paper proposes an exact algorithm for CKP by partitioning CKP to some subproblems, then solving them with the improved expanding-core technique. The proposed algorithm solves the subproblems in the special processing order resulting in the reduction of computing time. Experimental results show that the proposed algorithm is an efficient approach for various random instances of size up to 1000.