Core problems in bi-criteria {0,1}{0,1}-knapsack problems

The most efficient algorithms for solving the single-criterion {0,1}{0,1}-knapsack problem are based on the core concept (i.e., based on a small number of relevant variables). But this concept is not used in problems with more than one criterion. The main purpose of this paper is to validate the existence of such a set of variables in bi-criteria {0–1}{0–1}-knapsack instances. Numerical experiments were performed on five types of {0,1}{0,1}-knapsack instances. The results are presented for the supported and non-supported solutions as well as for the entire set of efficient solutions. A description of an approximate and an exact method is also presented.