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

The most e¢cient algorithms for solving single criterion {0,1}-knapsack problems are based on the core concept and the core problem. However, those concepts remain unnoticed in the multiple criteria case. In this paper we bring them to this topic. A large amount of e¢cient solutions are considered for analysing the importance of the core itself and the core problem. The results show that the properties of the core in single criterion experiments are also observed in the solutions of the bi-criteria problem. These observations are used to derive a simple but e¤ective method for solving the bi-criteria {0,1}-knapsack problem. Key-words: Bi-criteria knapsack problem, Core problem, Exact methods, Combinatorial optimization ¤Corresponding author yVisiting Researcher (January-February, 2004) at the Operational Research Department, London School of Economics, Houghton Street, London WC2A 2AE, U.K.