A Heuristic for the Multidimensional 0-1 Knapsack Problem

This paper deals with the concepts of core and core problems for multidimensional 0-1 knapsack (MKP) problems. Core problems were introduced by Balas and Zemel (1980) and have been widely studied in the literature. The core refers to the seet of variables for which it is hard to decide what their value will be in an optimal solution; and the core problem is a reduction of the original problem in which only the core is considered, i.e. the variables with high (low) efficiency measures are fixed to 1(0). However, it is not obvious how to determine the efficiency function that yields efficiency measures for the MKP. In a study by Puchinger et al. (2010) an approximate core is generated by using the dual efficiency measures as an approximation of the efficiency function; and the corresponding approximate core problems are solved in order to obtain near optimal MKP solutions. In the same line of research we propose in this paper a different way of exploiting the concept of core. Instead of using dual efficiency measures, our exploitation tries to obtain a statistical approximation of the true efficiency function. Computational results on a large set of instances are presented.