The core concept for the multidimensional knapsack problem

Authors:
Jakob Puchinger;Günther R. Raidl;Ulrich Pferschy
Affiliations:
Institute of Computer Graphics and Algorithms, Vienna University of Technology, Vienna, Austria;Institute of Computer Graphics and Algorithms, Vienna University of Technology, Vienna, Austria;Institute of Statistics and Operations Research, University of Graz, Austria
Venue:
EvoCOP'06 Proceedings of the 6th European conference on Evolutionary Computation in Combinatorial Optimization
Year:
2006

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Abstract

We present the newly developed core concept for the Multidimensional Knapsack Problem (MKP) which is an extension of the classical concept for the one-dimensional case. The core for the multidimensional problem is defined in dependence of a chosen efficiency function of the items, since no single obvious efficiency measure is available for MKP. An empirical study on the cores of widely-used benchmark instances is presented, as well as experiments with different approximate core sizes. Furthermore we describe a memetic algorithm and a relaxation guided variable neighborhood search for the MKP, which are applied to the original and to the core problems. The experimental results show that given a fixed run-time, the different metaheuristics as well as a general purpose integer linear programming solver yield better solution when applied to approximate core problems of fixed size.