An exact algorithm for the multiple-choice multidimensional knapsack based on the core

Abstract

In this paper, we propose a branch and bound algorithm to solve the multiple-choice multidimensional knapsack problem. The branch and bound tree is arranged based on the orderings in the core and navigated in a depth first manner, which while consuming low memory effectively causes the core to be expanded by need. We use Osorio's mixed constraint and the linear programming solution of the surrogated problem for bounding tests. The computational results and comparison with the previous best exact algorithm shows that the algorithm has significant performance improvement over the previous algorithm. © 2008 Springer-Verlag.