New hybrid matheuristics for solving the multidimensional knapsack problem

Abstract

In this paper we propose new hybrid methods for solving the multidimensional knapsack problem. They can be viewed as matheuristics that combine mathematical programming with the variable neighbourhood decomposition search heuristic. In each iteration a relaxation of the problem is solved to guide the generation of the neighbourhoods. Then the problem is enriched with a pseudo-cut to produce a sequence of not only lower, but also upper bounds of the problem, so that integrality gap is reduced. The results obtained on two sets of the large scale multidimensional knapsack problem instances are comparable with the current state-of-the-art heuristics. Moreover, a few best known results are reported for some large, long-studied instances.