Local branching-based algorithm for the disjunctively constrained knapsack problem

In this paper, we propose to solve large-scale disjunctively constrained knapsack problem. We investigate the use of the rounding solution procedure and an effective local branching. The method can be viewed as a combination of two complementary stages: (i) a rounding solution stage and (ii) a restricted exact solution procedure. The method is analyzed computationally on a set of problem instances of the literature and the provided results are compared to the best solutions of the literature. For these instances, most of which cannot be solved to proven optimality in a reasonable runtime, the proposed method is able to improve several solution values of these instances.