Reactive VNS algorithm for the maximum k-subset intersection problem

This paper proposes a reactive VNS metaheuristic for the maximum intersection of k -subsets problem (kMIS). The kMIS is defined as: Given a set of elements, a subset family of the first set and an integer k . The problem consists of finding k subset so that the intersection is maximum. Our VNS metaheuristic incorporates strategies used in GRASP metaheuristics, such as the GRASP construction phase and the Reactive GRASP. Both were used in the shaking phase as a reactive components to VNS. We also propose what we call teh Dynamic Step, a new way to increase the VNS neighborhood. All of these strategies, as well as the Skewed VNS, were added to our Reactive VNS algorithm for kMIS. Computational results showed that the new algorithm outperforms the state-of-the-art algorithm.