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.

针对k个子集问题（kMIS）的最大交集，本文提出了一种反应式VNS元启发式方法。所述kMIS被定义为：给定一组元件，所述第一组的子集的家庭和整数ķ。问题包括找到k个子集，以便交集最大。我们的VNS元启发式方法结合了GRASP元启发式方法中使用的策略，例如GRASP构建阶段和反应式GRASP。两者均在摇动阶段用作VNS的反应成分。我们还提出了所谓的动态步长，这是增加VNS邻域的一种新方法。所有这些策略以及Skewed VNS，都已添加到我们针对kMIS的Reactive VNS算法中。计算结果表明，该新算法优于最新算法。