求解推广k-CARD问题的一种变邻域搜索方法

k—CARD问题是在一个无向网络G中寻找一棵k条边的子树，使得这棵树的权和最小。目前有很多启发式算法用来解决这类NP难问题。一般的研究都只考虑点带权或边带权的k—CARD问题。将k-CARD问题进行推广，考虑边和点都带权的情况。该推广模型不仅统一了传统的边或点带权的问题，更重要的是，它在现实中有着一定的应用背景。针对推广模型的特点，提出了一种变邻域搜索（VNS）方法进行求解。数值实验结果表明此VNS方法求解推广k—CARD问题是有效的。

Variable Neighborhood Search for an Extended K-Cardinality Tree Problem

The minimum k -cardinality tree problem on graph G consists in finding a subtree of G with exactly k edges whose sum of weights is minimum. A number of heuristic methods have been developed recently to solve this NP-hard problem. In general, only vertex-weights or edge-weights are considered. In this paper, an extend- ed k-CARD problem is considered whose edges and vertex are both weighted. This extended model unifies vertex-weights and edge-weights problem, and more importantly, it has a certain application in practice. Based on the characteristics of this problem, a modified variable neighborhood search method （VNS） is proposed for solving it. Preliminary numerical results are reported, which show that this modified VNS method is effective for the extended k -CARD problem.