The generalized minimum spanning tree problem: Polyhedral analysis and branch‐and‐cut algorithm
The generalized minimum spanning tree problem: Polyhedral analysis and branch‐and‐cut algorithm
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广义最小生成树问题：多面体分析和分支割算法
作者：
C. Feremans;M. Labbé;G. Laporte
提出了一种求解广义最小生成树问题(GMSTP)的分支割算法。给定一个无向图，它的顶点集被划分成簇，GMSTP包括确定一棵最小代价树，其中每个簇恰好包含一个顶点。GMSTP的应用在电信领域遇到。给出了一个整数线性规划公式，发展了一类新的有效的不等式，其中几个被证明是刻面定义的。提出了分枝切割算法和禁忌搜索启发式算法。大量的计算实验表明，根据边成本是欧几里得的还是随机的，涉及多达160或200个顶点的实例可以求解到最优。©2004威利期刊公司。
This article presents a branch‐and‐cut algorithm for the Generalized Minimum Spanning Tree Problem (GMSTP). Given an undirected graph whose vertex set is partitioned into clusters, the GMSTP consists of determining a minimum‐cost tree including exactly one vertex per cluster. Applications of the GMSTP are encountered in telecommunications. An integer linear programming formulation is presented and new classes of valid inequalities are developed, several of which are proved to be facet‐defining. A branch‐and‐cut algorithm and a tabu search heuristic are developed. Extensive computational experiments show that instances involving up to 160 or 200 vertices can be solved to optimality, depending on whether edge costs are Euclidean or random. © 2004 Wiley Periodicals, Inc.