Models and Branch-and-Cut Algorithms for the Steiner Tree Problem with Revenues, Budget and Hop Constraints

被引：32

作者：

Costa, Alysson M. ^{[1
]}

Cordeau, Jean-Francois ^{[1
]}

Laporte, Gilbert ^{[1
]}

机构：

[1] HEC Montreal, Montreal, PQ H3T 2A7, Canada

来源：

NETWORKS | 2009年 / 53卷 / 02期

关键词：

prize collecting; network design; Steiner tree problem; budget; branch-and-cut; hop constraints; MINIMAL TREES; GRAPHS; FORMULATIONS; FACETS; REQUIREMENTS; POLYHEDRA; POLYTOPE;

D O I：

10.1002/net.20274

中图分类号：

TP3 [计算技术、计算机技术];

学科分类号：

0812 ;

摘要：

The Steiner tree problem with revenues, budget and hop constraints is a variant of the Steiner tree problem with two main modifications: (a) besides the costs associated with arcs, there are also revenues associated with the vertices, and (b) there are additional budget and hop constraints, which impose limits on the total cost of the network and on the number of edges between any vertex and the root, respectively. This article introduces and compares several mathematical models for this problem and describes two branch-and-cut algorithms, which solve to optimality instances with up to 500 vertices and 625 edges. (C) 2008 Wiley Periodicals, Inc. NETWORKS, Vol. 53(2), 141-159 2009

引用

页码：141 / 159

页数：19

共 41 条

[1]

[Anonymous], 2006, Handbook of Optimization in Telecommunications

[2]

BEASLEY JE, 1990, J OPER RES SOC, V41, P1069, DOI 10.2307/2582903

[3] A NOTE ON THE PRIZE COLLECTING TRAVELING SALESMAN PROBLEM [J].