A decomposition approach for solving a broadcast domination network design problem

作     者：Shen, Siqian Smith, J. Cole 

作者机构：Univ Florida Dept Ind & Syst Engn Gainesville FL 32611 USA 

出 版 物：《ANNALS OF OPERATIONS RESEARCH》 (运筹学纪事)

年 卷 期：2013年第210卷第1期

页      面：333-360页

核心收录：

学科分类：1201[管理学-管理科学与工程(可授管理学、工学学位)] 07[理学] 070104[理学-应用数学] 0701[理学-数学] 

基　　金：Air Force Office of Scientific Research [FA9550-07-1-0404, FA9550-08-1-0189] Defense Threat Reduction Agency [HDTRA1-10-1-0050] 

主　　题：Broadcast domination Integer programming Benders decomposition Cutting-plane algorithms 

摘      要：We consider an optimization problem that integrates network design and broadcast domination decisions. Given an undirected graph, a feasible broadcast domination is a set of nonnegative integer powers f (i) assigned to each node i, such that for any node j in the graph, there exists some node k having a positive f (k) -value whose shortest distance to node j is no more than f (k) . The cost of a broadcast domination solution is the sum of all node power values. The network design problem constructs edges that decrease the minimum broadcast domination cost on the graph. The overall problem we consider minimizes the sum of edge construction costs and broadcast domination costs. We show that this problem is NP-hard in the strong sense, even on unweighted graphs. We then propose a decomposition strategy, which iteratively adds valid inequalities based on optimal broadcast domination solutions corresponding to the first-stage network design solutions. We demonstrate that our decomposition approach is computationally far superior to the solution of a single large-scale mixed-integer programming formulation.