A DC programming approach for solving multicast network design problems via the Nesterov smoothing technique
A DC programming approach for solving multicast network design problems via the Nesterov smoothing technique
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DOI：
10.1007/s10898-018-0671-9
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发表时间：
2017-09
影响因子：
1.8
通讯作者：
W. Geremew;N. M. Nam;Alexander Semenov;V. Boginski;E. Pasiliao
中科院分区：
文献类型：
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作者：
W. Geremew;N. M. Nam;Alexander Semenov;V. Boginski;E. Pasiliao
本文继续我们最近的努力，应用连续优化技术来研究最优多播通信网络模型的双层层次聚类问题。给定有限数量的节点，我们考虑两种不同的模型的组播网络，确定一定数量的节点作为集群中心，并在同一时间，定位一个特定的节点，作为一个总的中心，以最小化整个网络的总运输成本。聚类中心和总中心必须在给定节点之间的事实使得这些问题成为离散优化问题。我们的方法是将离散问题重新表述为连续问题，并将Nesterov的平滑逼近技术应用于作为距离测度的Minkowski规范。这种方法使我们能够提出两个可实现的基于DCA的算法来解决问题。数值结果和实际应用来说明我们的方法。
This paper continues our recent effort in applying continuous optimization techniques to study optimalmulticast communication networksmodeled as bilevel hierarchical clustering problems. Given a finite number of nodes, we consider two different models of multicast networks by identifying a certain number of nodes as cluster centers, and at the same time, locating a particular node that serves as a total center so as to minimize the total transportation cost throughout the network. The fact that the cluster centers and the total center have to be among the given nodes makes these problems discrete optimization problems. Our approach is to reformulate the discrete problems as continuous ones and to apply Nesterov’s smoothing approximation techniques on the Minkowski gauges that are used as distance measures. This approach enables us to propose two implementable DCA-based algorithms for solving the problems. Numerical results and practical applications are provided to illustrate our approach.