Relay Placement for Maximum Flow Rate via Learning and Optimization Over Riemannian Manifolds
Relay Placement for Maximum Flow Rate via Learning and Optimization Over Riemannian Manifolds
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DOI：
10.1109/tmlcn.2023.3309772
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发表时间：
2023
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影响因子：
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通讯作者：
Imtiaz Nasim;A. Ibrahim
中科院分区：
文献类型：
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作者：
Imtiaz Nasim;A. Ibrahim
网络拓扑可以在黎曼流形上表示（即，曲面），给出它们的谱图的对称正定（SPD）性质。此外，通过中继放置来最大化基线网络拓扑的流率可以等效于找到最大化测地距离的中继位置（即，黎曼流形上的中继辅助网络拓扑和基线拓扑之间的表示。因此，在本文中，我们提出了两种互补的方法来找到中继位置，最大限度地提高黎曼度量，如对数欧几里德度量（LEM），从而最大限度地提高网络流量。首先，我们提出了一个黎曼多臂强盗（RMAB）强化学习模型来跟踪中继位置，这增加了LEM向基线网络。特别地，选择可能的中继位置被认为是一个动作，而LEM表示RMAB模型的奖励。其次，我们提出了一个黎曼粒子群优化（RPSO）算法，迭代尝试找到表示的中继辅助网络拓扑结构的最大LEM对基准网络的黎曼流形。仿真结果表明，这两个RMAB和RPSO方法收敛到近最优的解决方案，其中在单继电器放置的情况下，分别达到94.3%和90.6%，最大可能的网络流量。
Networks topology can be represented over Riemannian manifolds (i.e., curved surfaces), given the symmetric positive definite (SPD) property of their spectral graphs. Moreover, maximizing flow rate of a baseline network topology through relay placement can be equivalent to finding the relay location that maximizes the geodesic distance (i.e., Riemannian metric) between the representations of a relay-assisted network topology and the baseline one over Riemannian manifolds. Therefore in this paper, we propose two complementary approaches to find relay locations that maximize Riemannian metrics, such as Log-Euclidean metric (LEM), and hence maximize the network flow rate. First, we propose a Riemannian multi-armed bandit (RMAB) reinforcement learning model to track the relay positions, which increase the LEM towards the baseline network. Particularly, selecting a possible relay location is considered as an action, whereas the LEM represents the reward of the RMAB model. Second, we propose a Riemannian Particle Swarm Optimization (RPSO) algorithm that iteratively attempts to find the representation of relay-assisted network topology with maximum LEM towards that of the baseline network over the Riemannian manifold. Simulation results show that both the RMAB and RPSO approaches converge to near-optimum solutions, which in the case of single relay placement achieve 94.3% and 90.6%, respectively, of the maximum possible network flow rate.