Energy optimization routing protocol is considered an essential problem in wireless sensor networks (WSNs) as it can affect the network lifetime. Most of the existing routing algorithms are designed for two-dimensional networks, which cannot be transferred to three-dimensional WSNs. Due to a lack of knowledge about the third dimension, 2D routing algorithms perform badly in a real-life 3D environment such as a hill, an urban area, an underground area, an underwater area, and so forth. These networks also suffer from problems such as routing stretch, energy efficiency, and load balancing. Therefore, in this paper, a mixed integer linear programming is formulated as an optimal WSN topology control problem to address the energy optimization routing problem in 3D terrain. The proposed method is a self-organized network that uses clustering and sleep/wake-up schemes to maximize the network lifetime and minimize energy consumption. Simulations revealed that our algorithm is robust to various terrains and significantly increases the network lifetime when compared to a well-known protocol, i.e., the multi-hop low energy adaptive clustering hierarchy (LEACH), with an improved average of 44.94 %. The results also suggested that the energy balancing strategy provided better solutions than the minimizing total energy scheme due to the optimal load balancing scheme of the cluster head selection at each decision round. Furthermore, our global optimal solutions can serve as a benchmark for all heuristic algorithms. Though the number of variables in our optimization problem grows nonlinearly with the number of sensor nodes, the computation time is rather practical as the problem is linear.

中文翻译：

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三维无线传感器网络的能量优化拓扑控制

能量优化路由协议被认为是无线传感器网络（WSN）中的一个基本问题，因为它会影响网络的寿命。现有的路由算法大多是针对二维网络设计的，无法迁移到三维无线传感器网络中。由于缺乏对三维的了解，2D 路由算法在现实生活中的 3D 环境（例如山丘、市区、地下区域、水下区域等）中表现不佳。这些网络还面临路由延伸、能源效率和负载平衡等问题。因此，本文将混合整数线性规划表述为最优 WSN 拓扑控制问题，以解决 3D 地形中的能量优化路由问题。所提出的方法是一种自组织网络，它使用集群和睡眠/唤醒方案来最大化网络寿命并最小化能耗。模拟表明，我们的算法对各种地形具有鲁棒性，并且与众所周知的协议（即多跳低能量自适应聚类层次结构（LEACH））相比，显着增加了网络寿命，平均提高了 44.94%。结果还表明，由于每轮决策中簇头选择的最佳负载平衡方案，能量平衡策略提供了比最小化总能量方案更好的解决方案。此外，我们的全局最优解可以作为所有启发式算法的基准。尽管我们的优化问题中的变量数量随着传感器节点的数量非线性增长，但由于问题是线性的，计算时间相当实用。