Energy Optimization in Three-Dimensional Wireless Sensor Networks Using Hybrid K-Means and Mixed Integer Linear Programming

Energy optimization is a major issue in wireless sensors networks (WSNs) due to its direct impact on the network's lifetime. This paper proposes the use of the K-means algorithm combined with linear programing to lengthen the lifetime of three-dimensional WSNs. First, the K-means algorithm is used to obtain simple but effective initial clustering of the WSN and then the communication links between the sensors are optimized using linear programing to decrease energy consumption and improve the lifespan of the network. Linear programming is applied here to determine which sensor connections should remain active to minimize a formulated linear objective function while ensuring that a minimum number of sensor nodes remain connected. A sleep/wakeup scheme is implemented in this proposal in order to reduce energy consumption further and increase the lifetime of the network. The proposed method is evaluated alongside two existing algorithms: The first one is based on mixed integer linear programming (MILP) algorithm and the second one is the multi-hop low energy adaptive clustering hierarchy (MH‑LEACH) algorithm. Across simulations, the proposed technique consistently outperformed both algorithms in terms of network lifetime and energy consumption. Specifically, on average, the proposed algorithm extended network lifetime by 48% versus MILP and by 78% versus MH‑LEACH, while reducing energy usage by 22% and 54%, respectively. Furthermore, our proposed approach uses only homogeneous sensors with finite energy while the MILP approach assumes that the sink nodes have infinite energy, which might be impractical. Therefore, the proposed approach is more practically implementable, reduces the number of the communication links to be optimized, and avoids the need for infinite energy sink nodes.