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

Energy optimization is a critical challenge in wireless sensor networks (WSNs) due to its direct impact on the network lifetime. This paper proposes the use of the K-means algorithm combined with linear programming to extend the lifetime of three-dimensional WSNs. First, the K-means algorithm is employed to obtain an effective initial clustering of sensor nodes. Then, mixed integer linear programming (MILP) is used to optimize the communication links, thereby reducing energy consumption and extending network lifetime. 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. An inherent sleep/wake mechanism, guided by the optimization process, is employed to further minimize energy consumption. The proposed method is evaluated alongside two existing algorithms: the first one is based on the MILP algorithm, and the second one is the multi-hop low energy adaptive clustering hierarchy (MH-LEACH) algorithm. Simulation results demonstrate that the proposed technique consistently outperforms 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. Consequently, the proposed approach is more practical, reduces the problem size for optimization, and eliminates the unrealistic requirement for sink nodes with infinite energy.