Deploying relay nodes is a significant mechanism to prolong the network lifetime of wireless sensor networks (WSNs). However, most existing studies overlook the energy consumption of relay nodes, leading to imperfections in the optimization process. Additionally, there is also a lack of analysis of conflicts between different optimization objectives. In this regard, a multi-objective antlion with fuzzy clustering algorithm (MOALO-FCM) is designed to obtain a better trade-off between different optimization objectives. And an adaptive membership function revision strategy is introduced to improve the energy balance of relay nodes. To verify the performance of the proposed algorithm, simulation experiments are set in 2-dimensional and 3-dimensional scenes with correlative algorithms, respectively. The main evaluation indexes include performance of Pareto optimal solution sets, the life cycle of network, the energy consumption of sensor nodes, the energy consumption of relay nodes, the number of living nodes, and the running time of algorithms. The results indicate that the proposed algorithm has better performance in various indexes.
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