For energy-constrained wireless sensor networks, enhancing network fault tolerance and extending lifetime are of paramount importance. In this study, we focus on addressing the Minimum Power k-Coverage (MinPKC) problem. The objective of MinPKC is to minimize and balance the transmission (Tx) power by sensor nodes (SNs), thus extending network lifetime. Furthermore, MinPKC requires satisfying the constraints of k-coverage for the targets to enhance network fault tolerance. The problem is non-convex, multimodal, and NP-hard. To address this problem, we propose a novel metaheuristic algorithm named Elite Global Growth Optimizer (EGGO), which incorporates efficient global search and elite evolution strategies into the GO and utilizes time-varying multi-strategies for population updates. This study extensively compares EGGO with ten popular algorithms on 20 classic benchmark test functions using the Friedman and Wilcoxon rank-sum tests. The results indicate that EGGO significantly outperforms all the compared algorithms. Ablative experiments confirm the crucial role of the proposed mechanisms in EGGO for improving algorithm performance. Meanwhile, the study implements ten MinPKC methods based on comparative algorithms and compares them with the EGGO-based MinPKC method in terms of total Tx power, network lifetime, and simulation time. The experimental results indicate that the EGGO-based MinPKC method significantly increases the network lifetime by approximately 14.2%, 38.2%, and 1.9% compared to the second-best algorithm, and by 57%, 451%, and 84.8% compared to the GO, while balancing the Tx power among SNs and reducing the total Tx power by approximately 28%, 12.7%, and 0.5% compared to the second-best algorithm, and by 47.1%, 72%, and 30% compared to the GO, respectively, when k=1,2,3. Additionally, a detailed analysis is conducted on the impact of the number of SNs, the maximum target coverage capacity of each SN, as well as the effects of obstacles and their distribution on signal strength attenuation in reducing Tx power. The source code is available at https://github.com/iNet-WZU/EGGO.
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