Because the sensors are constrained in energy capabilities, low-energy clustering has become a challenging problem in high-density wireless sensor networks (HDWSNs). Usually, sensor nodes tend to be tiny devices along with constrained clustering abilities. To have a low communication energy consumption, a low-energy clustering scheme should be designed properly. In this work, a new cloned chaotic parallel evolution algorithm (CCPEA) is proposed, and a low-energy clustering model is established to lower the communication energy consumption of HDWSNs. By introducing CCPEA into the low-energy clustering, an objective function is designed for evaluating the communication energy consumption. For this problem, we define a clone operator to minimize the communication energy consumption of HDWSNs, use the chaotic operator to randomly generate the initial population to expand the search range to avoid local optimization, and find the parallel operator to speed up the convergence speed. In the experiment, the effect of CCPEA is compared to heuristic approaches of particle swarm optimization (PSO) and simulated annealing (SA) for the HDWSNs with different numbers of sensors. Simulation experiments demonstrate that the presented CCPEA method achieves a lower communication energy consumption and faster convergence speed than PSO and SA.

中文翻译：

---

高密度无线传感器网络中低能量聚类的克隆混沌并行进化算法

由于传感器的能量能力受到限制，因此低能量群集已成为高密度无线传感器网络（HDWSN）中的一个难题。通常，传感器节点往往是具有受限聚类能力的小型设备。为了降低通信能耗，应适当设计一种低能耗的集群方案。本文提出了一种新的克隆混沌并行进化算法（CCPEA），并建立了一种低能耗聚类模型来降低HDWSN的通信能耗。通过将CCPEA引入低能耗集群，设计了一个目标函数来评估通信能耗。针对这个问题，我们定义了一个克隆运算符，以最大程度地减少HDWSN的通信能耗，使用混沌算子随机生成初始种群以扩大搜索范围以避免局部优化，并找到并行算子以加快收敛速度​​。在实验中，将CCPEA的效果与具有不同数量传感器的HDWSN的粒子群优化（PSO）和模拟退火（SA）的启发式方法进行了比较。仿真实验表明，与PSO和SA相比，本文提出的CCPEA方法实现了更低的通信能耗和更快的收敛速度。将CCPEA的效果与带有不同数量传感器的HDWSN的粒子群优化（PSO）和模拟退火（SA）的启发式方法进行了比较。仿真实验表明，与PSO和SA相比，本文提出的CCPEA方法实现了更低的通信能耗和更快的收敛速度。将CCPEA的效果与带有不同数量传感器的HDWSN的粒子群优化（PSO）和模拟退火（SA）的启发式方法进行了比较。仿真实验表明，与PSO和SA相比，本文提出的CCPEA方法实现了更低的通信能耗和更快的收敛速度。