###### Abstract  
Extending the lifetime and stability of wireless sensor networks (WSNs) through efficient energy consumption remains challenging. Though clustering has improved energy efficiency through cluster-head selection, its application is still complicated. In existing cluster-head selection methods, the locations where cluster-heads are desirable are first searched. Next, the nodes closest to these locations are selected as the cluster-heads. This location-based approach causes problems such as increased computation, poor selection accuracy, and the selection of duplicate nodes. To solve these problems, we propose the sampling-based spider monkey optimization (SMO) method. If the sampling population consists of nodes to select cluster-heads, the cluster-heads are selected among the nodes. Thus, the problems caused by different locations of nodes and cluster-heads are resolved. Consequently, we improve lifetime and stability of WSNs through sampling-based spider monkey optimization and energy-efficient cluster head selection (SSMOECHS). This study describes how the sampling method is used in basic SMO and how to select cluster-heads using sampling-based SMO. The experimental results are compared to similar protocols, namely low-energy adaptive clustering hierarchy centralized (LEACH-C), particle swarm optimization clustering protocol (PSO-C), and SMO based threshold-sensitive energy-efficient delay-aware routing protocol (SMOTECP), and the results are shown in both homogeneous and heterogeneous setups. In these setups, SSMOECHS improves network lifetime and stability periods by averages of 13.4%, 7.1%, 34.6%, and 1.8%, respectively. WSNs; sampling SMO; energy efficient CH selection; SSMOECHS; network lifetime; network stability +
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0000-0001-9991-4500-3899-2/10/0000-0000-0000-0000-0000-0000-0000-0000-00000-00000-00000-00000-0000-00000-00000-00000-00000-00000-00000-00000-000  
nodes are evenly and probabilistically selected as CHs, disregarding the state and characteristics of the selected nodes, such as remaining energy, predicted energy consumption, and the number of neighboring nodes. The centralized use of information (e.g., battery status) from all nodes at the BS should be considered when selecting CHs. However, it is difficult to simultaneously acquire this information at the BS during transmission. In LEACH-C [7], to obtain the remaining energy information from nodes, the synchronization of node information is achieved by methods such as time-division multiple access. LEACH-C not only makes a variety of information available, it also enables higher computing power at the BS than that at the nodes. Thus, such a type of centralized operation can be leveraged to improve clustering. Clustering based on swarm intelligence is a highly accurate approach that has been widely used for optimization protocols. This approach has been included in protocols based on particle swarm optimization (PSO) [8; 9; 10], bee colony optimization [11; 12], ant colony optimization [13; 14], among others. The recently proposed spider monkey optimization (SMO) mimics the behaviors of spider monkeys seeking food to quickly and accurately determine feasible solutions compared to other optimization algorithms based on swarm intelligence [15]. Therefore, various studies have used SMO for CH selection [16; 17; 18]. We modified the original SMO algorithm in this study to further improve CH selection. In most existing studies using clustering for WSNs, the nearest nodes to the optimal location are defined as CHs during selection. Thus, clustering mainly locates CHs at the cluster center, and operation problems may arise when the optimal CH locations differ from the actual node positions. First, the calculation burden increases when determining the nearest nodes after defining the CHs, thus increasing energy consumption and shortening the network's lifetime.