## 1 Introduction  
Wireless sensor networks (WSNs) compose a large number of sensor nodes, which are scattered in the sensing region, and one or more sink nodes [1]. Generally, sensor nodes are low-cost, energy-limited, static, and randomly deployed in the sensing region. They are used to obtain such data as temperature, humidity, and air pressure in a physical environment. Communication between sensor nodes or between sensor nodes and sink is realized through wireless signals. Sensor nodes can send data obtained from an environment to a sink in one hop or multiple hops. WSNs have been widely used for environment detection, surveillance and defense reconnaissance, and medical monitoring [2, 3, 4]. Prolonging the network lifetime is one of the fundamental requirements in WSNs. The lifetime of a network is mainly affected by energy consumption by sensor nodes. A significant amount of the energy consumed by sensor nodes is used for data transmission [5, 6, 7]. However, replacing or charging batteries of sensor nodes is not possible in some environments such as mines and battlefields [8]. Therefore, it is crucial to make an effective strategy for transmitting data sensed by sensor nodes to the sink node to prolong the network lifetime. Sensor node clustering is one of the effective strategies for prolonging the network lifetime [9; 10; 11; 12]. According to this strategy, sensor nodes are divided into several groups, referred to as clusters. For each cluster, one sensor node is selected as a cluster head (CH), while the remaining sensor nodes are considered as cluster members. These cluster members send their sensed data to their CH. Then, the CH transmits the data aggregated from all the cluster members to the sink in one hop or multiple hops. The sensor node clustering strategy has many benefits such as energy efficiency, low latency, and scalability [13; 14]. Many clustering methods have been proposed to prolong the network lifetime. One of the methods divides the sensing region equally into many grids (subregions) [10; 11; 12], with sensor nodes in each grid being regarded as a cluster (Figure 1a). Another popular clustering method called low-energy adaptive clustering hierarchy (LEACH) can prolong the network lifetime [9]. In LEACH, CHs are selected from sensor nodes based on a random probability, with the remaining sensor nodes being assigned to their corresponding nearest CH (Figure 1b). Furthermore, in order to improve the performance of clustering sensor nodes, scholars have improved the LEACH-based methods, for example, modifying CH selection algorithms [15; 16; 17], energy aware algorithms [18; 19; 20], and optimization in CH selection [21; 22; 23]. However, the clustering of sensor nodes still faces many challenges. Generally, sensor nodes are randomly scattered in the sensing region. Grid-based clustering or assigning sensor nodes to their corresponding nearest randomly selected CH may cause an imbalance in the number of sensor nodes between clusters, resulting in different energy consumption by CHs. A CH within a cluster containing a large number of sensor nodes would consume a lot of energy and be exhausted quickly. Furthermore, the number of clusters affects the performance of WSNs. On the one hand, a small number of clusters would increase the energy consumption of each CH when gathering data from sensor nodes within its cluster and sensor nodes far away from the CH when sending data to the CH. On the other hand, a large number of clusters would increase the traffic burden in the network. Therefore, a crucial task for increasing the network lifetime is to adaptively determine the number of clusters and group sensor nodes into clusters evenly according to their distribution. This is important to improve the performance of WSN such as the network lifetime. Recently, computational intelligence has been widely used in WSNs to provide solutions for some problems such as nodes deployment, task allocation, path planning, and movement control [24; 25; 26].