## 1 Introduction  
### Background  
Through the advances of wireless telecommunications, the development of micro-electronics devices, and implementation of Internet of Things (IoT) in large scales, in the recent decade wireless sensor networks (WSNs) have attracted great attention owing to lots of applications, such as environmental surveillance, smart cities and battlefield, traffic monitoring, tracking medicine and logistic events, military target monitoring [1], health care tracking, and so more [2]. WSNs have handled with distributed sensor nodes in the network on behalf of computational and managament operations for implementing these applications [3, 4]. In WSN applications, the clustering and routing mechanisms play an important role in energy efficiency and optimization issues [5]. Clustering refers to the division in the nodes in the sensor network into groups, called clusters, according to certain criteria and properties in order to more easily manage the operation of the network [6]. Each cluster has a cluster head (CH), which is selected according to certain algorithms, so that this node can collect data from other normal nodes and process and transmit them to the base station (BS) [7]. In this way, all of the nodes do not need to separately transmit data to BS, and they do not consume energy in vain. CH selection and management are important and difficult problems in clustering. Because, there is \(C(n,m)\) combination probability in the selection of m CHs from the \(n\) nodes [8]. In addition, passing the data through the relaying nodes while delivering to BS causes this probability to grow. In large-scale networks with very big n values, CH selection probability and the computational complexity increase as an exponential function. In the light of all this information, researchers develop CH selection algorithms that are based on energy efficiency [9; 10]. Routing is an important task in the collection of and transmission data to the related locations in WSNs [11; 12]. The routing mechanism is the part of the WSNs task that is required to conduct communication setup and data transmission between sensor nodes and CHs or CHs and BS [13]. In order to reduce energy consumption and improve the network life, it is important to develop routing protocols for addressing these problems [14]. Routing protocols are categorized according to many challenges, such as structure of the network, clustering methods, specific features of sensor nodes, node distribution, coverage, and security. Considering these problems for this purpose develop routing techniques. The data that were collected in traditional WSNs are usually transmitted to BS by means of multi-hop logic through specific nodes [15]. Multi-hop communication can provide a certain amount of energy distribution on the nodes, but it leads to a hot spot problem, which means that the energy of the nodes close to the sink node is consumed energy and will hence die earlier [16]. In order to overcome this problem, solutions, such as adapting the node distribution, mitigating the node load, balancing the cluster number, and sink mobility in WSNs are being investigated [12]. Mobility in WSNs brings many advantages that will enable the nodes to more easily transmit data and based on energy efficiency [17]. The data can be dynamically gathered from the respective nodes by means of the mobile sink nodes [18]. Mobile sink nodes collect data by visiting the coverage of nodes, such as CHs that are equipped with specific hardware or software features [19]. Thus, the problem is that the nodes that are remote from the scope of communication cannot directly transmit data to the BS. However, it is a challenging process to determine the motion trajectory of the mobile sink node in WSNs and to determine the least costly paths [20; 21]. The aim here is to develop motion paths of mobile sinks that take into account energy, latency, and connection quality.