## 2 Related Work  
Low-energy adaptive clustering hierarchy (LEACH) [16] is a widely referenced routing protocol for WSNs. Many routing protocols in WSNs are improved LEACH versions or LEACH variants [19; 20]. LEACH is a single-hop self-organizing clustering algorithm, in which the nodes in the network form clusters by self-organization and one of the nodes in each cluster is selected as the CH. All non-CH nodes transmit data to the CHs, which receive and aggregate data before transmitting them to the BS. LEACH minimizes energy consumption in WSNs through cluster formation and data aggregation. In LEACH, communication between BS and CHs is divided into rounds. The role of the CH is done randomly per _round_. Every round has two states: setup state and steady state. During the _setup_ state, every sensor node selects a random number between 0 and 1. If this number is less than the threshold \(T(n)\), the node becomes a CH. The threshold \(T(n)\) is assigned to sensor nodes \(n\) and is calculated as follows:  
\[T(n)=\left\{ \begin{array}{ll}\frac{P}{1-P\times(r\bmod\frac{1}{r})}&if\ \ n\in G\\ 0&otherwise\end{array} \right\}, \tag{1}\]  
where \(n\) is the node ID, \(r\) is the current round, \(P\) is the expected percentage of CH, and \(G\) is the set of nodes that are not elected as CHs in the last \(1/P\) rounds. When a node becomes CH, it creates a cluster and defines a TDMA frame for communication with other cluster members. During the _steady_ state, nodes transmit to the CH. The CH performs the aggregation of the received data and forwards them to the BS. In steady state, CHs allocate time slots to the normal nodes. Each normal node collects sensing data and transmits them to its CH using its designated time slot. After the CH receives all the data packets from its cluster members, it aggregates the data and sends a compressed packet to the BS. After all the data are sent to the BS, the network reverts to the setup state and restarts the cluster formation until the wireless network exhausts all its energy. There are various WSN applications, where the mobility of sensors is in use, either passive or active. During the passive navigation, under external influences (and not using their own energy) the sensors change clusters inside a round. This complicates the problem of establishing an energy-efficient organization of the sensor network [21]. However, there are specific applications, where the sensors move by using their own energy to cover the sensing area dynamically, to replace depleted sensors, or because of the nature of the sensing phenomenon. Therefore, the energy of the sensors of this type becomes an even more critical resource [22]. However, some researchers have figured out that sensors, which have the capacity to move with the help of their own energy, could take advantage of the savings in total energy consumption in the network. [PERSON] and [PERSON] in [23] provided a solution of a network that is heterogeneous in terms of the nodes mobility. This network contains a small number of resource-rich specialized CHs. Sensor nodes have limited amount of energy and can only reach nearby nodes within a limited range, while CHs can move to anywhere within the working area. Each CH knows the location and connectivity pattern for all of its sensors. [PERSON] et al. in [24] considered the case where the sensors and the sink are static, and the CHs are mobile and work as relay nodes. The low-energy static sensor nodes sense physical parameters and route the data to the higher energy-rich nodes (called MCHs), which transmit data directly to the BS. The MCHs move within its own cluster to change its neighborhood nodes so as to avoid the fixed set of sensors to continuously forward data to the MCH, which may otherwise result in network partitioning. Thus, a CH can regulate the flow of energy among the sensors in the cluster and, thus it increases the total network lifetime.