Enhancing the Lifetime and Energy Efficiency of Wireless Sensor Networks Using Aquila Optimizer Algorithm

Abstract

As sensors are distributed among wireless sensor networks (WSNs), ensuring that the batteries and processing power last for a long time, to improve energy consumption and extend the lifetime of the WSN, is a significant challenge in the design of network clustering techniques. The sensor nodes are divided in these techniques into clusters with different cluster heads (CHs). Recently, certain considerations such as less energy consumption and high reliability have become necessary for selecting the optimal CH nodes in clustering-based metaheuristic techniques. This paper introduces a novel enhancement algorithm using Aquila Optimizer (AO), which enhances the energy balancing in clusters across sensor nodes during network communications to extend the network lifetime and reduce power consumption. Lifetime and energy-efficiency clustering algorithms, namely the low-energy adaptive clustering hierarchy (LEACH) protocol as a traditional protocol, genetic algorithm (GA), Coyote Optimization Algorithm (COY), Aquila Optimizer (AO), and Harris Hawks Optimization (HHO), are evaluated in a wireless sensor network. The paper concludes that the proposed AO algorithm outperforms other algorithms in terms of alive nodes analysis and energy consumption.

1. Introduction

Wireless communication in modern smart device technologies has enhanced the spread of the Internet of Things (IoT) with pervasive sensing and computing capabilities everywhere to join huge physical objects to the Internet. Currently, the IoT denotes the internet of the future, and both the fields of academia and industry have a great chance to deliver customer services in many phases of modern life [1]. All industrial activities such as financial transactions, organizations, and other entities can use the IoT, which is utilised in logistics, manufacturing, services, banking, etc. This technology is well-defined in diverse ways by different researchers, opening up new research and commercial directions [2]. Let us discuss two of the most common definitions: First, the IoT is an interaction among the physical elements using a huge array of sensors and actuators, and digital worlds. Another definition: the IoT is a paradigm in which computing and networking abilities are embedded in any kind of feasible entity. Networking abilities are used to query the state of the object and to alter its condition if possible. In general, the IoT refers to a new world connecting all the devices and accessories to a network to complete complicated tasks that need a high degree of intelligence [3]. For this intelligence and interconnection, embedded sensors, actuators, processors, and transceivers are equipped in IoT entities to aggregate different technologies in one.

IoT applications include health care, entertainment, education, social life, environmental monitoring, energy conservation, home automation, and transportation systems, among others, to minimize human effort and increase the quality of experiences (QoE). Such is the set of areas in which applications have been established to enhance life quality in our countries. Figure 1 represents a whole classification of the IoT in the major fields of application. IoT theory may be summarised as creating everyday data from one entity and sending it to another. As a result of facilitating communication between things, IoT applications are broad, diverse, and unconstrained [3].

In an IoT network, data transmission is allowed by different protocols. The applied protocol’s job is to manage a device’s behaviour during data transfer. Designing an IoT network with several sensors is extremely difficult; these nodes are highly dependent on a steady energy supply, channel throughput capacity, and storage characteristics, necessitating smart resource management. It is critical to introduce a data sink to the network based on WSNs. The procedure begins by saving the data obtained in the sink before moving on to the other nodes and repeating the process. As the sensor and sink placement may enhance the IoT network capacity, the suitable choice of data transmission mechanism has a significant impact. The WSN is made up of sensor nodes that are linked together via wireless connections. After collecting data in the environment, the data is transferred to gateway devices, which then transport the data to the cloud over the Internet. Communication between nodes in a WSN can be either direct or multi-hop via its associated network and designated cluster head. Sensor nodes are limited in power and computing resources, but gateway nodes have enough resources. Many academics have been striving to validate the applicability of IoT devices for energy savings. When compared to the energy consumption of the devices they control, most IoT sensors need extremely little power [5].

An energy-efficient cooperative acoustic communication protocol has been presented in [6], to improve network lifetime and reduce energy consumption. The algorithm selects the destination nodes based on the signal-to-noise ratio (SNR) and distance among the communicating nodes.

A new scheme “A Content-based Adaptive and Dynamic Scheduling (CADS)”, with a two-way communication model in WSNs, is proposed in [7], to increase lifetime and offer an energy-efficient WSN. This scheme changes a node’s states dynamically via data aggregation. Each node adapts a new state based on the transmitted packets.

According to the previous ideas declared above, the paper’s main contributions are:

• The clustering (AO) algorithm is presented to locate optimal cluster heads and ensure the network is clustering efficiently and stably, resulting in reduced energy consumption and increased network lifespan.
• The Aquila Optimizer is implemented in two phases. In the first phase, the AO simulation code is run with an optimal distribution for sensors to initially elect proper clustering heads (CHs), which are assigned in an optimal distributed way based on three input factors: residual energy(RE), distance from nodes to BS, and the number of surrounded nodes to gather the data from the environment to the cloud through gateway devices. In the second phase, the AO is used to improve system performance with less energy consumption and a high network lifespan.
• The performance of the proposed (AO) algorithm is compared with the well-known algorithms LEACH, COY, HHO, and GA. The results of the experiment prove that the AO algorithm has better performance than other algorithms in all applied scenarios.

The rest of this paper is organized as follows: Section 2 introduces an overview of previous studies related to this work. Section 3 designates the suggested system model. Section 4 presents the experimental outcomes. Finally, Section 5 presents the paper’s conclusion and future work.

2. Literature Review

Achieving low energy consumption in WSN is the main goal for many researchers by modifying some features to expand the energy-saving of nodes. To attain this goal, more studies were introduced in terms of clustering head selection protocols and energy consumption.

2.1. Clustering Heads Selection Protocols

Clustering routing protocols help enhance a network’s lifetime and play a vital role in improving energy efficiency in WSNs. To reach this goal, many researchers have offered papers in terms of clustering head selection approaches.

The authors in [8] introduced two combined methods, selecting the ideal CH and establishing a dynamic clustering procedure. Moreover, the proposed protocol employs both types of election procedures (random and periodic) in the same round, with the random method taking precedence at the start of each round/cycle. Furthermore, both the random and periodic election procedures are followed by testing the residual energy to remove the dead nodes and continuing with the remaining nodes in the round regularly. Furthermore, the proposed protocol is well-known for removing dead nodes from the network topology list during the re-clustering process to report black holes and routing latency issues. Finally, the mathematical modelling and analysis of the suggested algorithm are described. In terms of power consumption and network longevity, the experimental findings show that the proposed protocol outperforms the LEACH and FBCFP protocols.

In [9], the decision is based on four factors: energy, distance to the center, mobility, and the data queues’ length, utilized to simulate an appropriate CH selection. A unique way to tackle this difficulty is presented using the cluster splitting process algorithm (CSP) and the analytical hierarchy process method (AHP). The approach is compared to the base station controlled dynamic clustering protocol (BCDCP) algorithm using four parameters. The simulation results reveal that the proposed strategy for extending network lifetime outperforms the BS-controlled dynamic clustering protocol methodology. The suggested approach reduces energy more than the BCDCP method and has a lower rate of packet loss.

In [10], the authors present a cluster-based routing scheme for a heterogeneous (CRSH) network that enables node clustering and data aggregation. The proposed approach selects the most energy-efficient node as the CH based on the node’s energy level and accomplishes data combinations to eliminate duplicate data packets. To evaluate its efficiency, the suggested method is simulated in MATLAB and compared to current protocols using numerous performance factors such as network lifetime, energy consumption, and throughput. The data aggregation strategy is used to decrease duplicate data in the network, and the CH aggregates the important information into a single packet and passes it to the BS. The data aggregation approach conserves energy spent on redundant information processing and minimizes network energy consumption; consequently, network lifespan, stability period, and energy expenditure will improve.

In [11], the author applies a novel clustering routing topology to raise the LEACH protocol. Selecting the CHs remains as it had been in the original Leach protocol but is based on the high residual energy. Rectangular area regions from the entire network area are applied to the LEACH algorithm, respectively. The mechanism of routing is adjusted in the MAC layer to reduce the congestion and improve the network performance metrics such as throughput, delay, overhead, and average energy through the Network Simulator 2 platform. A better result for homogeneous networks in comparison to LEACH is provided.

For selecting cluster heads and non-cluster heads, paper [12] introduces a novel dynamic multipath routing protocol (DMPRP), which is based on a modified particle awarm optimization (M-PSO) algorithm. The best selection of CHs has been taken after calculating the probabilities. Segmenting the network field topology into many groups (clusters) is predicated to get a more efficient energy consumption ratio (ECR) to balance the load and improve performance by selecting the cluster head (CH). The results have been used to optimize the shortest path using a genetic algorithm (GA), which uses an objective function consisting of a network to define the optimal path.

In [13], the authors use game theory to choose CH by sending data with game theory incentives and detecting the position of other nodes. Then, using game theory, high-priority data about the proposed method is delivered. In NS3 software, the simulation results show that the suggested technique has satisfactory results in comparison to the artificial bee colony algorithm (ABC), cuckoo search algorithm (CS), firefly algorithm (FA), grey wolf optimization algorithm (GWO), and GA.

In [14], the authors provide a novel CH selection method based on (GWO), which considers residual energy and sink distance. The presented approach is validated in several WSN scenarios by varying the number of sensor nodes and CH. The observed findings indicate that the offered method beats existing algorithms to achieve a top network performance.

In the paper [15], the author proposes a fuzzy decision-making method for choosing CHs. Decision-making with fuzzy multiple attributes (MADM) is based on three criteria: residual energy, the distance between the nodes to the BS, and the neighbour’s number, the method chooses the suitable CHs. In homogenous settings, the simulation results show that this technique outperforms the distributed hierarchical agglomerative clustering (DHAC) protocol in terms of network lifespan extension.

2.2. Energy Consumption

Energy consumption plays a vital role in enhancing the performance and energy efficiency of the network. To reach this goal, many researchers have offered papers in terms of energy consumption in WSNs.

In [16], the author introduces a novel routing algorithm in WSN for bacterial foraging and a mobile sink, named the ultra-innovative algorithm, which leads to energy efficiency. In the provided method, the number of sensor nodes is determined by two criteria including the energy amount on the battery surface and the distance from the sink ahead, which establish regular clusters, and assuming a multi-step routing scheme to link with the sink and consume uniform energy. The simulation results show better performance of the given method for energy consumption, throughput rate, end-to-end delay, signal-to-noise ratio (SNR), and delivery of data at a higher rate successfully to the sink.

The authors in [17] describe an energy-efficient coverage optimization strategy based on the Voronoi glowworm swarm (VGS) optimization K-means algorithm. In this technique, GS Optimization, K-means method, and Voronoi cell optimize coverage area with the fewest number of living nodes considering the optimum sensing radius calculation for well-organized sensor deployment. Furthermore, the suggested solution extends the lifespan of the established network by lowering the energy required by the sensor nodes via multi-hop send and the sleep-and-wake technique. The simulation results show that the suggested strategy achieves more area coverage with the optimum number of living sensor nodes.

In [18], the authors present an improvement strategy for reducing energy consumption and increasing network lifespan by expanding energy balancing in clusters across all sensor nodes to reduce energy dissipation during network communications. A CH selection mechanism underpins the improved method. Finally, the technique compares LEACH and other protocols in terms of network lifespan, number of CHs, energy usage, and the number of packets sent to BS. The simulation results demonstrate that the suggested technique is successful and that the energy consumption of WSN has been lowered, extending the network lifespan more than LEACH.

To improve current systems for extending lifespan, authors in [19] offer a scheme that organizes sensor nodes for charging. To begin, an inspection algorithm is created to visit and inspect sensor nodes to identify the sensor nodes that require charging. Second, using a greedy charge method, calculate the shortest distance in which the WCV must go. The energy for nodes algorithm was presented to decide the ending point and when the WCF must return to BS. Simulation tests are also carried out to control the performance, and it was discovered that our suggested method outperformed existing systems in the literature using metrics.

In [20], the authors investigate the influence of energy-aware routing on network performance. In software defined networking (SDN) with multiple controllers, a new energy-aware technique is proposed to decrease the number of active connections while accounting for in-band control traffic. Two heuristic approaches are developed to reduce overall power consumption: static network architecture and dynamic energy-aware routing. In simulations using real topologies and demand data, significant values of switched-off connections are obtained. Furthermore, the performance-agnostic energy-aware model influences critical network metrics such as control traffic delay, data channel latency, link usage, and ternary content addressable memory (TCAM) occupancy.

Paper [21] provides a fuzzy logic (FL) and (LEACH) approach-based (PSO) technique for choosing the primary cluster head (PCH) and secondary cluster head (SCH) (FL). The suggested protocol is compared to existing techniques, such as fuzzy c-means (FCM) clustering and FLS-based CH selection, LEACH–fuzzy clustering protocol, and LEACH based on energy consumption equilibrium, to increase the sustainability of WSNs for environmental monitoring applications. The suggested protocol properly balances energy usage to improve WSN performance and throughput. The simulated results concluded that the network’s lifespan and packet transmission were increased.

In [22], the authors introduce a model that uses a two-step approach. In the first step, a model employs a trust model to choose the CHs that manage the data communication between the BS and nodes in the cluster area. Moreover, a new hybrid algorithm that combines the PSO algorithm and GA is proposed to define the routes for data transmission. PSOGA simulation results confirm the efficacy of the proposed hybrid algorithm and the results are compared with the existing LEACH method and PSO, with a random route selection for five different cases. The results establish the efficiency of the proposed approach, as it outperforms existing methods with increased energy efficiency and network throughput, high packet delivery rate, and high residual energy throughout the whole iteration.

A novel marine observation buoy with built-in wave-excited energy to achieve real-time measuring of the marine environment was suggested in [23]. A small-scale prototype is designed, fabricated, and tested. A mathematical model of the system was presented, and simulation results were confirmed by experimental data, considering the influence of the mooring system and electric load. Numerical simulations and physical experiments have solidly demonstrated the feasibility of this novel wave-powered marine observation buoy.

3. The Proposed System

The power performance with the techno-economic evaluation of wave power farms is studied in accurate wave climates [24]. To maximize the converted energy and reduce the levelized cost of energy (LCOE), a numerical model is provided where the power take-off systems of wave energy converters are controlled/tuned. Numerical results illustrate that power performance and LCOE of wave power farms differ over wave climates, and the machinery restrictions of power take-off force is taken into consideration.

3.1. Network Model

The paper defines the network model as a set of motionless sensor nodes diffused at random in a network place with (N × N) measurement. The nodes are associated jointly to make clusters and a CH is defined and represented in WSN. The nodes of a cluster are combined in such a way that they must have connected at a minimum distance from CH. A node can serve as an active sensor and CH during data transmission. Commonly, a design of WSN is hooked up to data sensing, topology features, radio communication, allocation of sensors, and energy usage, properly. During the operation, the total sensor nodes gather data from the presumed location and send it to CH. Then, the specific CH translates the respective data to the BS. All nodes have different heterogeneous energy means. These energy losses during the transfer of data among the nodes will be defined in the energy model.

3.2. Energy Model

The network requires energy for a variety of purposes, including sensing, receiving, aggregation, and transmission. The sensor node can be changed during the data transmission or receiving at any moment. A sensor node consumes energy when transmitting or receiving data. The node energy in the network has an initial value of P0 and also the energy of the node is not rechargeable [KK16]. The energy squandering PTk whilst transferring K bits/packet, d distance from regular node a_th to CH b_th follows [YM22] delineated as per Equation (1). If the connection distance d for the transmission model is small (free space model) d2 else the distance is multi-path d4, they are based totally on the distance between the senders as well as the receivers. The received energy, PRk, required for receiving k bits/packet at a distance d follows delineated as per Equation (2). Pel, the electronic energy consumed per bit, represents several modules, such as spreading. Pmp denotes the multi-paths energy model while P_fs provides the free space energy model. d0 is the threshold distance determined as shown in Equation (3).

$$P_{TK}\left(K.d\right)=\{\begin{array}{cc}K\left(P_{el}+P_{fs}\ast d^2\right)& if d<d_0\\ K\left(P_{el}+P_{mp}\ast d^4\right)& if d\ge d_0\end{array}$$

(1)

$$P_{TK}\left(K.d\right)=K\ast P_{el}$$

(2)

$$d_0=\sqrt{P_{fs}/P_{mp}}$$

(3)

The suggested protocol is designed to increase the lifetime of the network, energy efficiency, stability, and load balance. The energy dissipation during transmission is calculated using the energy model given above. Data reception and collecting: The proposed protocol operates in two phases, the setup phase, and the stationary phase. Cluster construction, CH selection, and data transfer from CH to BS are all performed. The WSN that is being utilized is essentially heterogeneous. It is made up of ordinary and advanced nodes. Due to network non-uniformity, advanced nodes with higher initial energy improve network performance. Advanced nodes are more energy-efficient than regular nodes and fewer than standard nodes. Inspired by nature, meta-heuristics are optimization strategies that simulate nature to solve optimization issues. Striking results increase the potential and viability of nature-inspired algorithms and also their research in various fields. Stable and energy-efficient clustering algorithms are offered for WSNs in this section, similar to LEACH, as traditional protocols, GA, COY, AO, and HHO. We compared the algorithms to obtain convergence on the optimal solution.

3.2.1. LEACH Protocol

Since LEACH is a common clustering routing protocol that has high representativeness, it is used as a research object. These are the preconditions assumed by the LEACH protocol:

• There are no differences between sensor nodes, and radio signals in every direction consume the same energy; each node has the same initial energy, and energy is limited, so each node can tell how much energy is left. Every node possesses sufficient computing power to control the transfer distance and transmit power.
• All nodes communicate together and are directly connected to the BS.
• The sink nodes are fixed and some distance from the whole WSN, as they are assumed to have adequate power supply.

The round is the cycle in which a cluster reconstruction process in the LEACH protocol cycles. The round is separated into the setup phase (cluster) and the ready phase (transmission). The setup phase is shorter than the ready phase.

CH Node Selection: In the setup phase, select the CH based on the number of CHs needed in the network and the number of times each node became a CH.

$$T_n=\{\begin{array}{ll}\frac{P}{1-P\left(r\ast mod\left(\frac{1}{P}\right)\right)}& if n\in G\\ 0& if n\notin G\end{array}$$

$$P=\frac{l}{k}$$

where:

T_n Threshold selected random value from [0, 1]; r is the round’s number; G is a group. P refers to the percentage of the CH node in the network, l denotes the CH nodes needed in the network, and k denotes the total number of sensors. After the CH node is determined, the entire network is notified through broadcast. Sensor nodes provide data to the CH node during the ready phase. The CH node gathers data from all cluster nodes and sends it to the BS [25].

3.2.2. The Genetic Algorithm (GA)

GA is a famous algorithm, which results from a process of biological evolution. The fundamental components of GA are chromosomal clarification, fitness selection, and biologically-inspired operators. Holland also introduced a new element, inversion, which is often used in GA apps [26]. GA is mainly calculated by these evolutionary plans and the encoding schemes are either binary coding or real coding [27].

3.2.3. The Coyote Algorithm (COY)

The Coyote Optimization (COY) Algorithm was introduced by [28]. The algorithm depends on the adaptive behaviour of the coyote through the environment as well as the exchange of coyote experiences. COY has an interesting technique for balancing exploration and exploitation. The algorithm starts with population and coyotes as nominee solutions. COY models the social behaviour of coyotes as a function of cost.

Coyotes hunt their prey in packs and the pack is controlled by an alpha male. The population size of coyotes is divided into a multiplication of the number of packs n_pak and with n_coy coyotes per pack. The social status of each coyote specifies a candidate solution S a nominee solution to the optimization problem [29]. The COY algorithm starts by assigning the coyotes coy^th randomly to the packs pak^th at t time. The social conditions for each coyote represent a single solution known as:

S = (S₁. S₂. S₃…S_D)

(4)

where D denotes the problem dimensions in the search space. In the first step: of (COY), the coyotes are commenced randomly within the previous search space. So, the random position solution is defined by:

$$S_{coy,j}^{pak,t}={\left(1-r_j\right)}_j+r_j+u{b}_j$$

(5)

• lb_j and ub_j represent the lower and higher bounds of the search space.
• j ∈ 1.2. … D.
• The rj is a random number in the range [0, 1].

The second step: the fitness function evaluates the adaptation of the coyotes to their special social environment as the following:

$$fi{t}_{coy}^{pak.t}=f\left(S_{coy}^{pak.t}\right)$$

(6)

Coyotes have a proclivity to abandon their existing packs and join another pack. A coyote fluctuates based on pack size. This technique promotes global information sharing among coyote packs, which increases population diversity. The alpha coyote in any pack is the one who is the most familiar with the surroundings.

The alpha may be calculated for a minimization issue by the following equation:

$$alph{a}^{pak.t }=\left\{S_{coy}^{pak.t}| ar{g}_{coy}=\left\{1.2\dots \dots n_{coy}\right\}\min f\left(S_{coy}^{pak.t}\right)\right\}$$

(7)

The third step: after the coyote shares its special social environment with the rest of the pack to enhance the pack’s survivability. In that regard, the new social condition of the coyote is updated by the equation:

$$S_{coy,j}^{pak,t}=S_{coy,j}^{pak}+r_1\ast {\delta }_1+r_2\ast {\delta }_2$$

(8)

where:

• δ₁: the alpha’s impact on a random coyote.

  $${\delta }_1=alph{a}^{pak,t}-S_{coy,r_1}^{pak,t}$$
• δ₂: the space between the average location of all coyotes in a pack and any other coyote in the packs.

  $${\delta }_2=alvg{d}^{pak,t}-S_{coy,r_2}^{pak,t}$$
• The r₁ and r₂ is a random numbers in the range [0, 1].

The fourth step: the fitness function of the new solution using the next equation:

$$newfi{t}_{coy}^{pak.t}=f\left(new{S}_{coy}^{pak.t}\right)$$

(9)

The final step: If the new social conditions are judged to be better than the prior, the coyotes might elect to maintain them. Otherwise, the latter will continue to be used as in equation:

$$S_{coy}^{pak.t+1}=\{\begin{array}{cc}new{S}_{coy}^{pak.t}& \hfill if newfi{t}_{coy}^{pak.t}<fi{t}_{coy}^{pak.t}\\ S_{coy.j}^{pak.t}& \hfill otherwise\end{array}$$

(10)

Finally, the coyote’s social state that has best adapted itself is chosen and employed as the problem’s overall solution.

3.2.4. The Aquila Optimizer Algorithm (AO)

Aquila Optimizer (AO) is a novel optimization method, which results from Aquila’s behaviors in the environment pending prey being caught. The AO algorithm’s optimization procedures are divided into four categories: selecting the search area by high flying with a vertical stoop, discovering within a separate search space by contour flying with a short glide attack, utilizing within a converged search area by low flying with a slow descent attack, and pouncing by walking and grabbing prey [27]. AO can swap shooting strategies for varied prey and then attack prey with its fast speed combined with strong feet and claws. Asghar et al. [30]. The next is a summary of the mathematical model.

There are two methods, exploration and exploitation [8].

▪

Firstly, In the expanded exploration.

▪

In the explorationag1, the Aquila flies above the ground and discovers the search space, followed by a vertical dive just after the Aquila has determined the prey location.

▪

The narrowed explorationag2: contour flight with short glide attack is the most common way for Aquila to hunt; it attacks the prey with short gliding after descending within the selected area and flying around the prey.

The mathematical formula for the exploration and narrowed exploration is represented, respectively, as the following:

$$a{g}_1\left(t+1\right)=a{g}_b\left(t\right)\ast \left[\left(\frac{1-t}{mn}\right)-r_1\right]+a{g}_m\left(t\right)$$

(11)

$$a{g}_m\left(t+1\right)=\frac{1}{N} {\displaystyle \sum }_N^{1}a{g}_i\left(t\right)$$

The average value of the current position of all agents. 1 − t

During the exploration phase, the search is directed by $\left(\frac{1-t}{mn}\right)$ Equation (11)

• t and mn: the current iterations and the maximum number of iterations.

  $$a{g}_2\left(t+1\right)=a{g}_b\left(t\right)\ast \left(LEVY(D\right)+a{g}_R\left(t\right)-\left(y-r\right)\ast r_2$$

  (12)

  $$LEVY\left(D\right)=0.01\ast u\ast \sigma \ast {\left|V\right|}^{\frac{-1}{\beta }}$$

  $$\sigma =2^{\raisebox{1ex}{$\left(1-\beta \right)$}\!\left/ \!\raisebox{-1ex}{$2$}\right.} sin\left(\frac{\pi \beta }{2}\right)\ast \left(\frac{\mathsf{\Gamma }\left(1+\beta \right)}{\beta \ast \mathsf{\Gamma }\left(\frac{1+\beta }{2}\right)}\right)$$

  $$x=r\ast sin\left(\frac{300\pi -D_1}{200}\right),y=r\ast cos\left(\frac{300\pi -D_1}{200}\right),r=r_3+ 0.0057D_1$$

  (13)

The exploitation adjustment parameters fixed to 0.1.

• ub and lb: the upper and lower bound of the problem.
• D: the dimension size LEV Y (D) represents the Levy flight function.
• r₁. r₂. r₃. r₄. r₅. r₆. r₇. r₈: random numbers in the range [0, 1].
• D₁: an integer number in the range [1, D].
• r: the number of search cycles in the range [1, 20].

Secondly: Expanded exploitationag₃: low-flying with a slow descent offensive.

After determining the approximate location of the prey and descending vertically to launch a preliminary attack, Aquila uses the chosen area to get close to the prey and attack it. This behaviour is illustrated as follows:

$$a{g}_3\left(t+1\right)=\alpha \left(a{g}_b\left(t\right)-a{g}_m\left(t\right)\right)+\delta \ast \left(lb(1-r_s\right)+r_{sub})-r_4$$

(14)

The narrowed exploitation: walking and snatching prey.

The Aquila hunts the victim and attacks it on the ground in this fashion. The next is a mathematical depiction of this behaviour:

$$a{g}_4\left(t+1\right)=q\left(t\right)\ast a{g}_b\left(t\right)+\left(2r_8-1\right)\left(r_7-r\ast x\left(t\right)-2LEVY\left(D\right)\left(1-\frac{t}{mn}\right)\right)$$

(15)

$q\left(t\right)$: The quality function is used to equilibrate the search strategy.

3.2.5. Harris’s Hawks Optimization Algorithm (HHO)

HHO was offered by [31] as a new meta-heuristic optimization method inspired by Harris’s hawk’s cooperative foraging behaviour. Harris’s hawks can show a range of pursuit patterns that are compatible with the dynamic nature of the environment and the prey’s fleeing tendencies. Harris’s hawks are hunters who hunt in groups. Several hawks strike the victim from different random positions at a predetermined interval in this interesting hunting tactic. The quest might take a single dive or numerous fast dives over several minutes. A brief description of a mathematical model is as follows [32].

Firstly: Exploration Phase (H): Harris’s hawks frequently sit in unusual places, wait, and scan the desert for prey. Two perching strategies are used, namely, one related to the locations of other family members and the prey, and the other on the random value r.

$$H\left(t+1\right)=\{\begin{array}{ll}{H}_r\left(t\right)-r_1|H_r\left(t\right)-2r_{2}H\left(t\right)& r\ge 0.5\\ (H_{pray}\left(t\right)-H_r\left(t\right))-r_3\left(lb-r_4\left(ub-lb\right)\right)& r<0.5\end{array}$$

(16)

$$H_M\left(t+1\right)=\frac{1}{N}{\displaystyle \sum }_N^1{H}_i\left(t\right)$$

where:

• (t): the current position.
• HM: the average value of the current position of all hawks.
• (t): the random hawk position.
• (t): represents the best position of the prey.
• ub and lb: the upper and lower bound of the problem.

Secondly: The Phase Change from Exploration to Exploitation.

The HH algorithm uses a transition mechanism based on the prey’s fleeing energy to move from exploration to exploitation when |e| < 1, and then alters the exploitative behaviours. The prey’s energy is modelled as follows, with a drop in energy as the prey flees.

$$e=e_0\left(1-\frac{t}{T}\right)$$

(17)

where:

• e. e₀ represents the initial state and the escaping energy of the prey, respectively.
• t and T, the current and maximum number of iterations, respectively.

Thirdly: The exploitation phase depends on the fleeing energy of the prey and the chasing methods of Harris’s hawks, four distinct chasing and attacking strategies are offered. The pursuit strategy is determined by parameter r, which determines whether the prey has a probability of successfully escaping (r < 0.5) or not (r ≥ 0.5) before being attacked.

• Simple besiege (H(t + 1))

When r ≥ 0.5 and |e| ≥ 0.5, the prey still has enough energy to try to flee, thus Harris’s hawks surround it softly to tire it before attacking it. The positions are updated as the following:

$$\begin{gathered} H\left(t+1\right)=\mathsf{\Delta }H\left(t\right)-\left|J\ast H_{prey}\left(t\right)-H\left(t\right)\right| \\ \mathsf{\Delta }H\left(t\right)=H_{prey}\left(t\right)-H\left(t\right) \end{gathered}$$

(18)

$$J=2\left(1-r_5\right)$$

2.

Harsh besiege (H(t + 1))

When r ≥ 0.5 and|e| < 0.5, the prey has low fleeing energy, allowing Harris’s hawks to easily encircle and attack it. The positions are updated as the following:

$$H\left(t+1\right)=H_{prey}\left(t\right)-e\left|a??H\left(t\right)\right|$$

(19)

3.

Besiege softly with a series of quick dives (H(t + 1))

When r < 0.5 and |E| ≥ 0.5, the prey has enough energy to flee, therefore Harris’s hawks engage in a gentle besiege by performing multiple fast dives around the prey, trying to gradually adjust its position and direction. Next is a model of this behaviour:

$$P_1=H_{prey}\left(t\right)-e\left|J \ast H_{prey}\left(t\right)-H\left(t\right)\right|$$

(20)

$$P_2=P_1+v \ast LEV Y \left(D\right)$$

$$H\left(t+1\right)=\{\begin{array}{ll}{P}_1& F\left(P_1\right)<F\left(H\left(t\right)\right)\\ P_2& F\left(P_1\right)<F\left(H\left(t\right)\right)\end{array}$$

(21)

4.

Harsh besiege with gradual rapid dives

When |e| < 0.5 and r < 0.5, because the prey lacks the energy to flee, the hawks launch a severe besiege to reduce the distance between their average position and the prey, and then attack and kill it.

The next is a mathematical depiction of this behaviour:

$$P_1=H_{prey}\left(t\right)-e\left|J \ast H_{prey}\left(t\right)-H\left(t\right)\right|$$

(22)

$$P_2=P_1+v \ast LEV Y \left(D\right)$$

$$H\left(t+1\right)=\{\begin{array}{cc}{P}_1& F\left(P_1\right)<F\left(H\left(t\right)\right)\\ P_2& F\left(P_1\right)<F\left(H\left(t\right)\right)\end{array}$$

(23)

where: ∆(t) represents the difference between the prey’s current and previous position.

J indicates the prey’s random jump strength.

P1. P2 two positions, the better next position selected between them.

3.3. Intra-Cluster and Inter-Cluster

The clustering procedure is optimized by attempting to determine both the CH nodes and the cluster member’s ideal placements in each cluster to improve both intra-cluster f_intra and inter-cluster f_inter communications. To construct compact clusters, decreasing the distances among all of the sensor nodes and their corresponding CH is the key to improving intra-cluster communication. Improving inter-cluster communication requires reducing distances between the BS and CH nodes, while also increasing average distances between each CH node and other CH, effectively covering network regions. f_intra and f_inter are denoted can be represented as in Equations (24) and (25), respectively [29]:

$$f_{intra}=\frac{1}{NN}{\displaystyle \sum }_{i=1}^{NN}dist\left(N_i.C{H}_m\right)$$

(24)

$$f_{inter}=\frac{avgD}{\frac{1}{c}{{\displaystyle \sum }}_{m=1}^c{{\displaystyle \sum }}_{N=1.m<m}^{c}dist\left(C{H}_m.C{H}_N\right)}$$

(25)

where

• c: the number of clusters.
• avgD: the average distance between the BS and the CHs.
• dist(CH_m. CH_N): the distance between two cluster heads CH_m and CH_N.

Many relative parameters, such as the alive nodes number and energy consumption, are used to measure and compare the performance of algorithms in WSNs using Matlab 2017b and take into consideration the comparative analysis and protocols of both the dead and alive nodes. In this case, the system is introduced with different levels of energy represented by progressive and normal nodes. The individually progressive node energy is more than the energy of each normal node; the increasing factor for the progressive can be represented using energy factor (a) where the energy increased directly by (1 + a) times of the normal nodes, where a is the factor.

The distribution of BS, cluster heads, and sensor nodes for some algorithms (LEACH, HHO, COYOA, and Genetics) are represented as shown in Figure 2a–c.

Simulation parameters of the proposed algorithms and protocols are listed in

Table 1. List of simulation parameters for the proposed algorithm.

Description	Parameters	Value
Network Area	Dx × Dy	100 × 100
Total number of Sensor Nodes	Num	100
Total number of cluster heads	m	10
Max. number of iterations	max_iter	4000
Communication range	c_r	20
Sensor node energy	energy	2
The length of data bits	k	4000
Sink node coordinate	Sensor_x, Sensor_y	0, 0
The energy consumed by the transmitter and the receiver	Eelec	50 × power (10,−9)
The energy consumed in the transmitter amplifier	Eamp	100 × power(10,−12)

. A scenario of the proposed algorithm is established in which the location of the BS will change according to the area dimension 100 × 100. The implementation is based on three different scenarios. In the first scenario, BS is at (0,0) at the start of the area coordination. In the second scenario, BS is at the centre of the area (50,50). In the third scenario, BS is at the corner of the area coordination (100,100). The heterogeneous system is started with initiated energy of different levels for CHs and normal nodes. The CHs energy is equal to (1 + a) times more than the energy of each normal node, where (a) is the energy factor.

After the components of the wireless sensor network are distributed, the network elects the head clusters, which verify the condition of the communication range with the neighbour nodes. Black nodes represent the dead nodes that cannot verify the condition. The number of alive nodes per round shows the power of the proposed algorithms.

4. Evaluation of the Proposed Algorithm

In this section, we evaluate the (AO) algorithm by the alive nodes number and energy consumption compared with LEACH, COY, HHO, and GA algorithms for three BS locations scenarios (0,0), (50,50), and (100,100).

4.1. The Number of Alive Nodes

In the first scenario, the base station location is at (0,0); Figure 3 shows that the genetic and LEACH (traditional) algorithms lose almost 70% of the nodes after 500 rounds and 800 rounds, respectively, whereas the COY algorithm at 1100 rounds and (AO, and HHO) algorithms lose the same amount at 1250 rounds. In this case, the proposed AO algorithm has the best loss rate at 1250 rounds.

In the second scenario, the BS location is at (50,50); Figure 4 shows that the genetics and LEACH (traditional) algorithms lose 70% of the nodes after 500 rounds and 1700 rounds respectively, whereas the COY algorithm at 1800 rounds and (AO and HHO) algorithms lose the same amount at 2000 rounds. In this case, the AO algorithm has the best loss rate at 2000 rounds.

In the third scenario, the BS location is at (100,100); Figure 5 shows that the genetic and LEACH (traditional) algorithms lose 70% of the nodes after approximately 500 rounds, whereas COY and AO algorithms at 1200 rounds and the HHO algorithm lose the same amount at approximately 1250 rounds. In this case, the proposed AO algorithm has a normal loss rate at 1200 rounds.

4.2. The Energy Consumption

In the first scenario, the base station location is at (0,0); Figure 6 shows that the genetic and LEACH (traditional) algorithms lose 80% of the energy after approximately 350 rounds and 370 rounds, respectively, whereas the COY algorithm at 400 rounds and (AO and HHO) algorithms lose the same amount at 450 rounds. The presented AO algorithm in this case has the best loss energy consumption at 450 rounds.

In the second scenario, the BS location is at (50,50); Figure 7 shows that the genetic and LEACH (traditional) algorithms lose 80% of the energy after 350 rounds and 400 rounds respectively, whereas the COY algorithm at 700 rounds and (AO and HHO) algorithms lose the same amount at 800 rounds. In this case, the presented AO algorithm has the best loss energy consumption at 800 rounds.

In the third scenario, the BS location is at (100,100); Figure 8 shows that the genetic and LEACH (traditional) algorithms lose 70% of the energy after approximately 350 rounds, whereas COY, and (HHO and AO) algorithms lose the same amount at approximately 400 rounds. In this case, the presented AO algorithm has a normal loss rate at 400 rounds.

Thus, in terms of the network lifetime and the network performance, the proposed AO algorithm has the best value of energy consumption compared with the existing algorithms, whereas LEACH and genetic algorithms have the least network performance. This is an important observation of the proposed algorithm over the traditional and metaheuristic algorithms. From Figure 3, Figure 4, Figure 5, Figure 6, Figure 7 and Figure 8 it is clear that the performance of AO on S2 is better than on S1 and S3. Moreover, AO has a positive effect on system stability.

According to three BS locations scenarios (0,0), (50,50), and (100,100), the proposed AO algorithm has achieved a maximum number of alive nodes and high energy compared to other algorithms. The mean of the alive nodes realized by the proposed AO algorithm in three scenarios are 1250, 1800, and 1200 rounds, respectively, outperforming the LEACH, COY, HHO, and GA algorithms. In this case, the presented AO algorithm has the best loss rate at 1800 rounds with BS location (50,50). Additionally, the means of the normalized energy of the proposed AO algorithm in three scenarios are 450, 800, and 400 rounds, respectively, outperforming the LEACH, COY, HHO, and GA algorithms. In this case, the presented AO algorithm has the best energy loss rate at 800 rounds with a BS location (50,50), allowing us to conclude that AO has a positive effect on system stability.

5. Conclusions and Future Work

This paper proposed an optimal algorithm for connecting nodes to their equivalent cluster heads. An applicable fitness function is designed considering essential factors of the network. The factors used to evaluate the algorithm include the lifetime and power consumption. The results are compared depending on proposed scenarios according to the position of the BS; S1 (0,0), S2 (50,50), and S3 (100,100). Simulation results show that the proposed AO algorithm has an optimal value compared with the existing algorithms in terms of network lifetime, whereas LEACH and GA have the least network lifetime. This is an important observation of the proposed algorithm over the traditional and metaheuristic algorithms. Furthermore, the network performance in the proposed AO algorithm has the best value of energy consumption compared with the existing algorithms, whereas LEACH and genetic have the least network performance. Thus, the proposed AO algorithm outperforms the traditional and metaheuristic algorithms. In addition, the performance of AO on S2 is better than on S1 and S3 in terms of network lifetime and energy efficiency. Therefore, AO has a positive effect on system stability.

In future work, for a secure model, the proposed clustering model will add the security feature to secure data transmission.