A novel cluster head selection using Hybrid Artificial Bee Colony and Firefly Algorithm for network lifetime and stability in WSNs

Wireless Sensor Networks (WSNs) are capable of achieving data dissemination between them such that exploration of their potential could be performed based on their frequency range. It is considered to be highly difficult for recharging sensor devices under adverse situations. The main drawbacks of WSNs concern to the issue of network lifetime, coverage area, scheduling and data aggregation. In particular, prolonging network lifetime confirms the success together with the energy conservation of sensor nodes, data transmission reliability and scalability of their operation in data aggregation. Clustering schemes are considered to be highly suitable for effectively utilising the resources with lower overhead, such that energy consumption is enhanced for upgrading the network lifespan. In this paper, a Hybrid Modified Artificial Bee Colony and Firefly Algorithm (HMABCFA) -Based Cluster Head Selection is proposed for ensuring energy stabilisation, delay minimisation and inter-node distance reduction for improving the network lifetime. This proposed HMABCFA integrates the benefit of the Firefly optimisation algorithm for generating a new position that which has the capability of replacing the position, which is not updated in the scout bee phase of ABC. This incorporation of Firefly optimisation algorithm into the ABC algorithm prevents the limitations of premature convergence, slow convergence and the possibility of being trapped into the local point of optimality in the clustering process. The modified ABC-based clustering process is phenomenal in improving the feasible dimensions for enhancing the process of exploitation and exploration. The results of the HMABCFA, on an average are confirmed to enhance the network lifetime by 23.21%, energy stability by 19.84% and reduce network latency by 22.88%, compared to the benchmarked approaches.

Keywords: Network lifetime; energy stability; Modified Artificial Bee Colony Algorithm; Firefly Algorithm; cluster head selection

The Wireless Sensor Networks (WSNs) generally consist of numerous number of small sensor nodes that has the capability of cooperating with one another for the purpose of attaining particular objectives that includes target area alerting, target area surveillance, target tracking, environment tracking, etc (Lee et al., [22]). The sensor nodes gather and sustain vital information for futuristic decision-making process, which are essentially taken the sink nodes (Alghamdi, [1]). The sensor nodes need to be deployed in an ad hoc or uniform manner for monitoring and smooth collection of potential information for handling different discrete events (Rao et al., [28]). However, the sensor network capability is highly restricted by the battery power availability and dead battery rechargeable characteristics of the deployed sensors (Farman et al., [12]). In most of the realistic situations, there exists a number of potential responsibilities such as data sensing, data processing and data relaying, which in turn utilises considerable amount of energy for facilitating information to the Base Station (BS). Hence, the battery power of WSNs is considered to be the scarce asset and need to be effectively and efficiently utilised (Baradaran & Navi, [3]). Clustering is the predominant approach that organises sensor nodes in a larger scalable way to eliminate the challenge of energy utilisation in WSNs (Kaur, & Mahajan, [19]; Kumar et al., [21]; RejinaParvin & Vasanthanayaki, [29]; Sharma et al., [35]; Sharma & Kumar, [32]; Sharma & Kumar, [33], [34]; Zhang et al., [41]). This clustering process is a significant way to sustain battery life of sensor nodes with maximised energy efficiency (Gupta & Sharma, [15]). In the clustering process, CH nodes are also responsible for circulating the gathered data from the individual cluster member of the clusters to the BS node (Fatemeh et al., 2017; Dhiman & Kumar, [7], [8], [9]).

A number a clustering-based CH Selection schemes were contributed in the literature for the past two decades to handle the network lifetime and energy stabilisation in the network. Some of the predominant traditional CH selection schemes contributed with respect to energy stabilisation and network lifetime include Hybrid Energy efficient Distributed Clustering (HEED), Power Efficient Gathering in Sensor Information Systems (PEGASIS) and Low Energy Adaptive Clustering Hierarchy (LEACH) with its variants (Dhiman, [6], [5]; Kaur et al., [18]). However, CH selection schemes proposed using swarm intelligence and evolutionary algorithms are considered to be more significant on par with the aforementioned traditional CH selection schemes. Recent study has shown that swarm intelligence-based CH selection techniques have been developed by a variety of academics. However, the CH selection schemes suffers from a number of limitations like delayed convergence, falling into the local point of optimality and stagnation that are inherent with each of the utilised swarm intelligent approaches. Thus, hybridisation of swarm intelligence algorithms is considered to facilitate better CH selection for enhancing the network lifetime and energy stability by mutually handling their limitation that hinders the deviation between the rate of exploitation and exploration. Among the swarm intelligence schemes, ABC and its suitable hybridisation algorithms have attracted a huge number of researchers to predominantly explore them, such that it could be used for significant CH selection processes. In addition, the hybridisation algorithm propounded by Panniem and Puphasuk ([25]) motivated the option of integrating modified ABC with FFA towards the process of selecting potential cluster head that results in better energy stabilisation and network lifetime.

In this paper, a cluster head selection scheme using Hybrid Modified Artificial Bee Colony and Firefly Algorithm (HMABCFA) is proposed for improving the network lifetime expectancy by stabilising energy, minimising delay and reducing the inter-node distance. This proposed HMABCFA approach combines the modified ABC algorithm with the Firefly Optimization Algorithm (FOA) for replacing the positions, which is not updated with the newly generated positions of the scout bee phase. ABC's intrinsic drawbacks of delayed convergence, premature convergence, and the potential for falling into the local point of optimality have been addressed by adding FOA's algorithm to the mix. There's also a new search equation in the employed bee phase to boost the probability of determining the better places, which can largely replace some of the worst positions with possible ones in the onlooker bee phase.

The remaining sections of the paper are structured as follows. Section 2 presents the survey of the state-of-the art swarm intelligent cluster head selection techniques with merits and limitations. Section 3 details the description of HMABCFA with the merits as a potential cluster head selection process. Section 4 shows the results of HMABCFA scheme and the benchmarked approaches with suitable justifications behind their predominant performance. The paper ends in Section 5, with significant contributions and an improvement in the future.

In this section, the most notable swarm intelligence-based CH selection scheme propounded over the recent years is reviewed and detailed with their merits and limitations.

A Genetic Algorithm-based CH Selection (GA-CHS) Scheme was proposed by Elhoseny et al. ([11]) for balancing the energy and network lifetime in WSNs. GA-CHS scheme used the merits of crossover and mutation for stabilising the energy and node stability throughout the network. It included a reactive strategy for balancing energy consumption for greatly enhancing the network lifetime by permitting the energy of the sensor nodes to deplete uniformly. It was identified to greatly extend the network lifetime with respect to first-node-die and last-node death, on an average by 31.21% and 13.26%, compared to the baseline approaches used for comparison. It was also considered to increase the computational efficiency and aggregate mean time by 0.62 seconds with a standard deviation of 0.06, respectively. Then, an Integrated Harmonic Search Algorithm (HSA) and PSO-based CH selection (IHSA-PSO-CHS) scheme was proposed by Shankar et al. ([31]) with energy efficiency for the purpose of attaining global search with faster convergence. IHSA-PSO-CHS scheme was proposed by combining the dynamic potentiality of PSO and high exploring search efficiency of HSA for the objective of enhancing the lifetime of the sensor nodes. It was determined to enhance the throughput, sustain the number of alive nodes, residual energy and minimise the number of dead nodes. It was estimated to improve the throughput and residual energy by 29.12% and 83.94%, compared to the baseline PSO algorithm. An Integrated Multi-objective Bee Swarm Optimization and Differential Evolution-based CH Selection (IMBSO-DE-CHS) selection was proposed by Prasad et al. ([26]) for efficient clustering process. This IMBSO-DE-CHS scheme enabled the process of clustering based on energy consumptions, residual energy and communication distance. It was confirmed to enhance the network lifetime and packet delivery ratio by 23.32% and 34.82%, compared to the benchmarked approaches.

An ABC-based CH Selection (ABC-CHS) scheme was proposed by Mann and Singh ([23]) for minimising energy consumption with the least number of hop count during the data transmission process (Song et al., [37]; Wang & Feng, [38]; Yang et al., [39]). This ABC-CHS scheme was identified to improve the mean throughput by 21.96%, packet delivery ratio of 18.12% and minimise the energy consumptions by 20.84%, compared to PSO and ACO-based CH selection approaches. An Improved Fish Swarm Algorithm-based CH Selection (IFSA-CHS) scheme was proposed by Sengottuvelan and Prasath ([30]) for optimal clustering process in WSNs with better balance in the energy of the network. The results of this IFSA-CHS scheme was confirmed to improve network lifetime expectancy by 16.21%, energy stability by 14.96% and the packet delivery rate by 19.42%, compared to the traditional LEACH and GA-based CH selection schemes. An Energy-Balanced Node Clustering Protocol based on Cuckoo Search (EBNCP-CS) scheme was proposed by Gupta and Jha ([14]) for attaining the objective of uniform cluster head nodes' distribution. EBNCP-CS scheme included an enhanced HSA algorithm for facilitating data packet routing between the sink and the CHs in the network. The number of alive nodes, mean energy consumption and network lifetime was realised to be enhanced by 20.74%, 17.21% and 15.94%, compared to the state of art protocols.

A Harmony Search-improved Cuckoo Search-based Clustering Protocol (HSCSCP) was proposed by Gupta and Jha ([14]) for sustaining energy stability and prolonging network lifetime. This HSCSCP was proposed with a novel objective function that helps in uniform distribution of cluster heads in the network. In specific, harmony search is improved and included in the routing process for facilitating reliable data packet dissemination between the cluster heads and the sink. It handled the issue of unbalanced energy consumption of sensor nodes in the network as the nodes that are closer to the sink may be overloaded with a huge amount of traffic load. It considered the problem of routing between cluster heads and the sink with the energy balanced node clustering (Gao et al., [13]; Song & Li, [36]; Zhao et al., [42]). The mean energy consumptions, network lifetime and the number of alive and dead nodes attained by this HSCSCP was identified to be predominant over the state-of-the-art protocols. However, this clustering protocol suffers from the issue of network scalability and thus the network throughput is compromised to an unacceptable level. A Hybridized Fruit Fly and Glowworm Search Optimization (GSO)-based Clustering Protocol (HFFGSOCP) was proposed by Dattatraya and Rao ([4]) for handling the tradeoff between diversification and intensification during the cluster head selection process. This HFFGSOCP included the dynamic exploration efficiency of GSO and considerable exploiting characteristics of Fruit Fly for cluster head selection. It was developed with a cluster head selection model that maximises network lifetime and sustains energy efficiency. It included the factors of energy, delay and distance for achieving the optimal cluster head selection process. It focused on the multiple objectives of minimising delay and at the same time maximising energy based on the inter and intra-distance estimated between the sensor nodes and its associated cluster heads. The performance of this HFFGSOCP analyzed based on coverage, normalised energy and the number of alive and dead nodes confirmed their importance in the process of energy stabilisation and data packet delivery.

Furthermore, Rambabu et al. ([27]) contributed a Monarch Butterfly and Artificial Bee Colony Optimization Algorithm (MBABCOA) for clustering sensor nodes with the view to balance energy and minimising delay in the network. This MBABCOACP included the merits of mutated butterfly adjusting factor for replacing and improving the exploration capability of employee bee phase. It was propounded with the ability of preventing delayed convergence and the capability of preventing the solution from resulting in the local optimality point. It was formulated with the global search potential that eliminated the inadequacy of the primitive ABC algorithm. It was designed with the capability of preventing the overloading of cluster heads with a non-uniform sensor node count as they have the possibility of resulting in nodes' rapid death during the clustering process. The simulation results of MBABCOACP confirmed their significance in sustaining energy efficiency compared to the baseline approaches. A Krill Herd Optimization and Genetic Algorithm-based Clustering Protocol (KHOGACP) was proposed by Karthick and Palanisamy ([17]) for preventing frequent selection of cluster heads which hurdles energy stability of sensor nodes in the network. Cluster head selection in this KHOGACP was based on a fitness function that took into account the overall distance from cluster heads to base station as well as the total intra-cluster communication distance. A cluster head can be selected based on the qualities of physical diffusion, foraging action, and effort attributed by neighbouring krills. It was identified to consecutively improve the network lifespan with a mean packet delivery rate of 7.29% and 3.83%, compared to the LEACH and GA approaches. During the clustering phase, Kavitha et al. ([20]) introduced a Gravitational Search Algorithm-based clustering protocol (GSACP) for allocating sensor nodes to an appropriate cluster head in order to maintain energy stability in the network. To increase the network lifetime and minimise energy consumptions, this GSACP was proposed. Energy dissipation was found to be superior, as was the amount of packets sent from the base station, compared to standard cluster head selection systems. Due to a problem with delayed convergence in the krill and GSA algorithms, the tradeoff between exploitation and exploration cannot be maintained.

The limitations that are determined during the review of the existing state-of-the-art cluster head selection approaches are listed as follows.

• The majority of the clustering protocols contributed in the literature suffers from the aspect of maintaining the rate of diversification and intensification during the cluster head selection process.
• Most of the cluster head schemes were not able to handle energy stability and lifetime, parallel with scalable increase in the number of sensor nodes in the network.
• Only a few number of clustering approaches focused on the complete set of objective that need to be essentially explored during the process of cluster head selection.

This proposed Hybrid Enhanced Artificial Bee Colony and Firefly Algorithm-Based Cluster Head Selection (HEABC-FA-CHS) Scheme comprises of three phases that include the search agents that are associated with the employee phase, onlooker bee and scout bee phases for the selection of energy efficient cluster head. The employee bee phase is responsible for completely searching the effective cluster head nodes from the complete set of sensor nodes, such that it could act in the process of effective topology control that attribute towards minimised energy consumptions and extension of network lifetime. In this phase, each and every employee bee search agent comprehensively searches for a new sensor node through the process of establishing interaction between the sensor nodes in the network topology. During this employee bee search process, if a new sensor node is identified to be potential, then the search agent updates the memory with the currently selected cluster head sensor node and sends the information to all the sensor cluster members of each and every individual cluster. Then, the onlooker bee phase is enforced to making decisions based on the computation of fitness probability derived based on the information gathered from the employee bee phase. This onlooker bee phase is a second level of identifying a better cluster head node from the existing set of sensor nodes, such that it could be memorised and updated to the other cluster member nodes of the network. This employee bee phase and onlooker bee phase of this proposed HEABC-FA-CHS scheme constitutes the exploitation phase (local search). Finally, the sensor nodes that are determined as inhibited by the employee bee search agent for a considerable amount of time is taken as a scout bee with the updated sensor node positions, such that it is potential for the next process of searching. The detailed view of the proposed HEABC-FA-CHS scheme is presented as follows.

Step 1: Initialisation

In this initialisation phase, each ith sensor node (employee bee) associated with each and every kth cluster (food source) is generated initially based on search Equation (1)

Graph

$S_{N(i,j)}=L{T}_j+{\psi }_{ij}(U{T}_j-L{T}_j).$ (1)

However, the search equation is determined to fail in facilitating high quality solutions and hence the method of search space division is incorporated for modifying the search equation based on Equation (2)

Graph

$S_{N(i,j)}=L{T}_j+\frac{({\psi }_{ij}+2m-1)(U{T}_j-L{T}_j)}{2NS},$ (2)

where "i" represents the sensor nodes of the network

Graph

$(1\le i\le NS)$ , which is investigated for its potentiality using "j" possible dimensions

Graph

$(1\le j\le D)$ with

Graph

$NS$ being the complete set of sensor nodes with a random number

Graph

${\psi }_{ij}$ that satisfies the condition

Graph

${\psi }_{ij}\in [-1,1]$ .

Step 2: Employee bee phase

In this employee bee phase, the ith sensor node (employee bee) exchanges information with gth sensor node (employee bee) of the network with the view to generate a new cluster

Graph

$N_{i,j}$ based on Equation (3)

Graph

$N_{i,j}=\{\begin{array}{cc}{S}_{N(i,j)}+{\psi }_{ij}(S_{N(i,j)}-S_{N(k,j)})& j=j^r\\ S_{N(i,j)}& j\ne j^r\end{array}.$ (3)

In this context, the strategy of best position is determined to be superior in exploiting the search space in a more effective manner and hence it is modified through Equation (4)

Graph

$N_{i,j}=\{\begin{array}{cc}{S}_{N(\text{best},j)}+{\psi }_{ij}(S_{N(i,j)}-S_{N(k,j)})& j=j^r\\ S_{N(i,j)}& j\ne j^r\end{array},$ (4)

where the value of "k" is randomly selected from the set of sensor nodes that ranges from 1 to

Graph

$NS$ with

Graph

$k\ne i,j^r$ randomly determined from the dimensions that varies between 1 and

Graph

$D$ . It is important to note that

Graph

$N_{i,j}$ is completely different from

Graph

$S_{N(i,j)}$ only at the component

Graph

$j^r$ . The new cluster heads' potential is evaluated and investigated in possible perspectives with respect to the old cluster heads' potential in order to decide the change of cluster heads for the process of clustering. But, this process of changing cluster head is facilitated in the network only when the condition

Graph

$f\left(N_{i,j}\right)<f\left(S_{N(i,j)}\right)$ is satisfied. If the condition fails, then the old cluster head is retained with the number of trials incremented by one. At this juncture, trial implies the counter number that does not impose any enhancement in the local searching process.

Step 3: Onlooker bee phase

In this onlooker bee phase, the onlooker bee agent is responsible for selecting each and cluster for further exploitation such that potential sensor nodes can be selected as effective cluster heads for topology control and reduced energy consumptions.

Graph

$\begin{array}{rl}\text{PROB}\left(S{N}_{\left(i\right)}\right)& =\frac{Q-\text{Fit}\left(S_{N\left(i\right)}\right)}{\sum _{j=1}^{NS}Q-\text{Fit}\left(S_{N\left(j\right)}\right)}\end{array}$ (5)

Graph

$\begin{array}{rl}Q-\text{Fit}\left(S_{N(i,j)}\right)& =\{\begin{array}{cc}\frac{1}{\left(f\right(S_{N\left(i\right)})}& f\left(S_{N\left(i\right)}\right)\ge 0\\ 1+|f(S{}_{N\left(i\right)}|& f\left(S_{N\left(i\right)}\right)<0\end{array}\end{array}$ (6)

In addition, the sensor node with low capability are replaced by the highly potential sensor nodes (sensor nodes that has maximum fitness value to be elected as cluster heads for each and cluster formed in the network) based on Equation (7)

Graph

$S_{N\left(np\right)}=H(S_{N\text{(best})}+{\psi }_{\left(np\right)}(S_{N\left(np\right)}-S{}_{N(rs1})+{\phi }_{\left(np\right)}(S_{N\left(np\right)}-S_{N\left(rs2\right)}\left)\right).$ (7)

Step 4: Firefly Optimization Algorithm imposed Scout Bee Phase

In this scout bee phase, the un-updated position of the new solution is determined based on the strategy of the modified FOA algorithm (Explained in Section 3.2) specified in Equation (8)

Graph

$E_{n\left(i\right)}=\sqrt{\sum _{c=1}^D{(S_{N(i,k)}-S_{N(j,k)})}^2}.$ (8)

In this situation, the factor of attractiveness of each solution towards the other solution is presented using Equation (9)

Graph

${\alpha }_{S\left(i\right)}=\alpha {}_0\ast e^{-\text{β}{E}_{n\left(i\right)}^2}.$ (9)

In addition, the search equation of the primitive ABC is modified based on Equation (10) for handling the balance between intensification and diversification.

Graph

$S_{N(i,j)}=S_{N(i,j)}+{\alpha }_{S\left(i\right)}(S_{N\left(j\right)}-S_{N\left(i\right)})+\left(r\text{and}\right(0,1)-0.5)$ (10)

Moreover, levy flight is used for enhancing the rate of convergence based on Equation (11)

Graph

$S_{N(i,j)}=S_{N(i,j)}+{\alpha }_{S\left(i\right)}(S_{N\left(j\right)}-S_{N\left(i\right)})+\left(r\text{and}\right(0,1)-0.5)+\text{Levy}\left(\lambda \right).$ (11)

To facilitate maximal exploration rate during cluster head selection, the suggested HEABC-FA-CHS scheme's scout bee phase has been developed.

The Firefly Optimization Algorithm is based on the inspiration derived from the fireflies flashing activity. This FOA is a specific category of a PSO that is simple for implementation and comprehension in the process of optimisation. This FOA has developed three potential rules such as, (i) each fireflies are attracted to each other independent of their sex, (ii) The brightness of firefly determined its degree of attraction (the firefly with lower brightness march towards firefly that possesses higher brightness), (iii) The fitness value associated with the landscape is determined based on the fireflies brightness. Moreover, the attractiveness and brightness of a firefly is inversely proportional to the distance between them. In this context, the Cartesian distance between two fireflies

Graph

$f_i$ and

Graph

$f_j$ are estimated based on Equation (12)

Graph

$d_{c\left(ij\right)}=\sqrt{\sum _{m=1}^{D_{SP}}{(f_{i,m}^{}-f_{j,m})}^2}$ (12)

where

Graph

$f_{i,m}$ and

Graph

$f_{j,m}$ represents the mth dimensional spatial coordinate associated with the fireflies

Graph

$f_i$ and

Graph

$f_j$ , respectively.

At this juncture, the function of brightness in the general implementation is decreased monotonically based on Equation (13)

Graph

$\text{β}\left(d_{c\left(ij\right)}\right)={\text{β}}_0{e}^{-\gamma d_{c\left(ij\right)}^2}$ (13)

Further, when the firefly

Graph

$f_i$ march towards the other firefly

Graph

$f_j$ based on its higher attractiveness, then the movement of firefly

Graph

$f_i$ is determined based on Equation (14)

Graph

$f_i^{\text{NEW}}=f_i^{\text{OLD}}+{\text{β}}_0{e}^{-\gamma d_{c\left(ij\right)}^2}(f_i^{\text{OLD}}-f_j)+\alpha (r\text{and}-\frac{1}{2}).$ (14)

The primitive firefly algorithm is considered to suffer from the limitations of premature convergence. This issue of premature convergence related to the firefly algorithm can be handled by modifying the attractiveness factor and its related function that decreases its value in each and every iteration. In this situation, the formula of tidal force is considered to be a potential candidate for replacing the attractiveness factor included in the firefly algorithm. The tidal formula is considered instead of the attractiveness factor associated with the firefly through the incorporation of the mass of a body and the distance between them. Further, the coefficient of absorption existing in the firefly algorithm will not operate in the formula of tidal force due to the characteristics of the formula. The simple formula derived from the tidal force helps in eliminating the overhead phenomenon that is inherently present more adaptive to the strategy of the firefly. The inclusion of tidal force also induces the behaviour of firefly to be more sensitive, thereby attaining the global optimisation with the prevention of premature convergence and maintaining balance between the exploitation and exploration.

Tides in celestial physics refer to when each body (Tidal water) is influenced by the gravitational force of the second mass or body (Earth) and third body (Sun) in a particular way (Moon). Gravitational attraction between two bodies is directly proportional to the magnitude of their product and inversely proportional to the square of the distance between them, as stated by Newton's universal gravitational law Tides are gravitationally attracting forces that have only a single departure between them. The equation of tidal force

Graph

$\left(T{d}_{\text{Force}}\right)$ derived from the basic Newton law of gravitation is presented in Equation (15)

Graph

$T{d}_{\text{Force}}=\frac{G_C{M}_m{M}_{iob}{(d_{b\left(ij\right)}+\mathrm{\Delta }{d}_{b\left(ij\right)})}^2+G_C{M}_m{M}_{iob}{d}_{b\left(ij\right)}^2}{d_{b\left(ij\right)}^2{(d_{b\left(ij\right)}+\mathrm{\Delta }{d}_{b\left(ij\right)})}^2}$ (15)

After rearrangement and simplification, the tidal force is modified based on Equation (16)

Graph

$T{d}_{\text{Force}}=\frac{2G_C{M}_m{M}_{iob}\mathrm{\Delta }{d}_{b\left(ij\right)}}{d_{b\left(ij\right)}^3}\equiv \frac{G_C{M}_m{M}_{iob}}{R_u^2}-\frac{G_C{M}_m{M}_{iob}}{R_l^2}\text{with}{R}_u\ne R_l\ne 0.$ (16)

The tidal force defined in the aforementioned Equation (16) is used for refining the intensity of fireflies in the new updated formula.

This firefly optimisation modified using tidal force is capable of attaining the value of global minimum with the least number of generations. When the distance

Graph

$d_{b\left(ij\right)}$ decreases with intensity as

Graph

$I\alpha \frac{1}{d_{b\left(ij\right)}}$ , the intensity of light with a distance from the source of light is estimated to be equal to the increased intensity of light. Let the complete number of "n" population be

Graph

$f=(f_1,f_2,...,f_n)$ , then the individual solution of the population is represented through

Graph

$f=(f_{11},f_{12},...,f_{1\left(ds\right)})$ with the number of variables or dimensions (ds) considered in the objective of cluster head selection. At this juncture, each solution refers to the vector that depicts the complete information of each sensor nodes such as position, possessed energy, inter and intra-cluster distance. In every iteration, the comparison of solutions (fireflies) is attained pairwise. If the fitness value of a solution is less than the other comparable solution, then the current solution is updated with all possible dimensions considered in the search space. In the high dimensional problem of cluster head selection, the distance between the solutions are determined directly by complying to the formula of

Graph

$I\alpha \frac{1}{d_{b\left(ij\right)}}$ . Thus, the matrix "A" presented in Equation (17) represents the complete set of solutions (sensor node information presented in the multi-dimensional space).

Graph

$A=\left[\begin{array}{cccc}{f}_{11}& f_{12}& .......& f_{1n}\\ f_{21}& f_{22}& ........& f_{2n}\\ \begin{array}{c}.\\ .\\ .\end{array}& \begin{array}{c}.\\ .\\ .\end{array}& ...........& \begin{array}{c}.\\ .\\ .\end{array}\\ f_{m1}& f_{m2}& .........& f_{mn}\end{array}\right]$ (17)

Further, the matrix "B" depicted in Equation (18) highlights the complete set of solutions after the application of

Graph

$I\alpha \frac{1}{d_{b\left(ij\right)}}$ .

Graph

$B=\left[\begin{array}{cccc}{\displaystyle \frac{1}{f_{11}}}& {\displaystyle \frac{1}{f{}_{12}}}& .......& {\displaystyle \frac{1}{f_{1n}}}\\ {\displaystyle \frac{1}{f_{21}}}& {\displaystyle \frac{1}{f_{22}}}& ........& {\displaystyle \frac{1}{f_{23}}}\\ \begin{array}{c}.\\ .\\ .\end{array}& \begin{array}{c}.\\ .\\ .\end{array}& ...........& \begin{array}{c}.\\ .\\ .\end{array}\\ {\displaystyle \frac{1}{f_{m1}}}& {\displaystyle \frac{1}{f_{m2}}}& .........& {\displaystyle \frac{1}{f_{mn}}}\end{array}\right]$ (18)

In this case, each solution is portrayed through a single vector that possess "n" dimension as presented in Equation (19)

Graph

$S_{\text{Vector}}=\left[\begin{array}{cccc}\frac{1}{f_{11}}& \frac{1}{f_{12}}& ........& \frac{1}{f_{1n}}\end{array}\right]$ (19)

Further, the two different solution vectors are compared for determining the near and far distance based on Equations (20) and (21), respectively.

Graph

$\begin{array}{rl}{R}_l& =y=\text{Min}\left(S_{\text{vector}}\right)\end{array}$ (20)

Graph

$\begin{array}{rl}{R}_u& =z=\text{Max}\left(S_{\text{vector}}\right)\end{array}$ (21)

Then, the tidal force is determined based on Equation (22) in each specific dimension to replace the attractiveness factor through the utilisation of Equation (16)

Graph

$T{d}_{\text{Force}}=\text{β}=\frac{G_C{M}_m{M}_{iob}}{R_u^2}-\frac{G_C{M}_m{M}_{iob}}{R_l^2}\equiv \frac{G_C{M}_m{M}_{iob}}{z}-\frac{G_C{M}_m{M}_{iob}}{y}$ (22)

Thus, the use of tidal force prevents the issue of delayed convergence inherent with the basic FOA.

In the process of cluster head selection, the modified FFOA algorithm is added into the employee bee and a scout bee phase of ABC for the better exploitation process. At the same time, the scout bee phase of ABC into included in the ABC for a better exploration process. Thus, ABC and FOA are mutually combined for establishing a better tradeoff between intensification and diversification.

The proposed HMABCFA Scheme, thereby played a vital role in the cluster head selection processes with the objective of stabilising energy with the minimised inter-node distance and delay in order to sustain network lifetime expectancy to the expected level.

The performance evaluation of the proposed HMABCFA Scheme and the baseline MBABCOA, KHOGACP and GSACP schemes are conducted using Python 3.6 with the associated libraries such as MatplotlIB, Numpy and Networkx. The experiments of the proposed HMABCFA scheme and the baseline MBABCOA, KHOGACP and GSACP schemes are conducted with the homogeneous and heterogeneous setup(Ding et al., [10]; Janakiraman & Deva Priya, [16]; Lee et al., [22]; Mehta & Saxena, [24]; Yelghi & Köse, [40]). In the homogeneous setup, the initial energy possessed by all the sensor nodes of the network is considered to be same. While, the sensor nodes possess a varying amount of energy in the heterogeneous setup. The similar experimental settings were considered in carrying out the simulation fairly in order to the compare the energy efficiency and network lifetime. The simulation environment used for evaluating the proposed HMABCFA scheme consists of 1000 sensor nodes that are randomly distributed in the terrain area of size 400*400 square metres. The base station of the network is considered to be located at the centre of the network. The simulation parameters used for the implementation of the proposed HMABCFA Scheme and the baseline MBABCOA, KHOGACP and GSACP head selection schemes are presented in Table 1.

Table 1. Simulation parameters used in implementing the proposed HMABCFA.

It was found that HMABCFA had a higher potential than baseline MBABCOA, KHOGACP and GSACP schemes in terms of living nodes, dead nodes, residual energy and throughput with a different number of cycles in the first phase of inquiry. Number of alive nodes and number of dead nodes determined with a progressive number of rounds evaluated for implementation is depicted in Figures 1 and 2. As the number of rounds increases, so does the number of alive sensor nodes. However, the number of alive sensor nodes sustained by the proposed HMABCFA at 3500th round is considered to be 93 nodes. On the other hand, the number of alive nodes maintained by the baseline MBABCOA, KHOGACP and GSACP schemes are almost zero at the rounds of 2990, 3280 and 3500 rounds, respectively. The proposed HMABCFA is thereby identified to handle the energy balance of the sensor nodes in the network on par with the benchmarked schemes, since it utilised a tidal force improved FOA algorithm that enhanced the rate of exploitation to the expected level during the cluster head selection process. In contrast, the plots proved that the number of dead sensor nodes is determined to be systematically increased with a progressive increase in the number of rounds. However, the number of alive nodes that are still alive at 3500th round during the implementation of the proposed HMABCFA is considered to be 96 nodes. In the benchmarked MBABCOA, KHOGACP and GSACP schemes, the nodes are mostly dead at the rounds of 3250, 3280 and 3500 rounds, respectively. The proposed HMABCFA is thereby confirmed to sustain the lifetime of the sensor nodes compared to the benchmarked schemes, since it included a rapid and reliable tradeoff between exploration and exploitation that aided in preventing worst fitness nodes from being chosen as cluster heads with reduced frequency of cluster head selection.

PHOTO (COLOR): Figure 1. Proposed HMABCFA: Alive nodes with the number of rounds.

PHOTO (COLOR): Figure 2. Proposed HMABCFA: Dead nodes with number of rounds.

Using a progressive number of rounds, residual energy and throughput are shown in Figures 3 and 4. According to our calculations, the residual energy of both our proposed scheme, HMABCFA, as well as the baseline MBABCOA, KHOGACP and GSACP schemes, will decrease with increasing rounds. HMABCFA's mean residual energy is found to be comparable to that of the benchmarked schemes with an increase in the number of cycles. It's easy to see that the proposed HMABCFA method performs well because it avoids frequent cluster head selection. The planned HMABCFA scheme's throughput has also been confirmed to be considerably improved, with an increase in the number of rounds at par with the benchmarked schemes, as well. For the suggested HMABCFA scheme to achieve such an impressive performance, there must be a balance between exploration rate and clustering.

PHOTO (COLOR): Figure 3. Proposed HMABCFA: Residual energy with the number of rounds.

PHOTO (COLOR): Figure 4. Proposed HMABCFA: Throughput with the number of rounds.

As part of the second part of the investigation, the proposed HMABCFA scheme and the baseline MBABCOA, KHOGACP and GSACP schemes are evaluated, and they are compared based on network lifetime, energy consumptions, throughput and packet delivery rate with different densities of sensor nodes within the network. As shown in Figures 5 and 6, the proposed HMABCFA as well as the baseline MBABCOA, KHOGACP, and GSACP schemes with varied density of sensor nodes in the network have different lifetimes and energy consumptions. HMABCFA's suggested network lifetime increases with sensor node density since malevolent sensor nodes can't be selected as cluster heads, and energy waste is totally eliminated in the network. On top of all that, by preventing any conceivable limits during exploration and exploitation phases, the energy consumption of the sensor nodes is also significantly decreased with implementation of HMABCFA. In comparison to baseline MBABCOA, KHOGACP, and GSACP schemes with varied density of sensor nodes, the proposed HMABCFA is predicted to improve network lifespan by 19.21%, 17.54% and 14.29%, respectively. Additionally, energy consumption is lowered by 18.65%, 15.36% and 12.82% in the proposed HMABCFA compared to MBABCOA, KHOGACP and GSACP schemes with varied densities of sensor nodes.

PHOTO (COLOR): Figure 5. Proposed HMABCFA: Network Lifetime with different densities of sensor nodes.

PHOTO (COLOR): Figure 6. Proposed HMABCFA: Energy Consumption with different densities of sensor nodes.

Performance of the proposed HMABCFA is shown in Figures 7 and 8 for different sensor node densities in terms of throughput and packet delivery rate. According to the proposed HMABCFA, as the number of sensor nodes increases, the throughput and packet delivery rate will drop, as the maximum number of packets are broadcast and a large quantity of energy is dissipated in the network. While the proposed HMABCFA with different densities of sensor nodes has a higher throughput and packet delivery rate than the benchmarked approaches, this is due to the fact that only energy efficient and trustworthy sensor nodes are selected as cluster heads, preventing the clustering process from selecting cluster heads repeatedly. Because of this, the throughput of the suggested HMABCFA scheme has been enhanced by 17.64% compared to baseline MBABCOA, KHOGACP and GSACP schemes with varied densities of sensor nodes in the network, respectively. When compared to the baseline MBABCOA, KHOGACP and GSACP schemes with varying densities of sensor nodes, the packet delivery rate of the proposed HMABCFA is also reduced by 16.72%, 14.84%, and 11.292%.

PHOTO (COLOR): Figure 7. Proposed HMABCFA: Throughput with different densities of sensor nodes.

PHOTO (COLOR): Figure 8. Proposed HMABCFA: Packet Delivery Rate with different densities of sensor nodes.

PHOTO (COLOR): Figure 9. Network Lifetime Scenario of the proposed HEABCFA scheme.

The First Node Death (FND), Half Node Death (HND) and Full Node Death (FND) of the lifespan scenario for the network are illustrated in the third section of the study. In the proposed HMABC-FA-CHS scheme it is established that the first sensor node will run out of its power at 112 rounds, that half of the network's sensor nodes run out of energy at 468 rounds, that the network's last sensor node will die during the 512 round. Figure 10 highlights the results in respect of the protocols considered for the investigation of the HMABCFA suggested system, which was analysed based on the FND, HND and FND network existence scenario. This HMABCFA success is expected to improve network life by 18.21%, an average of 21.38% relative to IMBOA-ABC-CHS, CHS-OCHS, GSA-CRS and KHA-OCHS baseline approaches by 20.18% and 22.94%, respectively.

PHOTO (COLOR): Figure 10. Network lifetime of the proposed HMABCFA scheme.

Tables 2 and 3 also include the secure network (sensor nodes alive), dysfunctional duration and life (in number of rounds) and benchmarked protocols tested by homogeneous and heterogeneous network configuration. Tables 2 and 3 suggested that HMABCFA is designed with 21.36%, 16.21%, 14.84% and 12.84%, in comparison to the MBABCOA, KHOGACP, GSACP and HSCSCP baseline methods to improve the stabilisation time. Similarly, the proposal to increase an HMABCFA scheme to 18.21%, to17.38%, to 13.96% and to 11.34% relative to the baseline approaches of MBABCOA, KHOGACP, GSACP and HSCSCP was considered to increase the stability time under heterogeneous establishment. All in all, the current system of HMABCFA is intended to improve network life respectively by 3.48%, 4.98%, 5.96% and 6.36%. The findings thus confirmed that the proposed HMABCFA scheme is primarily designed to improve stable life with a minimum duration of unstable life equal to the CH selection techniques.

Table 2. Stable period, Unstable period and lifetime of the network (in number of execution rounds) of the proposed HMABC-FA-CHS scheme with homogeneous setup.

Table 3. Stable period, Unstable period and lifetime of the network (in number of execution rounds) of the proposed HMABC-FA-CHS scheme with heterogeneous setup.

Tables 4 and 5 show the live nodes decided based on the rounds used to perform the same and heterogeneous setup in the HMABCFA protocol. The proposed HMABCFA protocol has shown a higher performance with respect to first node death, half nodes death, and full node death, both in homogeneous and heterogeneous installation, since adaptive tidal force is used to improve exploitation to avoid the limitations of updated ABC used in cluster head selection.

Table 4. Alive nodes determined based on the rounds used for executing the proposed HMABCFA protocol with Homogeneous setup.

Table 5. Alive nodes determined based on the rounds used for executing the proposed HMABCFA protocol with heterogeneous setup.

In this paper, HMABCFA has been proposed as a stable energy stabilisation clustering protocol with the reduced internode distance and delay in order to maintain the predicted degree of WSN network life expectancy. It was suggested that FOA be incorporated in ABC to improve its operating process by adding tidal force to avoid the problem of delayed convergence. In this integration of the modified ABC and FOA, positions which have not been updated with the newly created positions of the scout bee process are replaced. In the employed bee process, it also included a new search equation to increase the chance of estimating better positions, mostly substituting for some worse positions with potentials in the bee viewing phase. The simulation results of the proposed HMABCFA scheme confirmed the stability time of the homogeneous set-up of the base-line approaches MBABCOA, KHOGACP, GSACP and HSCSCP by 21.36%, 16.21%, 14.84% and 11.34%, respectively. The stability time in heterogeneous form is also considered to increase by 18.21%, 17.38%, 13.96% and 11.34%, relative to baseline systems. Spotted Hyena Optimization and Simulated Annealing clustering protocol are expected to be developed in the near future in order to compare them to the proposed HMABCFA system.

No potential conflict of interest was reported by the author(s).

Correction Statement

This article has been republished with minor changes. These changes do not impact the academic content of the article.