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An African vulture optimization
algorithm based energy ecient
clustering scheme in wireless
sensor networks
Mohit Kumar1, Ashwani Kumar2, Sunil Kumar3, Piyush Chauhan4 & Shitharth Selvarajan5
Energy eciency plays a major role in sustaining lifespan and stability of the network, being one
of most critical factors in wireless sensor networks (WSNs). To overcome the problem of energy
depletion in WSN, this paper proposes a new Energy Ecient Clustering Scheme named African Vulture
Optimization Algorithm based EECS (AVOACS) using AVOA. The proposed AVOACS method improves
clustering by including four critical terms: communication mode decider, distance of sink and nodes,
residual energy and intra-cluster distance. Through mimicking the natural scavenging behavior of
African vultures, AVOACS continuously balances energy consumption on nodes resulting in an increase
in network stability and lifetime. For CH selection, we use AVOACS, which considers the following
parameters: communication mode decider, the distance between sink and node, residual energy,
and intra-cluster distance. In comparison to the OE2-LB protocol, simulation ndings demonstrate
that AVOACS enhances stability, network lifetime, and throughput by 21.5%, 31.4%, and 16.9%,
respectively. The results show that AVOACS is an eective clustering algorithm for energy-ecient
operation in heterogeneous WSN environments as it contributes to a large increase of network lifetime
and signicant enhancement of performance.
Keywords AVOA, WSNs, Cluster Head, Sensor Networks, CMD
In recent years, Wireless Sensor Networks (WSNs) have become indispensable in many applications such as
healthcare systems, environmental monitoring and military surveillance or smart cities et cetera1. ese networks
are composed of an assemblage of physically disseminated sensor nodes which all together operate to collect,
process and transport data/mote towards impel sink node2. ese devices face serious energy considerations,
even though they are used for many purposes. While sensor nodes are normally battery powered, and the small
energy available in them limits life of an operating network3,4. erefore, prolonging the lifetime of wireless
sensor networks along with their stable and ecient performance have been important issues addressed in
design of WSNs. WSN can enable such virtual and real-world connections. Nonetheless, sensor nodes have
limited computing power, memory, and battery5. ey require batteries and are commonly employed in large-
scale unsupervised environments where battery maintenance or recharge is challenging.
In clustering is a major technique where many researchers focus to increase energy eciency in WSNs. It
utilizes cluster-based protocols, i.e., it groups sensor nodes into clusters that consist of a CH to aggregate data and
deliver these to the sink6. e selection of CHs and the management of clusters are key factors which inuence
network performance even though this method reduces energy consumption7. Intra-cluster communication
should be reduced to a minimum for energy eciency and an ideal clustering algorithm helps in distributing
the workload of all nodes across individual clusters, as well as minimizing intra cluster hops. Every cluster
has a CH whose main responsibility is to collect data from the other members of the cluster. CH is chosen
depending on several important factors such as intra-cluster distance, CMD, residual energy, etc. Using a meta-
heuristic method in CH selection has proved attractive in achieving optimum network performance8,9. When
1Department of Information Technology, School of Computing, MIT Art, Design and Technology University, Pune
412201, India. 2School of Computer Science Engineering & Technology, Bennett University, Greater Noida, UP,
India. 3Department of CSE, Galgotias College of Engineering & Technology, Knowledge Park-II, Greater Noida,
India. 4Symbiosis Institute of Technology, Nagpur Campus, Symbiosis International (Deemed University), Pune,
India. 5Department of Computer Science and Engineering, Chennai Institute of Technology, Chennai, India. email:
ShitharthS@kdu.edu.et
OPEN
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intra-cluster communication occurs, the nodes closest to the sink use much energy. is issue is known as the
hot-spot problem because these relaying nodes quickly consume energy10,11.
However, the existing cluster-based algorithms suer from drawbacks: shorter operational duration of sensor
nodes, high energy expenditure, delay in data delivery, hot-spot problems in large-scale applications, residual
energy dependence, connection failure, etc12–16. From this current perspective, several studies have been
conducted, each suggesting a unique energy-ecient routing strategy with the goal of extending the network’s
useful life by reducing the drain on the sensor nodes’ batteries: the proposed approach analyses and monitors
data from the wireless sensor networks17–19. However, despite its benets of energy eciency and network
lifetime extension eect, there are limitations if the African Vulture Optimization Algorithm-based Energy
Ecient Clustering Scheme (AVOACS) is applied. Among its drawbacks, it does not have the strong scalability
powered by being enormous and possessing many clusters along with cluster heads that large-scale WSNs do;
e resulting conciliation of both processing time as well as energy consumption is increased.
In this paper, we design a new energy ecient clustering scheme for WSN named AVOACS that is nature
motivated approach of scavenging behavior in Africa vultures. e AVOACS (An algorithm for Optimization
in energy Consumption using the four mandatory factors which improves network life) that is an ecient
method to reduce power consumption and lifetime of networks by having four important parameters Based
on communication mode decider, Sink –node distance, residual energy & intra cluster distance. AVOACS
uses these parameters to dynamic cluster head selection and optimizing the clustering process for reducing
energy consumption. e proposed AVOACS method is experimentally validated in terms of performance
by comparing it with the performances for some well-known existing state-of-the-art clustering algorithms:
PSO-ECSM, HWSHO, OE2-LB and ABC-DE. Experimental results indicate that AVOACS not only has better
network stability, but also prolongs the lifetime of a wireless sensor network compared with another algorithm.
us, a retrospective assessment reveals a few characteristics that might signicantly increase network lifetime
e major contributions of this paper are highlighted as follows:
• e proposed AVOACS for WSNs formulated the cluster formation through several essential parameters
such as communication mode decider, distance to sink, residual energy of sensors and intra-cluster distance.
• e optimal selection of cluster heads is compatible with the characteristics shown in AVOACS which demon-
strated signicant advantages on energy eciency for network Longevity.
• e dynamic clustering adapts cluster head selection and communication strategies by considering factors
such as node energy levels or distance to the sink, optimizing energy usage and load sharing based on network
conditions.
• To test and validate the proposed methodology with the state-of-the-art optimized routing methods based on
particle search, such as PSO-ECSM7, HWSHO20, OE2-LB21, and ABC-DE22, and it is shown to have achieved
higher overall performance.
e remainder of the manuscript is summarised in the sections below. Sect“Literature review” provides the
background research, while Sect“Preliminaries”describes the proposed strategy. e simulation ndings are
detailed in Sect“Proposed methodology”, and the conclusion is in Sect“Experimentation, results and analysis”.
Literature review
Clustering algorithms have an important role to play in the energy eciency of a Wireless Sensor Network
(WSN), and lot of research has been done on developing ecient clustering algorithm for increasing the lifetime
of network. Existing optimization-based clustering schemes are good energy conservation approaches, and
some further improved by utilizing certain issues regarding cluster formation to verify their performance under
dierent conditions. However, most of them experience diculties in scalability as they adapt into a large-scale
network rather than the target one for which these were proposed initially23–26. is part presents major works
in energy-ecient clustering algorithms, mainly inuenced by nature-based optimization methods27.
Deepa et al.28 proposed multi-path routing protocol utilizing swarm optimization. e cluster head is
selected near the sink coverage area, and the energy hole problem is solved by using a modied Particle Swarm
Optimization (PSO)-based clustering algorithm. A particle swarm optimization-based clustering technique with
a mobile sink was suggested by Wang et al.29. Rambabu et al.30 suggested a HABC-MBOA algorithm for CH
selection. HABC-MBOA was found to be useful in preventing sensor node overloading when used as CH. run
et al.31 presented the databionic swarm system. As a result, while Swarm-based algorithms are task-centred and
data independent approaches for WSN optimization issues they struggle with premature convergence problems
leading to suboptimal performance in Heterogeneous networks due to their static approach of deployment
irrespective the network dynamics and heterogeneous energy-based node implementation32.
Palattella et al.33 proposed that IoT-based WSN universality may be hindered by the need for reliable,
scalable, and cost-eective connectivity. It has been pointed out that these technologies may be used in diverse
contexts, such as for consumer IoT and industrial IoT. e article focuses on the signicant developments of
5G technology in IoT and the commercial implications that follow from them. Ilango et al.34 used mapper and
reducer programming to implement the ABC Algorithm in a Hadoop environment. e suggested ABC was
shown to reduce execution time and fault of classication for a collection of ideally designed clusters in empirical
testing. e ndings show that the suggested ABC scheme outperforms dierential evolution and PSO35.
In this paper, Gaikwad et al.36 has presented an enhanced ABC that optimizes large-scale data clustering. By
using the modied ABC, the cluster consumes less power. For selecting CHs, the protocol methodology uses a
distributed technique, and K-means is utilized to x the threshold power based on experimental data. Amiri et
al.37 proposed a novel fuzzy algorithm with enhanced discrete ABC for data clustering.
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Betzler et al.38 developed an IoT- based WSN technique for estimating round-trip times that incorporates
the age factor for retransmission timeouts. Cluster formation is most important part of clustering process which
has been accentuated by several researchers9,10. Das et al.39 presented a new clustering technique by utilizing
probability-based selection mechanism for allocation of a set of data in each cyclic rotation. Rani et al.40 presented
dynamic clustering-based technique utilizing Genetic algorithm. e CHs selection was made based on residual
energy and node’s location. Pan et al.41 proposed a search model utilizing best-of-random mutation strategy.
e performance assessment was done by employing various optimization techniques. e results obtained
strengthen the claim made by suggested method as it depicted signicant gain in performance42,43. Bagirov et
al.44 suggested approach’s performance is compared to that of other methods, and the ndings demonstrate that
the suggested method outperforms its rivals. e performance of Bee Colony Optimization (BCO) in clustering
datasets may be an essential research component, even if there are various clustering applications of BCO in
the literature. It is combined the suggested approach with k-means algorithms to improve its performance and
provide optimum solution45–47.
Verma et al.20 introduced the HWSHO approach in order to address the problem of green communication in
6G-enabled large WSN devices. is was accomplished by using cluster-based data distribution in the network.
is method is an excellent example of a solution that may be useful for a variety of malicious apps that are
interested in green communication via 6G-enabled Internet of ings devices. CH selection is found to be
an NP-Hard problem, and achieving optimal network performance is one of the dicult tasks that must be
accomplished. As a consequence of this, there is a requirement for a metaheuristic strategy that is able to meet
crucial characteristics in an optimum fashion. ese critical parameters are necessary for CH selection48. As a
result, many dierent metaheuristic approaches such as GA49, PSO50,51, WOA, MFO52, and were presented in
order to optimize the cluster selection53. e existing metaheuristic algorithms used for routing have several
limitations like lack of scalability, unbalanced exploration and exploitation and ineectiveness in handling the
dynamics of the network. Beside that the existing algorithms are still not able to truly optimize the decision
of clustering and routing leading to ineective energy consumption. e proposed optimization algorithm
addressed these deciencies and improves the performance on various metrics. Among the several metaheuristic
algorithms available, AVOA is used in this research to enhance network eciency. AVOA is used in this study to
improve the eciency of decision-making in order to provide the best possible value throughout the clustering
process. e current routing protocols cannot provide an energy-ecient solution for routing in wireless sensor
networks. AVOA may reduce application complexity by using the tness function54.
Nature-inspired optimization algorithms are promising for real-world engineering problems. One such
technique is the Arithmetic Optimization technique (AOA), designed for optimization23. AOA helps engineers
with constraint management tasks like resource allocation and system optimization traverse and use the solution
space. Kumar et al.24 proposed chaotic marine predators algorithm (CMPA) has promise. Chaos theory and
predator-prey interactions improve optimization exploration and convergence. CMPA optimises mechanical and
structural designs that traditional approaches struggle with. Optimizing shell and tube heat exchangers has been
successful. e AVOA solves complicated multi-dimensional and non-linear optimization problems by balancing
eciency and accuracy25. ese methods improve exploration-exploitation harmony to solve optimization
problems. Engineering situations benet from convergence rates and eective constraint management. Data
transmission mechanisms are essential for optimizing energy eciency and network durability. e ELFO
algorithm is inspired by eel foraging26. ELFO’s adaptive foraging technique allows ecient network exploration
to nd optimum paths while reducing energy. PROA uses reinforcement learning and optimization to improve
decision-making in scenarios like tuning automobile suspension elements for performance55. It might improve
clustering and node communication in WSNs, ensuring network stability even when circumstances change.
ese methods may improve energy utilization and operating eciency in WSN installations, overcoming
optimization challenges. ough, much work has been done on Energy ecient clustering algorithms but still
there is a requirement of adaptive and scalable solutions, especially for WSNs having heterogeneous nodes with
varying capabilities as well energy levels. Table1 shows the reference study of the optimization methods on IoT
based WSN.
Preliminaries
In this part, we outline the network assumptions before proposing the suggested work’s operational structure.
AVOACS network assumptions
It is vital to note that while replicating the proposed study, several network assumptions about medical things
must be considered.
1. e network is composed of randomly deployed sensor nodes, with node uniformly placed in a two-di-
mensional region. e nodes are battery-powered and, aer deployment, do not move from their respective
locations for the lifetime of the network. e nodes have the ability to sense, process and transmit data.
2. A single sink node or base station is located inside the sensor eld between sinks and source nodes. Sensor
nodes are presumed to be limited in power and incapable of remote recharging. Nonetheless, the sink has no
energy constraints since it gets a constant source of energy.
3. e network is clustered where sensor nodes clustered in clusters. In each cluster, a specic node called the
Cluster Head (CH) is responsible for collecting data from all the member nodes of her corresponding in its
hotspots and then transmit it directly to Sink. e cluster head is dynamically selected each round according
to residual energy, distance to the sink and intra-cluster communication costs.
4. e nodes are considered homogeneous, meaning they possess processing, initial energy, and sensing range
congurations.
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Energy consumption model
Energy consumption of the Network is one important factor which directly impacts on network lifetime and
performance as a whole, hence in the proposed AVOACS by considering energy consumed by each node. Energy
model. e energy consumption model used in this work is based on a generic radio power dissipation that
accounts for transmission and reception cost of the whole communication protocol. It includes the following
assumptions and equations for them as energy consumption model of sensor nodes in network. A distance
dij
between two nodes i and j is expressed as follows. e energy used by node i during the transmission of z-bit
data to node j is
Etx (z,dij)=
{
z∗Eel
+
z∗Eefs*dij
2
for dij ≤do
z
∗
Eel +z
∗
Eamp*dij 4f or dij > do (1)
e energy spent rather than starting a transmitter and reception circuit is denoted by
Eel
, and ‘do’ denotes a
minimum distance and has to be written as in Eq.(2).
do=
√
Eefs
Eamp
(2)
Where, Eqs.(3), (4)
Erx (z)
represent the energy spent by a node in accepting and aggregating z-bit data packets,
and
Edx (z)
represent the consumption of energy throughout aggregation of data respectively.
Erx (z)=z*Eel
(3)
And
Edx (z)=x*z*Eda
(4)
Equation(5) calculates the overall energy
ET otal
spent in packet forwarding, processing, and data aggregation.
ET otal =Etx+Eel +Edx
(5)
Proposed methodology
We aim to build a cluster-based data aggregation routing scheme in WSNs using the network above paradigm.
Using four important parameters, the proposed method extends the life of the network. As a result, the primary
goal to be explored is creating a load-balanced data aggregation routing scheme that eciently links all sensors
to the sink node. e remaining energy usage among multiple sensors in the Network utilizes a modied energy-
aware AVOA algorithm to choose the optimal CH for each cluster. AVOACS presents the Network’s energy usage
and reduces the Network’s overall energy transmissions. e AVOA meta-heuristic method was rst presented
by Abdollahzadeh et al.54 in the year 2021. Since that time, it has been implemented in a variety of real-world
engineering applications. In order to build the AVOA, simulations and models were used that were based on the
feeding behaviors and daily routines of African vultures. e following considerations are taken into account in
order to carry out the simulation that is known as AVOA. is simulation recreates the life patterns and foraging
strategies of African vultures, and it is carried out by using the following elements.
References Method Objective Research gaps
Pravin et al.56 Genetic Algorithm for Stochastic
cluster head selection Cluster head selection, energy balancing in IoT-WSN Energy balancing in IoT-WSN is considered, but the
optimization technique used there is crude.
Sahoo et al.57 Metaheuristic (CBA-EH) Method Network longevity, Cluster head selection, and energy
harvesting in WSN Application in WSNs restricted to IoT with wok on
multiple objective optimizations for energy conservation.
Moghaddasi et al.58 DRL method Energy consumption, resource eciency and task
ooading It concentrates on ooading eciency but has a shallow
clustering mechanism for WSNs.
Moghaddasi et al.59 DDQN method Multi-objective optimization and task ooading oroughly discusses security but do not emphasize
energy eciency in WSN clustering.
Gharehchopogh et al.60 Dynamic Harris Hawks
optimization (HHO) IoT security, botnet detection and dynamic HHO Security in IoT is the focus, but the main goal of this
paper is not energy-ecient clustering.
Gharehchopogh et al.61 AVOA optimization Method Multilevel thresholding and image segmentation For image processing; not applicable for WSN clustering
or energy eciency.
Gharehchopogh et al.62 Chaotic Quasi-oppositional
farmland fertility algorithm Optimization, solving optimization engineering
problems
Strictly related with engineering optimization, for signals
from a controlled experiment are not directly applicable
to optimizing the energy eciency of WSNs.
Kumar et al.63 Caddisfalcon optimization
algorithm Optimization and energy transfer in IoT network Only high-level energy transfer — not clustering in
WSNs.
Zhou et al.64 GSHFA-HCP clustering method Performance monitoring, Clustering with agricultural
IoT Applicability mostly on agriculture IoT system not
suitable for wider range of WSN applications.
Tab le 1. References study of the optimization methods on IoT based WSN.
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(i) ere are N vultures in the African vulture population, and the user of the algorithm decides how large N
should be depending on the conditions at the time of the calculation. e position space of each vulture is
represented by a grid with D dimensions; the size of D varies depending on the complexity of the issue.
(ii) e population of African vultures may be broken down into three distinct clusters according to the way
in which they make their livelihood. e rst cluster determines the most optimal viable solution by using
the tness value of the viable solution as a metric to evaluate the quality of the approach. e second cluster
of thought maintains that out of all of the potential solutions, the one that can really be implemented is the
one that is second-best. e third and nal group is made up of the remaining vultures.
Algorithm 1. AVOACS Procedure.
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(iii) e vulture hunts in groups throughout the population in which it resides. As a direct consequence of this,
several species of vultures full a variety of roles within the community.
(iv) Similarly, if the tness value of the population’s feasible solution may be understood to reect the advan-
tages and downsides of vultures, then the vultures who are the weakest and most hungry correspond to
the vultures that are the worst at the current time. On the other hand, the vulture that is the healthiest and
most numerous at this time is the greatest option. Vultures in AOVA strive to position themselves near the
greatest and away from the bad.
Based on the fundamental ideas about vultures and the four assumptions used to replicate the articial vulture’s
optimization algorithm, the problem-solving process can be broken down into ve stages that represent the
foraging behaviours of dierent vultures.
Identifying the best vulture in clusters
Aer the initial population has been formed, the tness of each solution is determined, and the best and worst
performers are chosen to serve as vultures for the rst and second groups, respectively. At each iteration of the
tness test, populations are subjected to a thorough analysis.
S(i)=
{
Bestv1if fi
=
P1
Bestv1if fi=P2, where fi=
F
v
(i)
∑
n
i=1Fv(i)
(6)
e probability that the chosen vultures will lead the other vultures to one of the best solutions in each cluster
is determined by Eq.(6), where
P1
and
P2
are the best solutions in the cluster. Both of the search operation’s
input parameters must have values between 0 and 1, with the total being 1. Using the rank selection to choose
the best tness from each set using fi
=
Fv
(
i
)
∑
n
i=1
Fv(i) increases the probability of selecting the optimal solution.
Vulture hunger rate
Vultures are remaining on the hunt for food, and when they get it, they have a burst of energy that helps them
to go further in their quest for more. On the other hand, they are more aggressive when they are hungry since
they lack the strength to y long distances or to hunt for food alongside larger, stronger vultures. is sort of
behaviour has been modelled mathematically with the help of Eq.(7). e rate at which the vultures are satiated
or hungry has also been used to mark the shi from the exploratory to the exploitative phase. Equation(7),
which accounts for the decreasing rate of satisfaction, has been used to predict this phenomenon.
Fv= (2
∗
r1+ 1)
∗⇕∗ (
1
−itr
i
itrmax )
+
⊔
(7)
⊔
=
\∗ (
sinw
(π
2∗itr
i
itrmax )
+cos
(π
2∗itr
i
itrmax )−
1
)
(8)
In Eqs.(7), (8), the symbol
Fv
indicates that the vultures have consumed all of the food available to them,
iteration
i
represents the number of the current iteration,
itrmax
represent the overall number of iterations,
and
⇕
is a random value ranging from − 1 to 1 that uctuates with each new iteration.
\
are an integer chosen at
random from the range − 2 to 2. rand1 returns a result that is completely random between 0 and 1. If the z value
goes below zero, it indicates that the vulture is starving, and if it goes above zero, it indicates that the vulture has
satiated.
Exploration
Here, we examine the AVOA exploration phase. Vultures have keen vision, which helps them nd prey and dead
animals. When searching for food, vultures y long distances and do detailed observations of their surroundings.
e vultures in the AVOA may use one of two methods to explore seemingly random sites, with the method
being selected at random. Exploration stage is need to provide a value between 0 and 1 for this option before
you can begin the search process. Which method is used is up to it. A random integer between 0 and 1 is created
during the exploration phase and used to decide which approach to pursue. e Eq.(9) is utilized if the number
is greater than or equal to the parameter. If, however, the digit count is under Eq.(11), the formula will be used.
is is shown by Eq.(12).
V(i+ 1) = S(i)−D(i)∗Fv
(9)
D(i)=|ϵ∗S(i)−V(i)|
(10)
V(i+ 1) = S(i)−Fv+r2∗((UB −LB)∗r3+LB)
(11)
V(i+ 1) =
{|
ϵ
∗
S
(
i
)−
V
(
i
)|
if V1
≥
rv1
S(i)
−
Fv+r
2∗
((UB
−
LB)
∗
r
3
+LB)if V
1
<r
v
1
(12)
e position vector of a vulture in the iteration that follows will be indicated by the
V(i+ 1)
, and the satiation
rate of the vulture in the current iteration will be denoted by the symbol
Fv
, which can be determined by using
Eq.(7). In Eq.(10),
S(i)
is a good example of the kind of vulture that is chosen by Eq.(12). e vultures patrol
the area randomly in order to protect their meal from the other vultures.
ϵ
is created via the formula
ϵ
=
r2
, where
r2
is a randomly produced number between 0 and 1, and
ϵ
is then utilized as a coecient vector to
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enhance the random motion, which shis with each iteration.
r3
is a randomly generated number between 0
and 1. e vector location is determined by the vulture’s
V1
. e variable boundaries are shown by
LB
and
UB
.
r3
increases the amount of unpredictability. If
r3
is somewhat close to 1, solutions that are comparable are
spread, which adds a random motion to the
LB
.
Exploitation stage-1
At this point, the AVOA’s eciency stage is being analysed for its eectiveness. e AVOA will proceed to the
exploitation phase if the value of
Fv
is less than 1, since this indicates that there is room for prot. is phase,
like the previous one, is divided into two sections, and each of those portions employs a distinct tactic. Two
factors,
V2
and
V3
, dene the likelihood that each approach will be selected throughout each of the phases that
take place internally. e strategy for the rst phase is determined by the parameter
V2
, whereas the second
phase is determined by the parameter
V3
. Both of the parameters need to be set to 0 and 1 before the search
operation can be carried out. When the value of |
Fv
| is between 1 and 0.5, the exploitation phase starts. During
the initial phase of the battle, both a rotating ying strategy and a siege-ghting strategy will be used. Before
performing a searching operation, the value of
V2
, which ranges between 0 and 1, will be used to choose which
strategy to use.
rv2
is constructed right at the beginning of this phase. If this amount is more than or equal to
V2
, the implementation of the Siege-ght will go more slowly. In the event that the random number is lower
than
V2
, the rotating ying method will be used. e Eqs.(13), (14) illustrates how to carry out this technique.
V(i+ 1) = D(i)∗(Fv+r4)−d(t)
(13)
d(t)=S(i)−V(i)
(14)
e value of
D(i)
may be found by using Eq.(10), and the value of
Fv
can be found by applying Eq.(7) to the
satiation rate of vultures. A random number between 0 and 1,
r4
is added to the formula to make the random
coecient even more unpredictable. In Eq.(14),
S(i)
represents one of the best vultures from the two groups
that was chosen using Eq.(17) during the current iteration.
V(i)
represents the current vector location of the
vulture, which is used to calculate the distance between the vulture and one of the best vultures from the two
groups.
Vultures typically perform a ying pattern that may be described as a rotating ight, and this ight pattern
can be utilized to mimic spiral motion. Mathematical modelling of circular ight has been accomplished via the
use of the spiral model. Using this approach will result in the formation of a spiral Eq.(18) involving all of the
vultures and one of the top two vultures. Equations(15) and (16) are used to compute
a1
and
a2
and provide
an expression for the rotational ight.
a1=S(i)∗
(
r5∗V
(
i
)
2π
)
∗cos (V(i
))
(15)
a2=S(i)∗
(
r6∗V
(
i
)
2π
)
∗sin (V(i
))
(16)
V(i+ 1) = S(i)−(a1+a2)
(17)
V(i+ 1) =
{
D
(
i
)∗(
Fv
+
r4
)−
d
(
t
)
if V2
≥
rv2
S(i)
−
(a
1
+a
2
)if V
2
<r
v
2
(18)
Exploitation stage-2
During the second stage of the exploitation process, the movements of the two vultures lure many other species
of vultures to the food supply, where a siege and a vigorous ght for food ensue. When the value of
Fv
is lower
than 0.5, the transition into this phase begins. During this step, the random number generator
rv3
will produce
a value between 0 and 1. If
rv3
is more than or equal to
V3
, a large number of dierent kinds of vultures should
converge around the source of food. Alternately, the aggressive siege-ght approach described in Eq. (23) is
adopted if the value created is less than
V3
. is occurs if the value generated is less than
V3
.
A1=Bestv1(i)−
Best
v1
(i)∗V(i)
Best
v1(
i
)−
V
(
i
)
2∗F
v
(19)
A2=Bestv2(i)−
Best
v2
(i)∗V(i)
Best
v2(
i
)−
V
(
i
)
2∗F
v
(20)
In the last step, the vultures are summed up with the help of Eq.(20), in which
A1
and
A2
come from the
previous Eqs.(19), (20), and
V(i+ 1)
is the vulture vector for the next iteration. e names given to the best
vultures in the rst and second groups of this iteration are
Bestv1(i)
and
Bestv2(i)
, respectively.
V(i)
stands
for the vector position of a vulture at any given moment.
V(i+ 1) = (A1+A2)/2
(21)
V(i+ 1) = S(i)−|d(t)|∗Fv∗levy (d)
(22)
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V(i+ 1) =
{(A
1
+A
2
)/2if V
3
≥r
v3
S
(
i
)−|
d
(
t
)|∗
F
v∗
levy
(
d
)
if V
3
<r
v3
(23)
When the value of |
Fv
| is more than 0.5, the head vultures begin to hunger, and as a result, they are unable to
compete with the other vultures in terms of strength. Equation(22) is utilized in order to simulate this motion
as accurately as possible.
d(t)
represents the distance that the vulture is from one of the best vultures in the two
groups, and this distance is determined by applying Eq.(21) to the equation found in Eq.(22). Patterns of Levy
ight65 have been exploited to improve the performance of the AVOA in Eq.(23), and LF has been recognized
and used in the operations of metaheuristic algorithms.
e IPSO-CS method that has been proposed can analyze the tness population to determine which node
is most suitable for becoming CH. e tness function evaluates each individual, or node, to determine their
level of physical tness and recommends the most eective method for preserving the nodes’ available energy.
In this particular scenario, one must be careful not to discount the signicance of tness-related factors. It is
of the utmost importance to provide those essential physical characteristics that will, in the end, determine
whether CH is selected. e parameters of tness include. To select the optimal CH, we base our decision on
four fundamental measures of tness.
1. Residual energy: e node’s remaining energy value, which is the most important parameter. e CH has
a higher per-second energy consumption than the other nodes. erefore, the node with the most energy must
be selected. All nodes have access to the starting energy, but their reserves decrease at dierent rates depending
on how close they are to the sink. erefore, the amount of energy still available plays a role in picking a CH.
rough the use of Eq.(26), we can calculate the residual energy of each sensor node, which can then be summed
to get the total residual energy.
f1=
1
N∑
N
i=1E(i
)
(24)
f2=
1
cl ∑
cl
i=1E(n) (25)
Obj1=
f
1
f2
(26)
2. Distance between sink and node: In this parameter, energy is used to calculate how far away each node in the
network is from the sink. In any case, the total amount of energy used by the sink is proportional to its separation
from the node. So, the base station may be improved in light of the parameters below the median spacing
between the member nodes, which are taken into consideration by the networking approach for CH selection.
Instead of basing decision-making on CH proximity,
Obj2
and Eq.(27) with distance is represented as:
Obj2=
∑
N
i=1(
D
(N(i)−S)
D
AV G(N(i)−S)
(27)
DAV G(N(i)−S)=
(∑N
i=1,D(N(i)−S)
N
)
(28)
Evaluating distance costs between nodes i and sink using the second tness parameter (
Obj2
) in Eq.(27), and
calculating Euclidean distance
DN(i)−S
and average distance
DAV G(N(i)−S)
in Eq.(28).
3. Communicating mode decider: e CMD is a crucial parameter in AVOACS that adaptively chooses the
communication scheme, which can be used for transmissions between sensor nodes and from them to the sink.
It decides some factors like whether the communication between nodes take place in single hop manner and
multi hops communication nature of transferring data packet by other nearby cluster head according residual
energy, distance with the sink node. Single-hop communication is used for short distances to reduce energy
consumption and multi-hop communication for long-distances due the expensive cost of high power. Minimum
CMD value for a Network CH node.
us, a node’s CMD may be calculated using the following formula and the h tness parameter (
Obj3
).
e total number of CHs or clusters in the Network is denoted by the variable
NC
.
Obj3=
(∑N
C
i=1,j=1D(CH(i)−CH(j))
NC
+D(N(i)−S)
)
(29)
e distance between the CHs is represented by
D(
CH
(
i
)−
CH
(
j
))
in the Eq.(29), while the distance between the
node i and sink is represented by
D(
N
(
i
)−
S
)
in the same equation. If the value of
Obj3
, is decreased, the value
of ‘CMD’ will increase in proportion.
4. Intra-cluster distance: e chance of becoming a CH increase for nodes that are both more energetic and
closer to the control centre. Better distribution of cluster leaders throughout the Network means less variations
in inter- and intra-cluster distances. e average distances between cluster members and cluster heads are
minimized using the new technique. e
Obj4
represent in Eq.(30) is as follows:
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Obj
4=
∑
N
i=1
(
D(N(i)−S)
DAV G(N(i)
−
S)
)
∗
1
0.1M (30)
e standard clustering procedure identies CHs and member nodes for each particle. Subsequently,
clusters are established by assigning each member node to the nearest location-based cluster leader.
e amount of error for each
ith
population is assessed using the suggested tness function. Here, we
presuppose that a certain tness function represents the network’s incorporation of four tness parameters:
F=
1
α∗Obj1+β∗Obj2+γ∗Obj3+δ∗Obj4
(31)
Improving network performance requires minimizing tness F in Eq.(31). Comprises a wide range of tness
metrics derived by the provided Eqs.(26), (27), (28), (29), (30). Parameters utilized in the integration of the
tness function are given varying degrees of importance according to the weight coecients in Eq.(31). It is up
to the user to ne-tune these settings for their specic sensor network deployment.
To determine the relative relevance of the variables in the tness function integration, the weight coecients
α, β, γ, and δ are used. It is up to the user to adjust these parameters so the sensor network works as intended. In
Eq.(32) the weights of these components are expressed dierently.
α+β+γ+δ=1
(32)
us, the optimizing Network performance by maximization of this function across metaheuristic processes is
the primary focus of search space.
e pseudocode for the suggested AVOACS algorithm is shown in Algorithm 1. e suggested algorithm
takes and returns the highlighted phrases as input and output.
As previously mentioned, the procedures outlined in Algorithm 1 are followed while using AVOACS.
e sink is positioned in the centre of the network once the nodes have been distributed in the network of
given dimensions. e AVOA operation, which involves many steps as previously mentioned, may be used to
understand the clustering and CH selection processes. Aer choosing the CH, the Network enters a steady-state
phase. e procedure will now end when all nodes’ energy has been utilized. e process of data transmission
from CH to sink is shown in Fig.1.
Complexity analysis of AVOACS
It is essential to perform real-time analysis in terms of the complexity and feasibility of suggested algorithms.
e algorithm’s complexity is determined to be O (
rmax ×N
), as seen in Algorithm 1, where
N
denotes the
population’s size (particle size) and
rmax
denotes the maximum number of rounds for which the Network is
conducted. e computational overload of the AVOA algorithm takes place due to two main reasons; rst is a
number of sensor nodes (
N
) while secondly, it occurs because several iterations are required for optimization
i.e., iteration
rmax
. e O (
rmax ×N
)in this function can be approximated as the number of nodes that need
to consider for cluster head selection and
rmax
is another constant-like iteration counts before it converges into
a specic value. For each iteration, cluster heads are selected intelligently based on various factors.
Experimentation, results and analysis
is section explores the simulation environment, evaluation metrics, and innovative methodologies for
performance assessment and analysis. All simulations were conducted on a system equipped with 8GB RAM,
1TB HDD, and an Intel i5 CPU with MATLAB R2022a. We have given the simulation Table2 that mentions the
various parameters used in the simulation analysis.
e simulation we performed had 100 nodes spread out throughout the (100 × 100m). Table2 summarizes
the consistency of sensor nodes and AVOACS parameters, and also oers accurate normative values for the
sample size. AVOACS procedures for CH selection use generational counts and other criteria to optimize
performance. e assessment of suitable values has been conducted by optimizing the control parameters of
proposed AVOACS method and rival methods like PSO-ECSM, HWSHO, OE2-LB, and ABC-DE. is has been
executed to ascertain the values that should be used. ree levels were established for control parameter tuning:
population size (P) = [20, 30, 40], personal learning coecient (
C1
)= [0.5, 1, 1.5], global learning coecient
(
C2
) = [1, 1.5, 2], and total vultures = [10, 30, 50]. e optimal conguration yielded the following results: [P,
C1
,
C2
, total vultures] = [30, 1, 1.5, 30]. Prior to its nalization, an elitist approach based on rank selection was
used. At some point, members of a given cluster may decide to adopt a dierent aesthetic. e truth is that all
node types will operate according to the same rules throughout the network’s existence.
Performance metrics
Performance of our proposed AVOACS (African vulture optimization algorithm-based energy ecient clustering
scheme) has been assessed in terms of dierent performance parameters- network lifetime, stability period,
energy consumption, and throughput. Lastly, the cluster head selection frequency as well as assessment metrics
allow for energy expensive tasks to be evenly distributed on dierent nodes enhancing network life span by
maximizing energy consumption. Together, these metrics validate the contribution of AVOACS in consummate
energy eciency and lifetime expansion to WSNs. For the purposes of measuring the AVOACS against with
PSO-ECSM7, HWSHO20, OE2-LB21, and ABC-DE22 protocols.
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Network’s remaining energy
e AVOACS algorithm balance the energy consumption in a better way across the network by having more
residual energies of nodes operating dierent stages on their life. e dynamic cluster head selection mechanism
also ensures that nodes with more remaining energy are selected for the tasks which consume lots of power
including data aggregation and communicating to sink. It has been shown that the AVOACS protocol expects
a decrease in network energy use as a result of data transmission. Networks’ residual energy performance
improved with the increase of iterations, as predicted. As shown in Fig.2, AVOACS outperforms other protocols
Fig. 1. Proposed method data transmission process between CH and sink.
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Fig. 2. Network’s remaining energy analysis of AVOACS with existing protocols.
Parameters Valu e s
Area covered 100 × 100m
No of sensor nodes 100, 200
Sink node 1
Initial energy (
Eo
)0.5
Essential transceiver energy (
Eel
)50nJ/bit
reshold-distance (
do
)86m
Packets size 4000bits
Eefs
10pJ/bit/m2
Emp
0.0013pJ/bit/m4
Eda
5nJ/bit/signal
α
,
β
,
γ
, and
δ
0.5, 0.25 ,0.15, and 0.1
P1
and
P2
0.8 and 0.2
Antenna type Omni Antenna
Simulation time 100s, 250s, 400s
MAC type IEEE 802.11
Simulation runs 30
w
2.5
Population size 30
Initial position of the vulture 0.5
Tab le 2. Simulation setting for AVOACS.
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like PSO-ECSM7, HWSHO20, OE2-LB21, and ABC-DE22 because it uses a greater number of iterations and
improves data transmission. Furthermore, AVOACS uses less energy each round than competing protocols in
dual hop communication.
Network longevity
e AVOACS scheme can prolong the lifetime of a general network, denoted as time duration among arriving
alive and leaving away from in valuable nodes. is enhancement is mostly due to the energy consumption model
of AVOACS being ecient and has adaptive communication strategies so that both near nodes from sink as well
as far away nodes contribute without depleting all their initial energies. AVOACS completed aer 9833 rounds,
and we can observe that PSO-ECSM42, HWSHO43, OE2-LB21, and ABC-DE22 all have much shorter network
lifetimes (3716) to (8470) rounds. Figure3 shows that compared to the PSO-ECSM7, HWSHO20, OE2-LB21, and
ABC-DE22 protocols, AVOACS completes 6117, 4285, 2353, and 1363 more cycles. rough the integration of
intra-cluster and CMD components into the objective function, AVOACS keeps an eye on the progress made in
extending the lifespan of the networks involved. Consequently, the average distance between a node and a CH is
greatly reduced when there are several such nodes in proximity.
Dead nodes versus rounds
e AVOACS algorithm shows a slower rate to the number of dead nodes, in contrast with other approaches
there are less periodic dead/alive over their round. We compare AVOACS to other protocols; we can observe that
it has less rounds for each dead node. Figure4 shows that the First Node Dead (FND) occurs aer 4762 rounds in
AVOACS but only aer 2096 rounds in PSO-ECSM, 2754 rounds in HWSHO, 3919 rounds in OE2-LB, and 4168
rounds in ABC-DE, and that the Half Nodes Dead (HND) occurs aer 7133 rounds in AVOACS but only aer
3011 rounds in HWSHO, 4976 rounds in OE2-LB, and 6112 rounds in ABC-DE. And in the improvement of last
node dead (LND), also known as the network longevity, AVOACS is also indicated covering 9833 rounds, while
PSO-ECSM, HWSHO, OE2-LB, and ABC-DE protocols cover 3716, 5548, 7480, and 8470 rounds, respectively.
Higher energy conservation is realized in AVOACS compared to other protocols individually when the CH
selection has been improved according to numerous criteria, as discussed above.
roughput (number of packet delivery)
AVOACS does an improvement with throughput, this combines the total amount of data that has been able to be
successfully sent over the wire and received by sink. e introduced method results in enhanced throughput as
a result of the reliable network topology and less delays derive from communication. Optimized clustering and
Fig. 3. Comparative analysis of alive node of AVOACS with existing protocols.
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communication mode decider to reduce energy wastage while in the transmission of data, for prolonged amount
of data transmission before nodes are dead. As illustrated in Fig.5, AVOACS sends 212,572 data packets whereas
PSO-ECSM7, HWSHO20, OE2-LB21, and ABC-DE22 transmit 80,284, 127,164, 181,726, and 186,841. In terms
of throughput, AVOACS improves PSO-ECSM, HWSHO, OE2-LB, and ABC-DE by 164.7%, 67.1%, 16.9%, and
13.7%, respectively. e proposed protocol’s throughput enhancements are a direct result of its lower reported
loss and its use of increased CH during data packet transfer.
Stability period
e stability period, the time duration where all nodes are observed to be alive (active) in AVOACS method is
much enhanced. As a result, by extending the stability period of the new network it is achieved that this network
has operational capacity for longer than much time in comparison to before. It can be noted that the rst node
is eliminated in AVOACS aer 4762 rounds, however in the scenario, PSO-ECSM, HWSHO, OE2-LB, and
ABC-DE protocols, it is reduced to merely 2096, 2754, 3919, and 4168 rounds, respectively, as shown in Fig.6.
e critical point is having an awareness that knowing AVOACS improves stability period by 127.19%, 72.9%,
21.5%, and 14.2% when compared to the protocols PSO-ECSM, HWSHO, OE2-LB, and ABC-DE, respectively.
Unifying four tness criteria to enable energy saving during data transmission improves both stability period
and HND. e distance between nodes and nodes and the sink and nodes has been reduced.
Analysis and interpretation
Table3 succinctly encapsulates the enhancements recorded by the AVOACS. According to the comparative
analysis, AVOACS surpasses other protocols in several performance metrics. Table 4 shows the percentage
improvement achieved by AVOACS in terms of FND, HND, LND, and roughput.
Statistical result
e signicance of the AVOACS statistical tests was determined by conducting the tests. Using the F-test, a
sample from the same normal group may be evaluated to see whether it has the same variance. When analyzing
data from three methods, an F-test (based on analysis of variance (ANOVA)) is used to see whether the data is
consistent or signicant dierences. irty samples from each procedure were used to calculate the remaining
energy values. In Table5, the residual energy for each method is described in detail. According to Tables5 and 6,
AVOACS has a greater mean residual energy value (= 33.403) than the other algorithms. e remaining energy
ANOVA test results are shown in Tables5 and 6. According to Table5, p-values of 0.000 to 0.05 are less than 0.05
in the ANOVA test results. Consequently, the eciency of the algorithm is dierent.
Fig. 4. Comparative analysis of dead node of AVOACS with existing protocols.
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Conclusion and future scope
is paper proposed the AVOACS method for Wireless Sensor Networks that aims to solve an essential problem
of energy eciency and prolonging network life in environments with limited resources. e strategies are
designed to elect dynamic cluster heads and communication properties based on residual energy, the intravalley
of intra-cluster distance between nodes as well and node-to-sink-distance. e superior results of AVOACS
using dierent evaluation metrics demonstrate that the proposed algorithm considerably enhances WSNs with
respect to other state-of-the-art methods (PSO-ECSM, HWSHO, OE2-LB and ABC-DE). It has been found that
AVOACS elongates the stability period by 127.19%, 72.9%, 21.5%, and 14.2%, and network lifetime by 164.6%,
77.2%, 31.4%, and 16.9% as compared to PSO-ECSM, HWSHO, OE2-LB, and ABC-DE, respectively. e
analysis of the remaining energy of network shows that AVOACS always maintains high residual energy over its
network, because it properly selects cluster heads and discharges balanced distributed even close nodes along
with their dierent low radii in proportion to their distance from base station. Several key benets of AVOACS
are derived from the enhanced power conservation technique, which includes energy eciency improvements
in WSNs as well as network life and performance. is makes it a promising solution for energy-constrained and
mission-critical applications in future WSN deployments, as the protocol is capable of serving heterogeneous
network environments; dynamic balancing of power consumption if needed further extend the operational life.
In future work, we plan to continue the investigation of our algorithm with respect to mobile nodes and more
challenging network conditions.
Fig. 5. Comparative analysis of throughput of AVOACS with existing protocols.
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Percentage (%) improvement by AVOACS Protocol
Algorithms FND Half node dead Last node dead roughput
PSO-ECSM 127.19 136.8 164.6 164.7
HWSHO 72.9 86.5 77.2 67.1
OE2-LB 21.5 43.3 31.4 16.9
ABC-DE 14.2 16.5 16.09 13.7
Tab le 4. Percentage improvement by AVOACS to existing algorithms.
Algorithms Total energy of network (Joules) FND HND LND roughput (packets)
PSO-ECSM750 2096 3011 3716 80,284
HWSHO20 50 2754 3823 5548 127,164
OE2-LB21 50 3919 4976 7480 181,726
ABC-DE22 50 4168 6112 8470 186,841
AVOAC S 50 4762 7133 9833 212,572
Tab le 3. Comparison of AVOACS with existing algorithms for dierent results. Signicant values are given in
bold.
Fig. 6. Performance analysis of AVOACS with existing protocols.
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Data availability
e datasets used and/or analysed during the current study are available from the corresponding author on
request.
Received: 12 June 2024; Accepted: 10 December 2024
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Source of variation Sum of squares df Mean square F F crit
Between groups 34563.02 4 8640.756 528217.1 2.408488
Within groups 4.007794 245 0.016358
Tot a l 34567.03 249
Tab le 6. ANOVA test result of remaining energy.
Protocols NMean Std. deviation Std. error
95% condence interval for
mean
Minimum MaximumLower bound Upper bound
PSO-
ECSM42 50 1.038 0.069 0.009 0.01 0.012 0.92 1.15
HWSHO43 50 15.651 0.186 0.026 0.09 0.11 15.33 15.95
OE2-LB21 50 26.372 0.142 0.020 0.10 0.13 26.13 26.61
ABC-DE22 50 30.052 0.125 0.017 1.03 1.08 29.84 30.26
AVOAC S 50 33.403 0.179 0.021 2.81 2.98 33.27 33.53
Tot a l 250 106.516 0.701 0.093 4.04 4.312 105.49 107.5
Tab le 5. Remaining energy analysis of respective protocols.
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Content courtesy of Springer Nature, terms of use apply. Rights reserved
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Author contributions
M.K: concept, design, analysis, writing—original dra. A.K: concept, design, analysis, writing—original dra.
S.K: design, analysis. P.C: analysis, writing—review & editing. S.S: analysis, writing—review & editing. All au-
thors contributed equally to the manuscript. All authors reviewed the manuscript.
Declarations
Competing interests
e authors declare no competing interests.
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