A walrus optimization algorithm (WOA) for cluster head selection to optimize energy-efficiency in UWSNs-based IoT

1 Introduction

IoT has evolved into a central domain of research, transforming numerous other essential research areas by facilitating seamless interaction and the intelligent exchange of data among physical things (Alsuwat and Alsuwat, 2025; Sennan et al., 2021a; Sankar et al., 2020; Madireddy and Yarrabothu, 2025). IoT plays an indispensable role in the development of many fields, like smart homes, healthcare, agriculture, transportation, and smart cities, to broaden operational efficiency and user experience (Mohapatra, 2025). Underwater Wireless Sensor Networks (UWSNs), as a large-scale wireless network, consist of numerous distributed and autonomous small nodes that monitor pollution and environmental characteristics at the sink or base station for further processing and storage (Alshammri, 2025; Sennan et al., 2021b).

UWSNs are becoming popular in various fields. These include military, marine environments, disaster prevention, and offshore resource management (Gola and Gupta, 2020; Mamta et al., 2022). Sensor nodes can be deployed in 2D or 3D based on how deep the water is. Using the aquatic environment to deploy sensors in WSNS has always been a challenge (Sathish et al., 2022). Data transmission in UWSN is done via acoustic communication mode among nodes due to the fact that radio communication is limited in underwater environments. UWSNs are composed of sensors that monitor the physical environment and communicate their data to a central server for further processing (Srinivasan et al., 2019; Rajput and Kumaravelu, 2021). Usually, the data gathered from the environment is first converted into analog signals for pre-processing and then sent wirelessly using specialized transceiver modules which are a crucial part of a UWSN (Wang et al., 2019; Sheikh et al., 2012a; Sheikh et al., 2015). With the recent advancements in microelectronics, small-sized sensors with low power requirements have been developed, and the opportunities for real-time applications have become even more significant. UWSNs have been extensively used in battlefield surveillance, industrial automation, and ocean health monitoring (Asghari et al., 2019; Tran et al., 2019). In particular, in some cases multiple sensor nodes are necessary to fulfill the real-time process requirements. Furthermore, it is in the nature of UWSNs to be dynamic and therefore can change the network configuration in response to external factors such as node mobility, changes in the environmental context and the addition or removal of nodes, thus always ensuring the efficiency of the network.

When it comes to UWSN-based IoT, routing is the key component without which, communications of data among nodes is impossible. A lot of applications send the same data through the routing protocol, which results in a resource-constrained network. To fix this, a clustering method is used and it enhances the lifetime. Three principal steps are involved in this process. They are the cluster formation, selecting CH nodes, and selecting the best route for data transmission. Overall network performance will be massively improved by carrying out the steps mentioned above. Energy in the sensor nodes can be efficiently controlled, and network lifetime can be increased by simply forming clusters. Sensor nodes are resource-limited devices with very few resources (Storage, battery power, computation, and acoustic communication) (Hassija et al., 2019). It is extremely challenging to maintain a sustainable network when it relies entirely on sensor nodes in UWSN (Li et al., 2017). Various proposals have been made for energy-efficient technology in the network (Poluru and Naseera, 2017; Kharrufa et al., 2019). Sensor nodes are spread throughout the network region and formed into different clusters. A CH node is assigned to each cluster, which communicates with the sink node (Thangaramya et al., 2019).

Clustering is one of the conventional methods that have been extensively used in UWSNs to save energy by significantly reducing the volume of data transmission among sensor nodes (Sheikh et al., 2012b; Kotary and Nanda, 2020; Hase et al., 2017). Within this model, the group nodes are organized into different clusters. Each cluster is directed by a Cluster Head (CH), which aggregates data from all Cluster Members (CMs) and passes it to the sink node. Several studies have proposed various cluster head selection methods utilizing optimization algorithms, where an optimal solution is selected from the numerous possibilities. Furthermore, multiple cluster head selection algorithms have been proposed using a variety of optimization techniques in the recent past, such as Crested Porcupine Optimizer (CPO), GA, DE, Gannet Optimization Algorithm (GOA), ACO (Sumida et al., 1990; Storn and Price, 1997; Abdel-Basset et al., 2024; Pan et al., 2022; Landge et al., 2025), or Atomic Orbital Search (AOS) (Azizi, 2021). However, the standard optimization algorithms based on CH selection suffer from slow convergence, resulting in inefficient cluster formation and maximized communication overhead. Consequently, the overall energy balance in the network is affected. Hence, the Walrus Optimization Algorithm (WOA) is selected to determine the appropriate CHs within clusters, thereby extending the overall lifetime of the network. The WOA optimization algorithm seems generic; it can be employed in a network model by using an objective function formulation to observe energy consumption behavior and communication among nodes in a deployment scenario. The main contribution of this research is:

• Initially, the sensor nodes are grouped into clusters based on their spatial proximity in a structured clustering framework, after which the energy-aware CH Node in the cluster is determined, which is responsible for RER and communication distance.
• The energy consumption and communication costs are balanced through the formulation of the objective function, improving network lifetime and Throughput under deployment conditions.
• In WOA, the fitness function is determined by considering both the Residual energy (RER) and distance in selecting the best CH.
• Performance of WOA formulation has been evaluated in MATLAB 2024a simulation environment and checked against the performance of existing CH selection approaches such as ZFO-SHO, TIOCHR, and M-PSO. The MOA enhances the efficiency of the entire network.

The remaining sections are detailed as follows: Section “Related work” discusses benchmark state-of-the-art works on cluster head selection in IoT. Section “System Preliminaries” presented an overview of the network model and an energy model. Section “Proposed Walrus Optimization Algorithm protocol for CH Selection” discusses the CH selection process. Section “Performance Evaluation and Analysis” presents the performance of the proposed approach, WOA, and comparison with existing works (ZFO-SHO, TIOCHR, and M-PSO). Finally, the summary of the proposed approach and future directions is discussed.

2 Related work

Energy remains a major restriction in UWSNs, although many ways for CH selection have been introduced. Lack of energy and CH selection challenges can be fixed if the right methods are used in UWSNs. Logically, a cluster is a set of nodes that are physically close to each other and hence the members of the set. One of the members of the group, the special node, which is the CH, will be in charge of collecting the data at the local level and sending it to the base station. Energy is saved and the communication load is decreased in this way.

Roberts et al. (2024) introduced a hybrid technique inspired by ZFO-SHO in the WSNs. In this class of network, essential services such as cluster head (CH) selection and energy conservation become quite challenging; however, a hybrid approach is then used to address these aspects. In this approach, the main interests are concentrated on dynamic cluster formation and path selection. The best node of CH selection is achieved with the improved ZO Algorithm (ZFO), which relies on the fitness function. Then, the energy consumption was reduced by utilizing an adaptive technique, namely SHO (Sea Horse Optimization). The distinction of the two-phase approach having a trade-off solution in both phases versus the previous methods is that a number of QoS parameters (RER, lifetime, PDR, and throughput) were utilized to check the ZFO-SHO effectiveness. OMNET++ 6.0, linked with MATLAB R2022b, was used to evaluate the ZFO-SHO using a simulation environment. Dynamic cluster formation is simulated and managed through the ZFO algorithm, whereas energy optimization is performed by the SHO in the MATLAB simulation framework. A node-based implementation of both algorithms (ZFO-SHO) was developed using OMNET++ to validate their operations in a dynamic environment. The evaluation of ZFO-SHO was computed by comparing it with the benchmark techniques NCOGA, FFARF, GAEO, MMABC, and MRP-GTCO. The effectiveness of ZFO-SHO is improved in terms of critical parameters, PDR by 1.8%–6.9%, throughput by 6.7%–24%, network lifetime by 1.86%–7.40%, and RER by 9.65%–37.95%. However, it takes more simulation time for selecting CH.

Babu and Geethanjali (2024) suggested a Trust Index Optimization driven CH selection method to extend the network lifetime in WSNs (TIOCHR). TIOCHR successfully identifies the best node in the network to communicate data to the sink node via the best transmitting path. Trust Index is used not only in the selection of a CH but also in finding the best path. The trust index is evaluated using three metrics: available energy, PDR, and packet consistency. Randomly, the CH node is selected in predetermined iterations. Afterward, the best path for sending packets in the network is chosen. Different performance metrics of TIOCHR are calculated, such as packet forwarding ratio (PFR), energy consumption (EC), routing overhead (RO), latency (L), and network longevity (NL). The TIOCHR method was executed in the NS3 simulation environment. TIOCHR’s performance is analysed against the selected techniques, energy-efficient algorithm, ANT algorithm, FCEEC algorithm, and TIOCHR algorithm through a comparative study. The energy consumption and network longevity of TIOCHR have been raised by 10%, 15%, and 20% when compared to the benchmark energy-efficient algorithm, the ANT algorithm, and the FCEEC algorithm, respectively. Nevertheless, it is necessary to have a larger number of iterations for selecting an optimal CH, which causes an increase in communication overhead.

Prakash et al. (2024) devised energy-efficient and CH selection in WSN through M-PSO and GA (DMPRP). In DMPRP, the CH node is chosen with M-PSO, and cluster members are picked through the GA algorithm. The DMPRP technique proposed in the paper first calculates the probability of a node in selecting the most optimal cluster head. The experiments for the DMPRP method were conducted using the NS2 simulation tool, and the obtained results were compared with the results of the state-of-the-art methods. Overall, the experimental results demonstrated that the performance of DMPRP was superior to the state of the art by 12%.

Mabunga and Dela Cruz (2025) proposed an energy-efficient routing protocol for the CH selection using the chronological wild geese optimization (CWGO) in WSNs. The method consists of three stages: CH selection, node energy prediction, and path finding. During the CH selection process, the deep recurrent neural network (DRNN) technique finds the best CH that satisfies the key limitations, such as the LLT, delay, energy, intercluster distance, and intracluster distance. Moreover, the best way from the node to the base station (BS) is obtained by the CWGO for data transmission which takes into account the multiple constraints of trust, delay, distance, and energy. The simulation of CGWO is carried out in a Python environment. The performance of CGWO is evaluated in comparison with conventional models EECHIGWO, DUCISCA, DE_SEP, and E_CERP. The effectiveness of CGWO is improved in terms of critical parameters, specifically distance (19.468 m), trust (0.252 s), energy (0.963 J), and delay (0.700). However, it takes more simulation rounds to choose the optimal CH.

Alshammri (2025) recommended improved CH selection using a squirrel search algorithm for enhancing network lifespan and efficiency (ISSA-C). The basic squirrel search optimization algorithm has been modified for the optimal CH selection. In ISSA-C, the solution quality is improved by adapting a series of adjustments and accelerating the convergence speed of CH selection. The capabilities of SSA, namely exploration and exploitation, are enhanced by implementing the Local search algorithm, dynamic step size control, and Adaptive population initialization. As a result, the optimal solution is achieved with more efficient convergence. The fitness function is evaluated with key parameters such as sink distance, CH balance, intra-cluster distance, and RER. The proposed ISSA-C is computed in different scenarios to assess its effectiveness in the network. In order to simulate the operations of WSNs, the authors implemented the MATLAB 2021a simulation environment. To attest to ISSA-C’s performance improvement, they employed GWO, CDO, SSA, SSO, MOCRAW, EEWC, and MAP-ACO methods as the benchmarks. The packet delivery ratio (PDR), energy consumption, cluster formation time, and CH selection time of ISSA-C are improved by 88%, 220 mJ, 82 s, and 67 s, respectively. Also, the ISSA-C technique is tested without the assistance of the above said methods. Still, it is intended for certain scenarios.

Alsuwat and Alsuwat (2025) proposed a hybrid Q-learning-based artificial bee colony optimization algorithm for CH selection and an optimum data transmission method in WSNs (IQ-ABC). This paper combined the strengths of the original ABC algorithm with a Q-learning mechanism for choosing the best CH in the network. IQ-ABC finds the energy-efficient path for data transmission from the sensor node (SN) to the base station. The selection of CH is enhanced by incorporating trust, energy-efficiency, and latency factors and balancing them via a multi-objective fuzzy logic function. The experiments of the IQ-ABC method were carried out in MATLAB 2021a as the simulation tool. The performance of the IQ-ABC framework was evaluated against the LEACH, HEED, PSO, GWO, ABC, and ACO. This method was exercised in three different scenarios by relocating the base station (BS). When the BS was located centrally, the energy consumption of IQ-ABC achieved 0.253 units over 1,200 rounds compared with other existing techniques, such as 0.38 units by LEACH, 0.361 units by HEED, and 0.6 units by ACO. Similarly, in other scenarios (edge and far), the proposed IQ-ABC approach outperformed with the lowest energy consumption of 0.30 and 0.33 units, respectively. Despite its effectiveness, it does not consider security threats for CH selection.

Amshavalli et al. (2025) outlined a multi-objective-based CH selection protocol using boosted sooty tern optimization Algorithm in WSNs (BSHPFMOCS). This approach aimed to address the formation of quality clusters and CHs. The potential CH selection makes the network stable and achieves low energy consumption in various scenarios. In BSHPFMOCS, the CH selection is achieved through an accurate search process, which helps extend the network lifetime in WSNs. The fitness value is computed to select the optimal CH that enhances cluster aggregation. The proposed BSHPFMOCS model integrated the advanced cluster formation methods by selecting cluster members that had the nearest intra-cluster distance. To address the issue of the hot spot in the network, the sink node mobility is optimized by the Piranhav Foraging Optimization Algorithm (PFOA). The effectiveness of the BSHPFMOCS method was compared to the most recent techniques such as FRHBMEB, MOCRAW, F2SORP, and GEIGOA. The simulation experiments were conducted using MATLAB version 2021a. The BSHPFMOCS performance has been raised by 21.94% energy consumption saving, 20.86% packet delay reduction, 18.42% throughput increase, and 10.76% network lifetime extension as compared to the benchmarked methods. However, it takes more simulation rounds to choose the optimal CH. However, the coverage efficiency of the proposed approach is limited. As a result, the energy is drained quickly.

Das and Dwivedi (2024) devised a scheme in which a CH is energy-aware and which detects a malicious node via a trust optimization algorithm in WSNs (LS-EATO). In LS-EATO the CH is selected by energy awareness through the harmonic search genetic algorithm (HSGA). Based on the trust value, the cluster member (CM) is not considered CH. Subsequently, with the use of the EAIICT (Energy-Aware Intra- and Inter-Cluster Trust) model, the node can be identified. The EAIICT estimation model is based mainly on two modules: direct trust (DT) and indirect trust (IT). The DT value is derived from the communication and data trust of the network. The IT value is derived from feedback trust. The CM is discovered based on trust value evaluation in central and distributed network scenarios. The residual energy (RER) is a key constraint considered when selecting potential CH with high energy in the EAIICT model. This article explores the capability of the newly introduced LS-EATO model besides a few essential parameters such as delay, detection rate of malicious nodes, and communication overhead. The clean LS-EATO method was run on the MATLAB simulation platform. The new approach, LS-EATO, was benchmarked against the existing baseline models, i.e., SQEER, EPO-TRM, FHTMS, and 2STM. Model performance evaluation results demonstrated that our model surpasses the existing ones.

Numerous optimization algorithms have been proposed for CH selection in WSNs. However, existing works demonstrated certain limitations, including communication overhead, poor PDR rate, and suboptimal CH selection. The key limitations of existing CH optimization techniques are listed in Table 1.

TABLE 1. Summary of prior optimization approaches for cluster head election.

There are several metaheuristic algorithms have been proposed to solve CH section problems by focusing on the substitution of algorithms. However, they have shown less attention to the objectives of energy awareness and system constraints.

3 System preliminaries

3.1 Network model

Multiple sensor nodes ‘n’ are present in WSN, where each sensor node is equipped with fixed resources. The sensor nodes can be placed randomly in the network. According to available resources, each node can be a CH or a CM. The sink node or the base station executes the proposed WOA CH selection algorithm, which has more processing power and storage capacity. Later, the cluster is formed with nearby nodes from CH using Euclidean distance. Figure 1 portrays the overall network model of WOA.

The following assumptions of WOA network model are presented below:

• The sensor nodes are distributed randomly in two-dimentional network area.
• All sensor nodes are divided into equal groups and distributed randomly in each group.
• The computation power and energy of all sensor nodes are equal.
• The distance among sensor nodes are computed using Euclidean distance.
• The sink node executes the CH selection algorithm and collects all aggregated data from CH for processing.
• The sink node’s location in the network area is placed in three distinct areas: the middle, the corner, and the outside.

3.2 Energy model

The acoustic communication can categorize UWSN from WSN. This work mainly focuses on a generalized energy consumption model, which is commonly adopted in WSNs. The proposed energy-aware cluster-head selection model is evaluated under controlled conditions to demonstrate the effectiveness of the proposed work. This work primarily aims to address energy consumption issues rather than to model the physical layer of acoustic in UWSN. Energy has been a big concern in WSN. The transmission of data demands that extra energy be sent to each node in the network space, and it is regulated by two different models: the free-space model and the multi-path model. In the case of single-hop transmission, a free space model is employed, whereas the multi-hop transmission utilizes the multi-path model, and this is derived from the radio energy model of the sensor node in the proposed WOA algorithm (Abu Salem and Shudifat, 2019). Figure 2 depicts the energy model of the proposed WOA.

The energy consumption for transmitting ‘e’ bit packets of data from node ‘s’ to ‘r’ over distance ‘d’ is computed using Equation 1. The energy consumption is calculated using free space attenuation model when distance among ‘s’ and ‘r’ nodes is shorter than d 0 or multi path attenuation model is used.

E T X e , d = e E e l e c + e ɛ d s , r α = e × E e l e c + e ɛ f s d s , r 2 w h e r e d s , r < d 0 e × E e l e c + e ɛ e p d s , r 4 w h e r e d s , r ≥ d 0 (1)

Where e ɛ f s d s , r 2 and e ɛ e p d s , r 4 denotes the energy consumption coefficient.

The value of the distance threshold d 0 is computed using Equation 2.

d 0 = ɛ f s ɛ e p (2)

The amount of energy consumed for receiving an e-bit data packet is computed and expressed in Equation 3.

E R X d = d × E e l e c (3)

4 The proposed walrus optimization algorithm protocol for CH selection

The proposed walrus optimization algorithm (WOA) focuses on optimal CH selection in wireless sensor network-based IoT using various network parameters. The proposed work seeks to achieve better network lifetime and throughput to manage energy consumption in the network. The CH selection is performed by utilizing a fitness function that is computed based on network factors such as RER and distance. The CH selection algorithm is executed in the sink node due to higher computing power than the sensor node. Then, the cluster is created by using Euclidian distance.

4.1 CH selection process

The walrus optimization algorithm is structured into multiple phases, each with a specific role in addressing critical problem. In the initialization phase, a set of candidate solutions (population) is enabled to cover a broad range of the search space. In the migration phase, the large number of new positions is allowed to perform global exploration and stop early convergence by finding new regions. The roosting phase is enabled by an algorithm when an optimal solution is identified. The local exploitation is emphasized via interaction among walrus agents in a structured format and a candidate solution modified accordingly. Afterwards, the gathering phase is responsible for leading agents to first send the best candidate solution by accelerating convergence. The robustness of the system is improved by the fleeing phase through introducing controlled perturbations in different stages of the optimization process. The last phase of WOA is convergence stabilization, which ensures convergence towards an optimal solution and reduces randomness in the end. Thus, the optimal balance between exploration and exploitation is gained with the help of all phases of WOA, which sustains during the optimization process. The walrus optimization algorithm is a swarm intelligent metaheuristic approach that obtains a searching procedure using exploration and exploitation phases (Han et al., 2024). This WOA approach was developed, inspired by the nature of the walrus animals. The lifestyle of walrus leads to migrating, feeding, gathering, roosting, breeding, and escaping via signals (safety signals or danger signals). Walruses are flexible in water compared to other marine animals. They can stay up to 2 h in a depth of 500 m water and dive up to 20 min, reaching the surface in 3 min whenever they need fresh air. They can adapt social habits to defend themselves from killer whales in the water when they encounter them and other walruses that help injure their kind.

The phase transition process is depicted in Figure 3. Various phases (such as migration, roosting, gathering, and fleeing behaviors) of the WOA approach are adapted based on the threshold value of the danger signal or the safe signal (≥1 and ≥0.5).

4.1.1 Initialization

The walrus Optimization algorithm (WOA) finds the best solution in range search space. Decision variables in multidimensional spaces represent the problem, and solutions are represented by solution space. The position of the walrus is a solution in search space. Each walrus is considered a sensor node in the vector. A set of candidate solutions W) is randomly generated to initiate the optimization process using Equation 4.

W = L B + r a n d U B − L B (4)

Where LB, UB and rand indicate the upper bound, lower bound of problem variable and random variable chooses between 0 to 1.

The position of walrus (Sensor node) is updated with every iteration in the optimization process. The walrus is represented using matrix in Equation 5.

W = W 1 , 1 W 1 , 2 ⋯ W 1 , d W 2 , 1 W 2 , 2 ⋯ W 2 , d ⋮ ⋮ ⋮ ⋮ ⋮ ⋮ ⋮ ⋮ W n , 1 W n , 2 ⋯ W n , d n × d (5)

Where ‘n’ indicates the population size and ‘d’ indicates the dimension of problem variables.

The objective function obtains a set of solutions associated with each walrus’s position. The array of fitness values ‘F’ is stored in a vector, as demonstrated in Equation 6. The walrus population is classified as 90% adults and 10% juveniles. The male-to-female ratio in the adult group is 1:1.

F = f i t 1 , 1 f i t 1 , 2 ⋯ f i t 1 , d f i t 2 , 1 f i t 2 , 2 ⋯ f i t 2 , d ⋮ ⋮ ⋮ ⋮ ⋮ ⋮ ⋮ ⋮ f i t n , 1 f i t n , 2 ⋯ f i t n , d n × d (6)

The walrus is always careful during the foraging and roosting stages. Among walruses, two of them act as guards to avoid danger and send danger signals immediately after noticing unexpected situations. The danger signal (D S) and safe signal (S S) are defined in Equations 7–10.

D S = X * Y (7)

δ = 1 − t T (8)

X = 2 × δ (9)

Y = 2 × s 1 − 1 (10)

Where, ‘X’ and ‘Y’ are Danger signal factors, ′ δ ′ referring values between 1 to 0 associated with several iteration ‘t’, and ‘T’ indicates maximum iterations. The safety signal is defined in Equation 11.

S S = s 2 (11)

Where, s 1 and s 2 refers random value between 0 to 1.

4.1.2 Exploration phase

The walrus migrate to suitable place for population when unexpected risk of survival increases. In migration phase, the position of warlus is updated using Equation 12.

W i , j i + 1 = W i , j t + M S (12)

M S = W p t − W q t . β . s 3 2 (13)

β = 1 − 1 1 + exp t − T 2 T × 10 (14)

Where, W i , j i + 1 and W i , j t indicates the new position and current position of i th walrus on j th dimension, respectively, M S means migration_step that measures step size of walrus moment, two walrus (W p t a n d W q t) are chosen randomly from population for vigilantes purpose, which is calculated using Equation 13, β refers controlling factor of M S, which may vary with iteration and s 3 refres random interval in [0,1] using Equation 14.

4.1.3 Exploration phase

In the exploitation phase, walruses like to breed when the survival risk is low. During the reproductive phase, they exhibit two distinct behaviors (roosting and foraging).

4.1.3.1 Roosting behaviour

The primary categorization of the walrus population separates them into males, females, and juveniles. Each category has its own way of redistributing changes in their location. Halton method is a low-discrepancy sequence, which can be used to generate randomly distributed sequences. Adjusting the male walrus location changing by the application of the Halton method, this method leads to the idea of separating the population with the search space. The whole search space is split into various parts to inculcate randomness and uniformity by selecting a random point from each part of the search space. The male walrus and lead walrus may affect the female walrus. During the iteration process, the female walrus is influenced more by the leader and less by the mate, which is calculated using Equation 15.

F i , j t + 1 = F i , j t + δ . M i , j t − F i , j t + 1 − δ . W b e s t t − F i , j t (15)

Where F i , j t + 1, M i , j t and F i , j t denotes the new position of the female walrus and the current position of the male and female walrus of the i th iteration on j th dimension.

The juvenile walrus J W position is updated to avoid attacks from killer whales and polar bears, as proposed in Equation 16 and Equation 17, respectively.

J W i , j t + 1 = S P − J W i , j t . K (16)

S P = W b e s t t + J W i , j t . V F (17)

Where J W i , j t + 1 and J W i , j t elucidates new position and current position of ith Juvenile walrus on jth dimention, K indicates random number in the interval [0,1] of distress cofficient of J W, S F refers safety position, V F represents vector of random number with Levy movement, as proposed in Equation 18.

L e v y a = 0.05 × u v 1 a (18)

Where u and v elucidates nornal distributed variables, u ∼ N 0 , σ u 2, v ∼ N 0 , σ v 2 as proposed in Equation 19.

σ u = ¬ 1 + δ sin π δ 2 ¬ 1 + δ 2 δ 2 δ − 1 2 1 δ , σ v = 1 , δ = 1.5 (19)

Where σ u and σ v indicates standard deviation.

4.1.3.2 Foraging behaviour

The fleeing and gathering behaviors are classified as foraging behaviors. The natural predator attacks walruses during underwater foraging and flees from its current position when it receives a danger signal from its group members. The fleeing behavior will occur during the last iteration of WOA. Global exploration is conducted using Equation 20.

W i , j t + 1 = W i , j t . R − W b e s t t − W i , j t . s 4 2 (20)

Where W b e s t t − W i , j t represents distance between the current walrus and best walrus, s 4 indicates random number in the interval [0,1]. Walruses can collect information about other walruses in the population, which helps them find food in the sea area. They can cooperate with their peers for forage and migration in gathering behavior as proposed in Equations 21–24, respectively.

W i , j t + 1 = W 1 + W 2 / 2 (21)

W 1 = W b e s t t − a 1 × b 1 × W b e s t t − W i , j t W 2 = W s e c o n d t − a 1 × b 1 × W s e c o n d t − W i , j t (22)

a = β × s 5 − β (23)

b = tan θ (24)

The gathering behaviour of walrus is effected using two weight factors W 1 and W 2, the second position of walrus during iteration is represented by W s e c o n d t, distance between current and second walrus is denoned by W s e c o n d t − W i , j t, a and b are gathering cofficients, s 5 is random number in the interval [0,1], θ indicates the value between 0 t o π.

4.1.4 Fitness function

It is a specific, distinct mathematical measure used to find the sea area with ample food. In WOA, the fitness function is evaluated based on RER and Distance (dis) constraints to find optimal CH in the cluster and ensure comparision with baseline CH techniques. The parameters of UWSN (link quality, mobility, and delay) are not considered in this study and are left for future extension.

• Residual Energy (RER):

The amount of energy left in a node after certain network operations (such as data processing, sensing, and communication) is called residual energy Equation 25 (Sankar et al., 2020). A node with higher energy extends the network’s lifespan.

R E R N i = E i − E d E i (25)

Where E i and E d indicated initial energy and depleted energy.

• Distance:

The distance between sensor node and sinknode is detemined by using Equation 26 (Sahoo et al., 2020).

d i s n i , s i n k = ∑ i = 1 n s i n k − n i 2 (26)

The best position of walrus fitness function is evaluated using folling Equation 27.

W i f i t n e s s = 0.5 × ( 1 − R E R W i + 0.5 × 1 − d i s t a n c e W i (27)

The WOA chooses either the exploration phase or the exploitation phase to perform based on the value of the danger signal (D S). The walrus moves to a new domain in the search space when the value of D S is leass 1. Thus, the exploration phase is performed first in the algorithm. Later, the exploration phase is performed in the algorithm, which produces walrus herd. When wlarus reaches to safe position during iterations, that walrus is considered a CH node. The process of CH selection pseudocode is described in detail in Algorithm.1.

Algorithm 1 Pseudo-code of WOA display of CH selction Algorithm.

4.2 Cluster formation

Cluster formation refers to grouping a set of nearby nodes to CH in a network area. The distance between CH and a neighbor node is calculated using the Euclidean distance (Panchal and Singh, 2021), as proposed in Equation 28.

d W i , W j = ∑ i = 1 n W j − W i 2 (28)

Where W j and W i are two independent nodes in network.

The workflow of the proposed WOA algorithm is represented in Figure 4.

5 Performance evaluation and analysis

A simulation network space of 500 m × 500 m is considered, with 300 sensor nodes distributed randomly. The fixed Random number generator (RNG 2025) is designed to produce identical results.

Simulation rules:

All nodes maintain the same energy and abilities.

The position of the base station is fixed at (250 m, 250 m).

The Cluster Members (CM) position is fixed in the network area.

The proposed approach, WOA, creates a set of clusters with equal nodes and chooses the CH node. The CH node collects data to send to the BS for further processing.

The average result is calculated after 20 rounds in each simulation.

The experiment simulation is run up to 3,000 rounds, and one round includes data collection, CH selection, and sending data to the BS. The average result is considered over 30 runs to avoid randomness.

The proposed WOA algorithm is compared with baseline optimization algorithms (such as ZFO-SHO, TIOCHR, and M-PSO). All baseline algorithms were implemented under a similar simulation environment. We have considered the same topology, number of iterations, and population size are similar for every approach while running the simulation. The tuning bias is avoided by keeping all simulation parameters constant throughout execution.

5.1 Algorithm parameters and runtime complexity

Each clustering round is completed with 30 walrus agents, which run up to 100 iterations. The fitness function is computed using various parameters, such as residual energy (RER), the distance between the CM and CH, and neighboring nodes. The computational complexity of the proposed WOA algorithm is evaluated as O N × P × I.

Where N = Total Nodes (300 nodes)

P = Population Size (30)

I = Number of Iterations (100)

Due to an efficient balance between exploration and exploitation, the proposed approach achieves stable convergence to a near-optimal solution, outperforming baselines. It takes less time to choose CH in the MATLAB 2024a environment, making it feasible for deployment. The results presented in this study are obtained by averaging values over multiple simulation rounds to minimize randomness. The statistical study of WOA will be considered in future work.

The effectiveness of the WOA approach is evaluated using the MATLAB 2024a simulation tool. The WSN environment is simulated with varying numbers of nodes (100, 200, and 300) to evaluate the performance of WOA against existing clustering techniques, including ZFO-SHO, TIOCHR, and M-PSO. The proposed framework WOA compared with recent optimization algorithms based on CH selection to ensure consistency. The nodes are distributed randomly in the network area. All nodes are in the network area, initialized with equal energy (1 J). The simulation was conducted over a 500 m × 500 m network area, with the sink node strategically placed at the center of the network area (250 m × 250 m). The WOA protocol performance was tested through its key parameters, and the results were deliberated in terms of lifetime of network, energy efficiency, throughput, and network stability. The CH node serves as an intermediate layer for uninterrupted communications. Each sensor node is located near at least one other sensor node. The simulation is conducted to evaluate the effectiveness of the proposed method and comparative algorithms under an identical environment. The effects of UWSN acoustic channels (such as bandwidth limitation, packet loss and delay) in the simulation are beyond the scope of this analysis and are considered in future work. Table 2 illustrates the complete simulation parameters and configuration settings necessary for the WOA method.

TABLE 2. Simulation parameters.

5.2 Network lifetime

Figure 5 shows how the network lifetime varies with network size (100, 200, and 300 sensor nodes). For a network of 100, the ZFO-SHO, TIOCHR, M-PSO, and WOA algorithms’ dead nodes are at 1,400, 1,600, 1,750, and 1,900 rounds, respectively. In the case of 200 nodes, the dead nodes of the ZFO-SHO, TIOCHR, M-PSO, and WOA algorithms were found at 1,450, 1,650, 1,850, and 1,950 rounds, respectively. Also, in the 300 nodes case, the dead nodes of the ZFO-SHO, TIOCHR, M-PSO, and WOA algorithms were found at 1,550, 1,800, 1,900, and 2,000 rounds, respectively. The proposed WOA algorithm was tested in all three scenarios, and it could be seen that the network lifetime was always improved. WOA expedites the CH selection process, thereby lowering the convergence time.

Table 3 illustrates the network lifetime for different network sizes of sensor nodes, specifically 100, 200, and 300 nodes, respectively. The performance of the WOA approach achieved superior network longevity compared to benchmark techniques. The improvement of network longevity is achieved due to the efficiency of WOA, which drives the CH selection process. In WOA, premature node failure is reduced by reducing convergence speed and extending the overall network lifespan.

TABLE 3. Network lifetime vs. Number of nodes.

5.3 Throughput

The throughput calculated from the count of the packets correctly received by the sink node from CHs in the network. In Figure 6 the throughput performances of the ZFO-SHO, TIOCHR, M-PSO, and WOA algorithms are shown for different network sizes 100, 200, and 300. When the network size is 100 nodes, the throughputs of ZFO-SHO, TIOCHR, M-PSO, and WOA are 150,000, 160,000, 170,000, and 190,000, respectively. When the network size is 200, the corresponding throughputs of ZFO-SHO, TIOCHR, M-PSO, and WOA are 210,000,240,000,260,000, and 270,000. Similarly, in network size 300, the successful packet delivery reached 330,000 for ZFO-SHO, 370,000 for TIOCHR, 390,000 for M-PSO, and 410,000 for WOA. Above all network configuration scenarios, the proposed WOA approach outperformed other benchmark techniques, ZFO-SHO, TIOCHR, and M-PSO. In WOA, the convergence time is minimized during the CH rotation process. As a result, the network lifetime is extended, and throughput is substantially improved.

Table 4 illustrates the throughput that the proposed algorithm, WOA, achieved in different network simulation settings. From the graph, it is evident that the proposed WOA algorithm significantly increased the packets’ delivery to the sink node compared to other benchmark algorithms, such as ZFO-SHO, TIOCHR, and M-PSO. The smart WOA approach was instrumental in attaining successful data transmission by facilitating quicker convergence in the CH selection rotation duration.

TABLE 4. Network lifetime vs. Number of nodes.

5.4 Energy consumption

Figure 7 presents the remaining energy concerning the network size of 100 sensor nodes. The remaining (residual) energy of the proposed approach, WOA, compared to benchmark techniques ZFO-SHO, TIOCHR, and M-PSO. After 1800 rounds, the proposed WOA approach records the highest remaining (residual) energy of approximately 13J against 1J for ZFO-SHO, 9J for TIOCHR, and 11J for M-PSO. The efficient remaining residual energy is attributed to the design of WOA, which achieves faster convergence time during CH rotation.

As shown in Table 5, the total remaining energy depends on the network size of 100 nodes. The proposed method, WOA, demonstrates the lowest energy usage compared to existing approaches due to the faster convergence time of WOA.

TABLE 5. Remaining (Residual) Energy (Network size is 100 nodes).

Figure 8 illustrates the Remaining Energy concerning the network size of 200 sensor nodes. The remaining (residual) energy of the proposed approach, WOA, compared to benchmark techniques ZFO-SHO, TIOCHR, and M-PSO. After 1800 rounds, the proposed WOA approach records the lowest energy consumption of approximately 30J against 24J for ZFO-SHO, 25J for TIOCHR, and 28J for M-PSO. The efficient remaining energy is attributed to the design of WOA, which has a faster convergence time during CH rotation.

Table 6 represents overall energy consumption with respect to network size 200 nodes. The proposed method, WOA, demonstrates the lower usage of energy compared to other approaches due to the faster convergence time of WOA. It reduces unnecessary communication overhead.

TABLE 6. Remaining (Residual) Energy (Network size is 200 nodes).

Figure 9 shows the total reaming energy of a network of 300 sensor nodes. The remaining energy of WOA after 1,800 rounds is 73J whereas, the energy consumption performances of the benchmark methods ZFO-SHO is 60J, TIOCHR is 64J, and M-PSO is 69J. The advantage of WOA delays nodes death is also supported by the fact that the WOA is structured in a way that it converges faster during CH rotation.

Table 7 indicates the total energy consumption for a network including 300 nodes. The proposed WOA demonstrated lower energy consumption compared to existing approaches. Enhanced outcomes are attained owing to the WOA algorithm’s quickened convergence time in fewer iterations.

TABLE 7. Energy consumption (Network size is 300 nodes).

5.5 Network stabilization time

Figure 10 depicts the network stable time as a function of network size. The proposed WOA technique achieved the longest network stabilization time across various network sizes. The WOA approach outperformed ZFO-SHO, TIOCHR, and M-PSO. The energy consumption is reduced at the node level due to accelerated convergence dynamics of the WOA approach. This approach is most likely suitable for dense network scenarios.

Table 8 reveals the different network stabilization times for various network sizes. It is observed that the suggested WOA method shows the longest network stabilization time when compared to ZFO-SHO, TIOCHR, and M-PSO algorithms. For a network size of 300, WOA maintains stability for up to 1,200 rounds. Consequently, it conserves minimal energy and prolongs the network’s operational lifespan.

TABLE 8. Network stabilization time Vs. network nodes.

5.6 Node failure assessment

The network lifetime is evaluated based on energy depletion of node. It is measure with three indicators such as First Node Dead (FND), Half Node Dead (HND), Last Node dead (LND). The network lifetime of the WOA protocol has been presented in Figure 9, where it is being compared with other existing methods (ZF-SHO, TIOCHR, and M-PSO) using three different metrics (FND, HND, and LND) and WOA is observed to give the best performance. The ZF-SHO method has a network lifetime of 2000, 2,200, and 2,600 rounds for FND, HND, and LND, respectively. The TIOCHR approach was able to get 2,100, 2,250, and 2,700 rounds for FND, HND, and LND, respectively. The M-PSO method lasted the longest with FND, HND, and LND rounds recorded at 2,200, 2,500, and 2,800, respectively. The proposed WOA method has outperformed other techniques for the network lifetime FND 2500, HND 2800, and LND 3000 rounds shown in Figure 11. This means that the developed technique is the most suitable for energy saving and CH selection.

6 Conclusion and future work

The Underwater Wireless Sensor Network (UWSN) consists of low-power devices, thus posing challenges for optimization methods. Extending the lifespan of networks through energy optimization is crucial. Sensor nodes communicate via a clustering protocol. A plethora of optimization algorithms use CH selection to propose optimal solutions to the problem. Nevertheless, many of these optimization approaches are slow in the CH selection process due to an unsteady exploration/exploitation trade-off. To address this, we proposed the Walrus Optimization Algorithm (WOA) to select the best CH in the network. In CH selection, the objective function is determined by the two main factors: maximum Residual Energy (RER) and distance. The WOA CH selection process comprises two stages: cluster formation based on Euclidean distance and CH selection using a WOA-optimized method. The WOA strategy was realized in the MATLAB 2024a simulation environment. The WOA method was benchmarked against popular optimization methods, including ZFO-SHO, TIOCHR, and M-PSO. The WOA is an average improvement of 7%–10% in PDR, and the network lifetime is extended by 10%–15% compared to ZFO-SHO, TIOCHR, and M-PSO. Hence, the WOA has enhanced the total network efficiency.

The proposed WOA method has many advantages, but it is still open to improvements to be made. Future work can be extended to real-time implementation by taking into account factors, fuzzy rules, latency, and RSSI as the main parameters and deployment conditions will be explored further. The traditional algorithms LEACH and HEED will be considered in future extension work. Additionally, CH selection in a hybrid approach can be achieved by integrating other optimization techniques.

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Footnotes

Edited by: Hitesh Mohapatra, KIIT University, India

Reviewed by: Duraimurugan Samiayya, St. Joseph’s College of Engineering, India

Krishna Reddy Maddikera, Rajeev Gandhi Memorial College of Engineering and Technology, India

Xuan Yang, China University of Mining and Technology, China