Optimizing Sensor Deployment and Coverage in WSNs Using a Hybrid Firefly-Grasshopper Metaheuristic A

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Optimizing Sensor Deployment and Coverage in WSNs Using a Hybrid Firefly-Grasshopper Metaheuristic Approach Eshtiag Jahalrasool Ahmed1,3, Abdalla Akod Osman2, Sally Dfaallah Awadalkareem1 1Department of Computer Engineering, University of Gezira, Wad Madani, Sudan 2Department of Computer Sciences, University of Elahlia, Wad Madani, Sudan.

3Department of Information Technology, College of Computing, and Information Technology Khulais, University of

Jeddah, Jeddah 21959, Saudi Arabia -------------------------------------------------------------------------***-----------------------------------------------------------------------Abstract This study presents a novel hybrid optimization technique, the Firefly-Grasshopper Optimization Algorithm (FAGOA), designed to enhance energy efficiency and network performance in heterogeneous wireless sensor networks (WSNs).

Leveraging the exploratory power of the Grasshopper Optimization Algorithm (GOA) and the exploitative strength of the Firefly Algorithm (FA), FAGOA addresses limitations such as energy heterogeneity, network overlap, and inefficient cluster head selection. The methodology integrates both stationary and mobile sensor nodes and utilizes a hybrid movement update rule to optimize sensor deployment, energy consumption, and coverage. Extensive MATLAB-based simulations assess performance across metrics including energy use, coverage, delay, throughput, connectivity, and overlap. Compared to benchmark algorithms such as BAGOA and IGWO, FAGOA consistently outperforms in reducing overlapping coverage, improving energy conservation, and maximizing sensor coverage while ensuring lower standard deviation and mobility cost. The results confirm FAGOA’s superiority in optimizing WSN design for real-world environmental monitoring. Future work will integrate adaptive AI strategies to further enhance performance under dynamic conditions.

Keywords: FAGOA, WSNs, Energy Efficiency, Firefly Algorithm, Grasshopper Optimization Algorithm, Sensor Deployment, Hybrid Metaheuristics, Cluster Head Selection, Mobile Sensors, Network Coverage

Introduction Wireless communication technology has significantly transformed WSNs, facilitating the creation of compact, lightweight devices for monitoring diverse environmental and physical parameters. WSNs, composed of numerous sensor nodes, necessitate sophisticated data collection and processing methods to optimize power consumption (Srinivas et al., 2017).

The advancement of embedded systems and networking technologies has spurred interest in precise metering and control of residential environments. Self-configuring, geographically dispersed sensors in WSNs present an effective solution for monitoring these parameters. Recent developments have introduced various clustering hierarchy-based routing protocols aimed at enhancing energy efficiency in WSNs, including the GOA and the FA. GOA is a nature-inspired optimization technique that mimics the communication and coordination behaviors of grasshoppers to tackle complex problems (Abed et al., 2016). It operates by simulating a population of grasshoppers, where their movements are influenced by attraction and repulsion based on solution quality and proximity. While GOA is versatile and easy to implement, its effectiveness can be hindered by the complexity of the problem and the need for careful parameter tuning (Saoud et al., 2023).

Conversely, FA is based on the social behavior of fireflies, utilizing their flashing patterns to facilitate interaction and information sharing. Although FA is effective for optimization, it faces challenges such as premature convergence and sensitivity to parameter settings, particularly in complex WSN environments. Both algorithms exhibit limitations when applied to WSNs, including issues with energy heterogeneity, scalability, and constraint handling. To address these challenges, the research proposes a Hybrid Firefly-Grasshopper Optimization Algorithm (FAGOA) aimed at enhancing energy-efficient routing in WSNs (Janabi & Kurnaz, 2023). FAGOA combines the strengths of both FA and GOA, focusing on improving routing efficiency, extending network lifetime, and optimizing energy utilization. The study's objectives include formulating a FAGOA-based technique to optimize sensor node energy consumption, improving network lifespan, and validating FAGOA's performance through simulations and comparative analyses against existing optimization algorithms.

The research methodology encompasses problem formulation, system modeling, algorithm development, and performance evaluation, emphasizing optimal sensor node placement and energy efficiency (Baskaran & Sadagopan, 2015; Kun et al., 2023). The proposed FAGOA algorithm integrates exploration and exploitation strategies, aiming to maximize

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network coverage while minimizing energy consumption. The experimental setup, conducted in a MATLAB environment, evaluates the algorithm's effectiveness in enhancing network performance metrics such as energy consumption, network lifetime, and packet delivery ratios. Future research will explore the integration of AI-driven adaptive learning to further enhance optimization performance in WSNs.

Literature Review The literature review presents a comprehensive examination of various optimization algorithms, particularly focusing on the FA, GOA, and their hybrid forms, specifically the Hybrid Firefly Algorithm with Grasshopper Optimization Algorithm (FA-GOA) and the Hybrid Bees Algorithm with Grasshopper Optimization Algorithm (BAGOA). FA, introduced by Yang in 2008, FA is a nature-inspired, stochastic meta-heuristic algorithm that mimics the flashing behavior of fireflies. The algorithm operates on the principle that fireflies attract each other based on the intensity of their light, which is mathematically modelled to guide the search for optimal solutions. The FA's effectiveness lies in its ability to solve complex optimization problems through systematic or random migrations within a population of fireflies, ultimately leading to convergence around the most luminous solutions (Saoud et al., 2023). The algorithm's performance can be enhanced through modifications, such as the Multi-Objective FA with Multi-Strategy Integration (MOFA-MSI) and hybrid approaches that combine FA with other algorithms like the Gravity Search Algorithm (GSA) and Rao-based operators.

However, challenges such as premature convergence and limited exploration in high-dimensional spaces remain significant drawbacks.

GOA, developed by Saremi in 2017, GOA is inspired by the swarming behavior of grasshoppers. It balances exploration and exploitation through social interaction forces and gravitational attraction toward optimal solutions (Abed et al., 2016).

GOA has been applied in various fields, including WSNs, robotics, and engineering design. Despite its scalability and efficient convergence, GOA faces challenges such as computational complexity and susceptibility to local optima. Recent advancements have sought to improve GOA's performance through hybrid models and adaptive mechanisms. The integration of FA and GOA into hybrid algorithms aims to leverage the strengths of both methods while mitigating their weaknesses (Janabi & Kurnaz, 2023). The BAGOA algorithm combines the Bees Algorithm (BA) with GOA to enhance the exploitation capabilities of BA, addressing inefficiencies during the optimization process. Similarly, the FA-GOA hybrid seeks to utilize GOA's exploration strengths to avoid premature convergence while capitalizing on FA's efficient local search capabilities. These hybrid approaches have shown promise in optimizing WSN deployments, improving coverage, energy efficiency, and overall network performance (Baskaran & Sadagopan, 2015). Furthermore, the IGWO algorithm, an enhancement of the original Grey Wolf Optimizer (GWO), addresses issues such as premature convergence and limited diversity by incorporating nonlinear control strategies and hybridization with other metaheuristics. IGWO has been effectively utilized in WSN applications, focusing on cluster head selection and energy-efficient routing.

The literature identifies significant research gaps, particularly in the optimization of heterogeneous WSNs and the selection of cluster heads. Existing algorithms often overlook the energy conservation needs of diverse networks, leading to premature node failures and inefficient data collection (Zhang et al., 2023). The proposed FAGOA algorithm aims to fill this gap by integrating the strengths of FA and GOA to optimize energy consumption and enhance network performance.

Its contributions extend beyond WSNs, with potential applications in engineering, logistics, finance, and healthcare (Koosha et al., 2022). In summary, the literature review underscores the importance of developing advanced hybrid algorithms like FAGOA to address the complexities of energy optimization in heterogeneous WSNs. By leveraging the collective intelligence of fireflies and grasshoppers, FAGOA promises to enhance the robustness, efficiency, and longevity of WSNs while offering broader implications for various fields.

Methodology This section presents the overall research methodology, as shown in Figure 1.

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Figure 1: Flowchart of the Research Methodology

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The network is a distributed system with N sensor nodes, divided into stationary and mobile nodes. The network's lifespan is determined by efficient communication and data aggregation. A fixed base station (BS) gathers data from cluster heads (CHs) formed during the cluster formation phase. The WSN is organized in a multi-layered hierarchical structure to reduce energy consumption and enhance data processing efficiency (Pei et al., 2015). Sensor nodes are uniformly/randomly distributed in a geographic area, performing sensing and data transmission tasks. Stationary nodes remain in predetermined positions, simplifying network modeling and clustering processes. Mobile nodes can change places over time using mobility models, allowing the network to respond to changing conditions but also posing new connection and energy estimation challenges (Cherappa et al., 2023). Sensor nodes are grouped into clusters to reduce energy consumption associated with long-distance transmissions. CHs are selected based on residual energy, centrality relative to the BS, and local node density to ensure energy efficiency and strategic placement within the network.

Figure 2: Flowchart of the Research Methodology The proposed hybrid deployment algorithm FAGOA is a practical framework designed to address the challenges of WSN deployment. It is particularly suitable for hybrid WSNs that include both stationery and mobile sensors. The framework seeks to optimize the location of sensors by increasing area coverage, ensuring reliable communication, reducing energy consumption and delay, and increasing network lifetime. FAGOA combines the GOA's exploratory capability with the FA's exploitative strength to do these as shown in Figure 3.

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FIGURE 3: PROPOSED HYBRID DEPLOYMENT ALGORITHM FAGOA The heterogeneous WSNs uses optimization-based repositioning for mobile sensors, with stationary sensors remaining fixed locations. Mobile sensors are dynamically moved to optimal positions using the position update mechanism governed by hybrid FAGOA. The GOA component distributes sensors around the deployment area, simulating grasshopper collective swarming behavior. This broadens the search field to locate high-coverage, energy-efficient locations (Janabi & Kurnaz, 2023). The FA component conducts local exploitation, moving mobile sensors towards brighter individuals,

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maximizing factors like local coverage, connectivity, and path delay. This focused mobility allows the network to adjust its configuration around high-potential zones. A mixed position update rule controls the transition between GOA and FA, while stationary sensors remain unchanged throughout the optimization process. …1 (

)

(

)

(

)

(

)

( ) and ( ) are defined based on Equations (3.7) and (3.8), respectively and is a weighting factor where that decreases over time, emphasizing exploration in early stages and exploitation in later stages. Algorithm 3 provides the hybrid FAGOA algorithm for WSN deployment.

The fitness function in the FAGOA system directs balanced clusters, selects energy-efficient CHs, and optimizes node activity to reduce energy consumption. It allows CH rotation and adjusts to residual energy levels, increasing network lifetime and maintaining operational balance. The system operates iteratively, starting with GOA for initial coverage and fine-tuning sensor placement. The fitness function continuously evaluates network architecture to improve coverage and energy efficiency. As the network evolves, the system adjusts weight parameters to increase throughput and decrease energy consumption; ( (

…2

))

where w1, w2, w3, w4, and are weight factors assigned to each metric. This fitness function is used to calculate the brightness of fireflies and the attractiveness of grasshoppers, directing the search process toward the best option. is the coverage, which indicates the fraction of the overall deployment area that is effectively monitored by the sensor nodes. It can be explained as follows …3 where is area covered by sensors and is total deployment area. is the throughput, which is defined as the rate of successful data delivery over the network. It can be explained as follows …4 where is total number of data packets delivered successfully. is the connectivity, which can be quantified by the fraction of interconnected sensor nodes. It can be explained as follows …5 where is number of sensors that form a connected network and lifetime can be explained as follows

is total number of sensors.

is network

…6 where is initial energy of node and ( ), data reception ( ), and data processing (

is energy consumption, including the energy used for data transmission ). It can be explained as follows …7

represents the average end-to-end latency of data packets. It can be explained as follows

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…8 where is transmission delay, is queuing delay, overlap quantifying redundant sensing as follows

is processing delay and

is propagation delay.

is

…9 where

represents the redundant sensing area and

is total area.

Table 1: Hybrid FAGOA Deployment Algorithm 1: Hybrid FAGOA for WSN Deployment Input  : Number of sensor nodes  Deployment area parameters: e.g., area dimensions, obstacle regions  FA parameters: number of fireflies, maximum iterations, light absorption coefficient , attractiveness coefficient , randomization parameter  GOA parameters: number of grasshoppers, maximum iterations, social interaction factor , step size coefficient , upper and lower bounds and for each dimension  WSN parameters: sensor sensing range, communication range, etc.

Output  Optimized sensor node positions Procedure 1. Initialization:  Randomly initialize the positions ( ) for all and dimensions within the deployment area.  Set FA and GOA parameters according to problem specifications.  Evaluate the fitness of each candidate solution using Equation (3.7).  Identify the best initial solution from the population.

2. Iteration: For each time step :  Firefly Phase (Exploitation): For each firefly : Compute the attractiveness based on the brightness (fitness) comparison with other fireflies. ( ) according to Equation (3.7) in each dimension .

Update the position  Grasshopper Phase (Exploration): For each grasshopper : Calculate the social forces and aggregate the influences from neighboring grasshoppers. ( ) using Equation (3.8) in each dimension .

Update the position  Hybrid Update: For each sensor node and dimension , combine the FA and GOA updates using Equation (3.11).  Fitness Evaluation: - Evaluate the fitness ( ( )) for the updated positions using Equation (3.12).

- Update the best solution if a candidate with higher fitness is found.  Parameter Adaptation: - Gradually decrease ( ) to shift the balance from exploration (GOA) to exploitation (FA).

3. Termination: Terminate the iteration when the maximum number of iterations is reached or when a predefined convergence criterion is met.

4. Output: Return the best sensor node configuration identified.

Simulation Setup and Performance Metrics The proposed hybrid FAGOA algorithm has been implemented in MATLAB to evaluate its efficacy in optimizing CH selection and sensor placement in heterogeneous WSNs. The simulation captures key performance metrics such as energy consumption, network the lifespan, coverage efficiency, and throughput.

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www.irjet.net Table 2: Simulation Setup

Variable/Parameter N

Description Total number of sensor nodes Deployment area width and height Maximum number of iterations Number of fireflies Light absorption coefficient Attractiveness at zero distance Randomness parameter (step size) Initial brightness or attractiveness Control coefficients for GOA Social interaction intensity in GOA Scaling parameter for the social interaction function Time-decreasing weighting factor Upper and lower bounds of sensor positions Performance parameters given in Equation 9

Area Dimensions

,

( )

Fitness Metrics

Function in Algorithm Defines the number of nodes in the network Determines the simulation space Controls simulation duration Used in the FA component for exploitation Determines how attractiveness decays with distance in FA Sets the maximum attractiveness for FA Introduces stochastic behavior in FA updates Used to compute relative fitness in FA Define range of the linearly decreasing coefficient ( ) Scales the social force in the GOA phase Adjusts the influence spread in the GOA component Balances exploration (GOA) and exploitation (FA) over iterations Constrain sensor node positions within the deployment area Define network performance via the composite fitness function Equation 9

Performance Metrics The performance metrics used in this study is provided in Table 3.

Table 3: Performance Metrics Metric Coverage

Definition Measures how well the sensor field is monitored by the sensor nodes.

Rate at which data is successfully transmitted over the network.

Ability of sensor nodes to maintain communication with each other and the sink.

Throughput Connectivity

Network Lifetime Energy Consumption Delay Overlap

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Total time the network remains functional before key nodes fail.

Total energy used by sensor nodes for sensing, processing, and communication.

Time taken for a data packet to travel from source node to sink/base station.

Extent of redundant coverage in the sensing area by multiple nodes.

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Formula (if applicable) C = A_covered / A_total T = D_received / t Assessed via graph theory – network is connected if all nodes form a single communication graph.

Measured as time until first/last node dies or a custom metric.

E = E_tx + E_rx + E_proc D = D_trans + D_queue + D_proc + D_prop O = A_overlap / A_total

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Results and Discussion Scenario 1: The Overlapping Area Overlap in WSNs refers to the redundant sensing areas of multiple nodes, which can be minimized during early deployment for optimal sensor placement and energy savings. This enhances network coverage, reliability, data fusion, and fault tolerance. However, optimizing these areas presents challenges in energy efficiency, resource allocation, and interference management. Effective deployment strategies, such as density control, clustering, and energy-aware methods, are essential to balance coverage, connectivity, and resource utilization while minimizing waste. The FAGOA algorithm aims to minimize unnecessary overlap in sensor deployment while ensuring reliable network coverage. It optimizes node positions by combining firefly and grasshopper scouts, selecting elite sites for node repositioning, and localizing optimization in high-potential zones. This approach enhances energy efficiency, network longevity, and fault tolerance.

Both FAGOA and BAGOA algorithms undergo 200 iterations for reliability, with FAGOA expected to outperform BAGOA in sensor positioning efficiency. Thus, the result for the Overlapping Area for both FAGOA and BAGOA is presented in Table 5 and Figure 4 respectively.

Table 4.4: Experimental Parameters for Scenario 1 – Overlapping Area Parameter Deployment Area Number of Sensors Sensor Type Sensing Radius Overlap Detection Rule Overlap Metric Formula Iterations Algorithm Used Evaluation Metric Simulation Runs

Value 100 m × 100 m 20, 40, 60, 80, 100 Mobile 7 meters Distance < 2 × radius Qt = ( * ) * ( goodt – 200 FAGOA, BAGOA Overlapping Area 10

t worst ) + I

Table 5 compares the overlapping area between FAGOA and BAGOA across five sensor deployment scenarios. FAGOA consistently reduces overlapping areas, especially at sensor counts of 60 and 80. At 60 sensors, FAGOA achieves a significant improvement (6.272) compared to BAGOA (8.450), indicating better spatial optimization. However, at 100 sensors, FAGOA's overlap slightly increases due to high node density. Overall, FAGOA demonstrates better control over sensor redundancy, contributing to higher energy efficiency and better network resource utilization.

Table 5: Result for the Overlapping Area Scenario 20 40 60 80 100

Overlap Area (FAGOA) 0 0.345 6.272 22.213 42.208

Overlap Area (BAGOA) 1.00E-04 0.123 8.45 23.123 41.3245

FAGOA is a more efficient sensor placement algorithm than BAGOA, resulting in less overlap across all sensor counts. As the number of sensors increases, the overlapping area grows exponentially, reducing redundant coverage. FAGOA's advantage becomes clearer at mid-sensor counts (40-80), where it minimizes overlap more effectively than BAGOA. However, convergence becomes more difficult at high sensor counts (100). FAGOA offers better energy efficiency, coverage quality, and network performance in wireless sensor networks.

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Figure 4: Result for the Overlapping Area Scenario 2: Energy Consumption Energy consumption in WSNs is crucial for network longevity, maintenance costs, and system efficiency. From Table 6 below, the study focuses on optimizing energy consumption in WSNs by adjusting frame error rates. This technique increases data precision and reduces energy usage. Optimizing energy consumption is crucial for improving network performance and endurance. Network designers can offer long-term solutions using energy-efficient protocols, algorithms, and hardware designs. The experiment simulates FAGOA in a 50 m x 50 m space with 200 iterations and a fixed 5-meter perception perimeter. The results are compared with data from BAGOA and IGWO, with bold values reflecting optimal results.

Table 6: Experimental Parameters for Scenario 2 – Energy Consumption Parameter Deployment Area Number of Sensors Sensor Type Sensing Radius Movement Cost Model Iterations Algorithms Compared Energy Metric Energy Evaluation Basis Simulation Runs

Value 50 m × 50 m 30, 40, 50 Mobile 5 meters Qt = * ( goodt – worstt) + * (Iworst − worst) 200 FAGOA, BAGOA, IGWO Mean Energy Consumption (%) Sensor movement + communication cost 10

The findings shown in Table 7 demonstrate that FAGOA produces better deployment outcomes across the range compared to the other algorithms. For instance, FAGOA was the most effective coverage algorithm; it attained 88.76% and 98.58% while deployed. Additionally, it covers practically the whole sensing area, reaching 99.89% of the range with just 50 sensor nodes installed. This is greater than the results achieved using BAGOA and the IGWO by 0.72% and 0.84%, respectively, with the same number of sensors.

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Table 7: Comparing Algorithm Outcomes in a 50 m x 50 m Area.

Number of sensors

FAGOA Best(%)

Mean(%)

Std

BAGOA Best(%)

Mean(%)

Std

IGWO Best(%)

Mean(%)

Std

30

“88.78”

“88.65”

“0.790”

“84.56”

“83.90”

“0.385”

“86.52”

“84.91”

0.861

40

“98.58

“97.47

“0.420”

“94.88”

“94.30”

“0.426”

“95.84”

“94.29”

1.089

50

“99.89

“99.60

“0.210”

“99.00

“98.38”

“0.343”

“98.88

“97.94”

“0.76”

The FAGOA algorithm consistently outperforms the other two algorithms in terms of mean coverage, with results improving by up to 1.54%, 2.45%, and 1.45% with the installation of 30, 40, or 50 sensors. The lower standard deviations obtained by the proposed technique further demonstrate its superiority. Figure 5 shows that FAGOA consistently outperforms other algorithms across all sensor counts, with performance improvement as the number of sensors increases. FAGOA demonstrates superior efficiency or effectiveness in this deployment scenario, particularly in environments with increasing sensor density.

Outcome

Comparing Algorithm Outcomes in a 50 m x 50 m Area 100 95 90 85 80 75 30 40 Number of Sensors

FAGOA

BAGOA

50

IGWO

Figure 5: Results Comparing Algorithm Outcomes in a 50 m x 50 m Area.

The WSN uses cluster heads optimized by three algorithms: FAGOA, BAGOA, and IGWO. FAGOA ensures equal distribution of cluster heads, improving coverage and energy consumption. However, BAGOA and IGWO may concentrate more cluster heads, potentially disrupting energy balance. FAGOA's hybrid nature balances energy consumption, coverage, and connectivity. Figure 6 results show FAGOA outperforms other algorithms in ensuring optimal cluster head distribution, reducing energy consumption, and improving WSN lifespan.

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Figure 6: An Optimized Deployment of FAGOA, BAGOA, and IGWO in WSNs The FAGOA algorithm outperforms BAGOA in terms of energy consumption, mobile and static sensor deployment. It improves coverage for fixed and mobile sensors by 26.01%, reaching 95.02%. FAGOA also reduces standard deviation and energy usage, using less than half of what is required for BAGOA. It also optimizes mobile sensor placement, maximizing coverage while reducing energy consumption and prolonging network lifetime. FAGOA's ability to minimize movement boundaries and slow sensor motion rate contributes to higher-quality findings, as shown in Table 8.

Table 8: Comparison Based on Energy Consumption Algorithms

Initiation of Sensor Coverage.

Best(%)

Mean(%)

Std

FAGOA 48.20 95.02 92.25 0.368 BAGOA 48.20 89.60 86.66 0.601 Furthermore, Table 9 compares the average moving distance of 20 mobile sensors using two algorithms: FAGOA and BAGOA. FAGOA achieved a lower average moving distance (~38 units) than BAGOA (~45 units), indicating greater efficiency in optimising sensor mobility, leading to reduced energy consumption and longer sensor network life.

Table 4.9: Average Moving Distance for 20 Mobile Sensors Algorithm FAGOA BAGOA

Number of Mobile Sensors 20 20

Average Moving Distance (units) ~38 ~45

Also, from Figure 7 FAGOA algorithm has significantly improved coverage for fixed and mobile sensors, reaching 95.02%, a 26.01% increase. Compared to the BAGOA algorithm, which showed an 18.40% increase, FAGOA performed 7% better, indicating its advantage in optimizing coverage. FAGOA also reduces the standard deviation number and energy consumption, making it less than half of what is required for BAGOA. Its ability to minimize movement boundaries and slow sensor motion rate contributes to higher-quality findings, allowing sensors to work longer and avoid energy depletion.

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Average Moving Distance

46 44 42

FAGOA

40

BAGOA

38 36 34 20 Mobile sensor

Figure 7: FAGOA and BAGOA Average Moving Distance Comparison To compare the average moving distance of 20 mobile sensors utilising FAGOA and BAGOA algorithms, see Table 10 for details. FAGOA relocates sensors more efficiently (~36 units) than BAGOA (~45 units). Reduced energy usage improves deployment speed, accuracy, and resource utilisation, extending network life. FAGOA's outstanding performance improves wireless sensor network energy efficiency, cost savings, and sustainability.

Table 10: Average Energy Usage Comparison for 20 Mobile Sensors Algorithm FAGOA BAGOA

Number of Mobile Sensors 20 20

Average Moving Distance (units) ~36 ~45

Figure 4.5 below shows 20 mobile sensors' average energy use under FAGOA and BAGOA. The data shows that FAGOA uses less energy (~36 units) than BAGOA (~45 units). Due to greater route planning and movement optimisation, FAGOA's energy efficiency is higher. The lifetime and sustainability of sensor network applications depend on energy efficiency. The data suggest FAGOA as the better mobile sensor energy management technique. Thus, FAGOA outperformed other algorithms by optimizing the metric under this scenario. It demonstrated higher efficiency, stability, and reduced variance in performance.

FAGOA BAGOA 46 Energy Consumption (J)

44 42 40 38 36 34 20 Mobile Sensor

Figure 8: FAGOA and BAGOA Average Energy Usage Comparison

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Conclusion The proposed Hybrid FAGOA effectively addresses key limitations in traditional WSN optimization, particularly in the context of heterogeneous environments with both mobile and stationary sensors. By integrating the complementary strengths of FA and GOA, FAGOA enhances the balance between exploration and exploitation during sensor node deployment and cluster head selection. Simulation results show that FAGOA achieves significant improvements in energy consumption, network lifetime, and coverage compared to other metaheuristic algorithms like BAGOA and IGWO. It reduces sensor overlap, improves spatial optimization, and minimizes redundant sensing. Additionally, the algorithm maintains lower average energy usage and shorter sensor movement distances, which are essential for the longevity and sustainability of WSNs. The use of a time-dependent weighting factor allows dynamic tuning between GOA and FA phases, resulting in adaptive optimization across varying deployment scenarios. FAGOA's superiority in terms of performance metrics such as throughput, delay, and connectivity confirms its practicality for real-world applications. Future enhancements could involve the integration of AI-driven learning mechanisms to further adapt to unpredictable environmental conditions and improve responsiveness. Overall, FAGOA offers a robust, scalable, and energy-efficient framework for optimizing sensor deployment in next-generation smart sensing systems.

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