Communications on Applied Nonlinear Analysis 

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Improved ACO for Energy-Efficient Wireless Sensor Networks 

 

1Tripti Chande, 2Prof (Dr) Asha Ambhaikar, 3Ankita Singh Baghel 
1 M. Tech. Scholar, 2 Director, 3Assistant Professor 

2, 3 Department of Computer Science & Engineering 

1, 2 MATS School of Engineering & IT, MATS University Aarang, 
1tripti.chande@gmail.com, 2drasha@matsuniversity.ac.in, 3ankitapariharresearcher@gmail.com 

 

Article History: 

Received: 12-01-2025 

Revised: 15-02-2025 

Accepted: 01-03-2025 

Abstract:  

Wireless Sensor Networks (WSNs) are increasingly becoming an integral part of many 

applications, including environmental monitoring, healthcare, and smart cities. 

However, a significant challenge faced by WSNs is energy consumption, as the sensor 

nodes are typically powered by batteries, which deplete over time, limiting the 

network's longevity. Traditional routing protocols often fail to optimize energy usage 

effectively, resulting in an uneven depletion of energy and premature node failures. In 

this paper, we introduce an improved Ant Colony Optimization (ACO) algorithm 

designed to optimize energy consumption and extend the operational life of WSNs. The 

enhanced ACO leverages multi-objective optimization and dynamic parameter 

adaptation, allowing for more energy-efficient routing by accounting for both the 

residual energy of nodes and the distance between them. This approach helps mitigate 

common issues such as the energy hole problem, imbalance in energy consumption, and 

rigid parameter settings seen in conventional algorithms. Our experiments demonstrate 

that the enhanced ACO significantly improves energy efficiency, achieving 19.6% more 

residual energy and reducing energy consumption by 38% compared to traditional ACO 

methods. Additionally, the network's lifetime is extended, maintaining over 90% 

connectivity for a large portion of the operational time. These results highlight the 

effectiveness and scalability of the proposed algorithm, particularly for large-scale 

deployments. Looking forward, the integration of machine learning techniques and 

support for mobile sensor networks could further enhance the algorithm's flexibility and 

performance in dynamic environments. 

Keywords: Wireless Sensor Networks (WSNs), Energy Optimization, Ant Colony 

Optimization (ACO), Dynamic Parameter Adaptation, Scalability. 

 

Introduction 

Many fields have begun to rely on Wireless Sensor Networks (WSNs) as a foundational technology, 

such as smart cities, healthcare, industrial automation, and environmental monitoring.  Sensor nodes 

in these networks are dispersed across the physical environment and communicate with one another 

wirelessly to gather and relay data.  Energy consumption, however, is a major obstacle for WSNs.  

Optimal energy utilization is crucial for extending the operating lifetime of the network and 

maintaining its sustainability, since sensor nodes are often powered by finite energy sources like 

batteries. 

 Most WSNs work by having sensor nodes regularly send data they've detected to a hub, also called a 

base station or sink.  The distance to the sink, the number of hops needed for data transmission, and 

mailto:tripti.chande@gmail.com
mailto:2drasha@matsuniversity.ac.in
mailto:ankitapariharresearcher@gmail.com


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the radio transmission power are a few of the parameters that affect the energy consumption of each 

node.  Due to energy consumption, the battery reserves of the sensor nodes gradually drain as the 

network runs. This can lead to node failure and the creation of energy holes, which can interrupt the 

connection of the network.  This phenomenon shortens the lifespan of WSNs and has a major effect 

on their overall performance. 

 A sensor node's power consumption is heavily influenced by the routing protocols used in WSNs.  

The energy limits are insufficiently addressed by conventional routing techniques like Direct 

Communication and Flooding.  Uneven energy depletion across the network is a common 

consequence of these protocols' failure to optimize routing paths depending on usage.  As a result, 

nodes in close proximity to the base station experience faster energy depletion, resulting in the 

network failing prematurely.  In order to circumvent this restriction and achieve a more equitable 

distribution of energy usage throughout the network, energy-aware routing methods are essential. 

 Optimization techniques like Ant Colony Optimization (ACO) have recently attracted a lot of 

interest for their potential to solve complicated routing problems, such as how to optimize energy 

consumption in WSNs.  An algorithm that takes its cues from nature, ACO mimics the way ants 

forage by sending fake ants out into a network to choose the best route to take in response to changes 

in pheromone levels.  Finding energy-efficient pathways for data transmission is one use case for 

ACO in WSNs.  Problems with parameter rigidity, metric imbalance, and the energy hole make 

typical ACO algorithms ineffective in large-scale WSNs. 

 In order to optimize energy consumption in WSNs, this study presents the Enhanced Ant Colony 

Optimization (ACO) method.  To tackle the issues of energy conservation, network lifetime 

extension, and efficient path selection, the suggested method enhances standard ACO by combining 

multi-objective optimization with dynamic parameter adaptation.  Minimizing the energy cost of 

routing paths while considering the residual energy of nodes and the Euclidean distance between 

them is the fundamental principle of the enhanced ACO algorithm.  To minimize energy usage and 

preserve network connectivity over time, the algorithm adjusts to the changing network conditions 

by dynamically altering parameters like α and β. 

These are the primary benefits that this study provides: 

1. Energy Optimization: By choosing the most effective paths for data transmission, the 

proposed augmented ACO algorithm decreases energy consumption in WSNs. This helps nodes 

conserve energy and stay connected for longer periods of time. 

2. The method improves its adaptability and flexibility in different network settings by 

incorporating dynamic parameter modification of critical parameters (α and β). This adaptation 

strikes a balance between pheromone influence, distance, and residual energy 

3. Network Lifetime Extension: By addressing the energy hole problem and optimizing energy 

consumption, the enhanced ACO algorithm significantly extends the operational lifetime of the 

network, ensuring that a larger portion of the network remains functional over time. 



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4. Scalability: The algorithm is tested across multiple network topologies with varying node 

densities and communication ranges, demonstrating its scalability and effectiveness in large-scale 

WSNs. 

1 Literature Review 

Many fields now rely on wireless sensor networks (WSNs), such as agriculture, environmental 

monitoring, healthcare, and industrial automation.  The energy economy of the network protocols 

utilized is crucial to the proper operation of these networks because they are often placed in remote 

or hard-to-reach areas.  Since most sensor nodes rely on fragile batteries for power, energy 

consumption is a major concern for WSNs.  Therefore, in order to ensure dependable operation and 

extend the lifetime of the network, it is crucial to optimize energy usage while keeping the necessary 

performance criteria. 

 Many solutions to the problem of energy limitations in WSNs have been suggested throughout the 

years.  Energy optimization relies heavily on routing protocols, which specify the routes that data 

takes on its way from sensor nodes to the base station.  The energy hole problem occurs when nodes 

far from the sink drain their energy supply at a significantly higher rate than other nodes in the 

network; these protocols attempt to equalize the load on the network and reduce energy consumption.  

The capacity of Ant Colony Optimization (ACO) to discover an optimal routing pattern within a 

network, which is based on the foraging behavior of ants, has made it prominent among optimization 

approaches. 

Table 1 Literature Review 

Reference Focus Area Key Contributions Methodology Outcome 

Narayan, V., 

et al. (2023) 

Energy-efficient 

Routing in WSN 

Proposes a fuzzy-

based routing protocol 

to enhance energy 

efficiency in WSNs 

Intelligent 

Decision-Making, 

Efficient Routing 

Enhanced routing 

protocols reduce 

energy consumption 

by efficiently 

selecting routing 

paths, improving 

overall energy 

efficiency 

Razooqi, Y. 

S., Al-

Asfoor, M., 

& Abed, M. 

H. (2024) 

Optimization of 

Energy 

Consumption in 

WSN 

Modifies Ant Colony 

Optimization to 

improve energy 

efficiency in WSNs 

Modified Ant 

Colony 

Optimization 

(ACO) 

The modified ACO 

algorithm 

demonstrates better 

energy conservation 

and reduced energy 

consumption 

compared to 

traditional methods 

Sharma, K., 

Kapoor, M., 

Energy-efficient 

Routing for 

Focuses on energy-

efficient algorithms 

Energy-efficient 

Routing 

Optimization of 

energy consumption 



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Shrivastava, 

A., 

Badhoutiya, 

A., Rao, A. 

K., & Pant, 

R. (2024) 

Precision 

Agriculture 

for WSNs in precision 

agriculture 

Algorithms results in improved 

performance in 

agricultural WSN 

applications 

Narayan, V. 

& Daniel, A. 

K. (2020) 

Smart Farming 

and WSN 

Introduces a multi-tier 

cluster-based 

approach for WSNs in 

smart farming 

Multi-Tier 

Clustering, WSN 

for Smart Farming 

Improved energy 

efficiency and data 

communication in 

precision 

agriculture 

environments 

Narayan, V. 

and Daniel, 

A.K. (2021) 

Cluster Head 

Selection in 

WSN 

Proposes a region-

based protocol for 

efficient cluster-head 

selection in WSNs 

Region-Based 

Cluster-Head 

Selection Protocol 

(RBCHS) 

The method 

optimizes energy 

efficiency and 

improves network 

lifetime by 

selecting 

appropriate cluster 

heads 

Kaveh, A., 

and  

Hamedani, 

K. B. (2022) 

Structural 

Optimization in 

WSN 

Discrete structure 

optimization is the 

focus of this new and 

enhanced statistical 

optimization method. 

Enhanced 

Algorithm for 

Arithmetic 

Optimization 

Shows enhanced 

optimization 

outcomes for 

structural issues, 

applicable in WSNs 

for resource 

optimization 

Agushaka, J. 

O., et al. 

(2022) 

Optimization in 

WSN 

Using dwarf 

mongoose behavior as 

inspiration, presents a 

novel optimization 

algorithm 

Dwarf Mongoose 

Optimization 

Algorithm 

The new algorithm 

shows promise in 

solving 

optimization 

problems in WSNs 

with better energy 

efficiency 

Safaldin, M., 

et al. (2021) 

Intrusion 

Detection and 

Optimization in 

WSN 

For intrusion 

detection, it integrates 

binary gray wolf 

optimizer with 

Support Vector 

Machine (SVM). 

Using SVM for 

Intrusion 

Detection and 

Binary Gray Wolf 

Optimization 

The approach 

improves the 

accuracy of 

intrusion detection 

systems while 

optimizing energy 

consumption in 

WSNs 



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Otair, M., et 

al. (2022) 

Intrusion 

Detection and 

Optimization in 

WSN 

Improving Gray Wolf 

Optimizer for 

Intrusion Detection 

via Particle Swarm 

Optimization 

Particle Swarm 

Optimization 

(Grey Wolf 

Optimizer) 

The hybrid 

algorithm enhances 

intrusion detection 

accuracy while 

improving energy 

efficiency in WSNs 

 

2 Methodology 

2.1 Proposed Method 

An improved Ant Colony Optimization (ACO) framework is available for use with WSNs; it 

integrates adaptive parameters with multi-objective optimization.  Our approach minimizes the 

energy-cost function given a network graph G = (V,E), where V stands for sensor nodes and E for 

communication links: 

𝒞(𝒫) = ∑ (
𝑑𝑖𝑗

2

𝐸𝑡𝑥
+

1

𝐸𝑟𝑥
)(𝑖,𝑗)∈𝒫 ⋅

1

𝐸𝑗
res       (1) 

where dij denotes Euclidean distance, Ej
res is residual energy, and 𝒫 represents routing paths. 

2.1.1 Motivation 

Traditional routing protocols exhibit three critical limitations: 

Energy hole problem: ∃vi ∈ V ∣ lim 1t→∞ Ei(t) = 0 

Metric imbalance: arg min.dij
≠ argmin.ΔEij

 

Parameter rigidity: Fixed α, β ∈ R+ prevent dynamic adaptation  

2.1.2 Mathematical Formulation 

The algorithm operates through three mathematical phases: 

(1) Path Selection Probability 

𝑃𝑖𝑗
𝑘(𝑡) =

[τ𝑖𝑗(𝑡)]
α

[η𝑖𝑗(𝑡)]
β

[ξ𝑖𝑗(𝑡)]
γ

∑ [τ𝑖𝑙(𝑡)]α[η𝑖𝑙(𝑡)]β[ξ𝑖𝑙(𝑡)]γ
𝑙∈\𝑁𝑠𝑒𝑡𝑖

       (2) 

where, η𝑖𝑗 = 1/𝑑𝑖𝑗 and ξ𝑖𝑗 =
𝐸𝑗

res

∑ 𝐸𝑘
res

𝑘∈\𝑁𝑠𝑒𝑡𝑖

 

(2) Pheromone Update Rule: 

τ𝑖𝑗(𝑡 + 1) = (1 − ρ)τ𝑖𝑗(𝑡) + ∑
𝑄

𝐿𝑘(𝑡)
𝐾
𝑘=1 ∥{(𝑖,𝑗)∈𝒫𝓀}     (3) 

(3) Energy Dissipation Model: 

𝐸𝑖(𝑡 + 1) =  {
𝐸𝑖(𝑡) − 𝜖amp ⋅ 𝑑𝑖𝑗

2 − 𝜖circ   𝑡𝑟𝑎𝑛𝑠𝑚𝑖𝑡𝑡𝑖𝑛𝑔

𝐸𝑖(𝑡) − 𝜖circ                                𝑟𝑒𝑐𝑒𝑖𝑣𝑖𝑛𝑔
    (4) 



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2.2 Algorithm 

 

The Enhanced ACO Energy Optimization Algorithm consists of several phases, including path 

selection, pheromone update, and energy dissipation. In the path selection phase, the probability of 

selecting a path between two nodes is influenced by the pheromone value, that which is negative of 

the distance between nodes plus the remaining energy of the node that is to be reached.  To increase 

the concentration of pheromones, the ant pheromone update rule modifies the pheromone levels 

along the ant's preferred pathways on successful paths to reinforce their selection in future iterations. 

The energy dissipation model accounts for energy consumption during both transmission and 

reception of data, adjusting the energy state of nodes after each communication event. The algorithm 

dynamically adapts the parameters α and β that influence the importance of pheromone and energy 

states in path selection. This ensures flexibility in the algorithm's response to different network 

conditions. The final output is the optimized routing paths that maximize the network's overall 

energy efficiency, ensuring prolonged network lifetime and effective connectivity. 

2.3 Flowchart 

To optimize energy consumption in WSNs, the suggested technique incorporates an improved Ant 

Colony Optimization (ACO) algorithm.  A network graph is defined at the outset of the process, with 

sensor nodes serving as vertices and communication links as edges.  An energy-cost function, 

representing the total energy consumption across all possible routing paths, is what we're aiming to 

reduce. The network consists of multiple iterations in which ants are deployed from random non-sink 

nodes. Each ant constructs a routing path based on pheromone updates and energy consumption, and 

updates the energy states of the nodes. The pheromone trails are updated after each iteration and the 

parameters α and β are dynamically adjusted to ensure better path selection. The flow of energy and 

the residual energy at each node are key factors in the path construction process, ensuring energy 

efficiency over time. The methodology iterates this process for a maximum number of iterations, 

ultimately optimizing the routing paths based on the energy states and the pheromone updates. 

 



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Figure 1 Methodology Flowchart 



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3 Result and Discussion 

The proposed energy optimization framework using Enhanced Ant Colony Optimization (ACO) was 

evaluated through various network configurations and performance metrics. The goal was to assess 

the energy efficiency, network lifetime, and scalability of the enhanced ACO algorithm compared to 

traditional ACO in Wireless Sensor Networks (WSNs). The experimental results demonstrated 

significant improvements over conventional approaches in regards to the longevity of the network 

and the preservation of energy. The evaluation involved several test cases, using different network 

topologies, energy consumption patterns, and parameter settings. 

3.1 Network Topologies 

The experimental setup involved three distinct network topologies with varying node density and 

communication range. These configurations allowed for a comprehensive understanding of the 

algorithm's performance in different real-world scenarios. 

1. 80-node WSN topology (100m x 100m area): In this configuration, the sensor nodes were 

distributed over a 100m x 100m area, with a communication range of 40m. This setup allowed the 

study of connectivity and energy consumption in a relatively small network with dense node 

placement. The center node acted as the base station, and nodes within a 40m communication range 

were considered to form clusters. 

2. 160-node WSN topology (200m x 200m area): The second topology expanded the network 

area to 200m x 200m, with nodes having a communication range of 60m. This configuration resulted 

in longer multi-hop paths and demonstrated the challenges of energy conservation in a larger-scale 

network. 

3. 240-node WSN topology (300m x 300m area): The final configuration used a 300m x 300m 

area with a communication range of 80m. This sparse connectivity emphasized the need for energy-

aware routing to prevent premature node failures in large-scale networks. 

The network topologies were visualized to assess how the connectivity and spatial distribution 

influenced energy efficiency, network lifetime, and routing performance. The increase in network 

size and sparse connectivity led to challenges in maintaining energy efficiency and connectivity over 

longer periods, necessitating the need for optimized routing protocols like Enhanced ACO. 

3.2 Network Topology Visualization 

Figure 2 demonstrates the network configurations used in our simulations, showing the impact of 

scale on connectivity patterns. 



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Figure 2 80-node WSN topology (100Ö100m area). Red center node represents the base station. 

Nodes within 40m communication range (gray lines) form connected clusters. 

 

Figure 3 160-node configuration (200Ö200m area) with 60m communication range. Increased 

spatial distribution creates longer multi-hop paths to the sink. 



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Figure 4 240-node deployment (300Ö300m area) using 80m range. Sparse connectivity highlights 

the need for energy-aware routing in large-scale networks. 

 

3.3 Performance Evaluation 

In this part, we examine the algorithm's performance on various different network topologies, with a 

particular focus on energy conservation, network lifetime, and scalability. The results are compared 

against traditional routing protocols to highlight the improvements brought about by the enhanced 

ACO approach. Key performance metrics, including residual energy, energy consumption rate, and 

network connectivity, are discussed in depth, supported by graphical representations and quantitative 

analysis. 

3.3.1 Energy Conservation Comparison 

A crucial performance metric in this study was energy conservation. The comparison between the 

traditional ACO algorithm and the enhanced ACO method highlighted a significant improvement in 

energy efficiency. The suggested technique resulted in a 19.6 percent increase in residual energy, 

according to the experimental results compared to the traditional ACO algorithm. 

Energy conservation comparison (50 iterations): In Figure 4, it was observed that the enhanced 

ACO algorithm maintained a higher residual energy throughout the simulation. The energy 

consumption rate for the traditional ACO was higher, as it showed an energy variance (σ²) of 8.7, 

while the enhanced ACO exhibited an energy variance of only 2.3. This difference illustrates the 

efficiency of the proposed algorithm in managing energy dissipation and ensuring that sensor nodes 

retain energy for longer periods. 



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Energy Consumption Rate: The rate of energy consumption improved significantly with the 

enhanced ACO. The energy dissipation rate for the proposed method was 0.18 J/iteration, while the 

traditional method consumed energy at a rate of 0.29 J/iteration. This reduction in energy 

consumption indicates that the enhanced ACO is more effective in minimizing unnecessary energy 

expenditure by selecting energy-efficient paths and optimizing the routing strategy. 

With better energy conservation, the network and sensor nodes have a better chance of lasting a long 

time, which is critical for long-term deployments in real-world WSN applications. 

 

Figure 5 Energy conservation comparison (50 iterations). Our method maintains 19.6% higher 

residual energy than standard ACO, with energy variance σ2 = 2.3 vs. 8.7 in traditional approach. 

 

3.3.2 Quantitative Analysis 

The experimental results validate three key advantages of our approach: 

(1) Energy Efficiency: As shown in Figure 4, the modified ACO reduces energy consumption 

rate by: 

𝑑𝐸

𝑑𝑡 improved

= 0.18 J/iter vs 
𝑑𝐸

𝑑𝑡 standard

= 0.29 J/iter 

(2) Scalability: Figure 5 demonstrates logarithmic relationship between network size and 

lifetime: 

𝑇net(𝑁) = −25.7 ln(𝑁) + 147.2 (𝑅2 = 0.98) 



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(3) Connectivity Maintenance: All configurations maintained. 90% network connectivity until 

75% of total lifetime (Figures 2-4). 

3.3.3 Network Lifetime Across Configurations 

Using the three different network topologies, we measured the network lifetime to see how well the 

Enhanced ACO algorithm kept the network connected when the sensor nodes' batteries ran out.  

Number of iterations until first node failure (when energy level dropped below 1J) and percentage of 

node connections over time were used to compare the algorithm's performance to that of the 

traditional ACO approach. 

Network Lifetime in 80-node configuration: As seen in Figure 5, the 80-node WSN topology 

achieved 120 iterations before the first node failure, while the network maintained 95% connectivity 

up until iteration 90. This indicates that the enhanced ACO algorithm significantly extended the 

operational lifetime of the network by optimizing energy consumption and ensuring efficient path 

selection. 

Impact of Network Size on Lifetime: The larger configurations (160-node and 240-node networks) 

further demonstrated the scalability of the enhanced ACO algorithm. In the 160-node configuration, 

the network achieved stable connectivity for a longer period, even with the increased spatial 

distribution and longer multi-hop paths. Similarly, in the 240-node configuration, the algorithm 

successfully handled the sparse connectivity and maintained over 90% network connectivity until 

75% of the total lifetime. 

 

Figure 6 Network lifetime across configurations. The 80-node network achieves 120 iterations 

before first node failure (Emin < 1J), while maintaining 95% node connectivity until iteration 90. 



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The results in terms of network lifetime were highly promising, with the enhanced ACO ensuring 

prolonged network operation and minimizing the chances of energy hole formation, a common 

problem in traditional ACO algorithms. 

Network Lifetime Model: The relationship between network size (N) and network lifetime (T_net) 

was found to be logarithmic, as shown by the equation in the results section. This indicates that as 

the network size increases, the network lifetime decreases at a slower rate, validating the 

effectiveness of the enhanced ACO in larger networks. The formula used for network lifetime 

prediction demonstrated a strong fit (R² = 0.98), showcasing the robustness of the algorithm in 

maintaining network connectivity even in large-scale deployments. 

4 Conclusion and Future Scope 

4.1 Conclusion 

When it comes to optimizing energy consumption in WSNs, the suggested Enhanced Ant Colony 

Optimization (ACO) method shows considerable progress.  The energy hole problem, metric 

imbalance, and parameter rigidity are some of the important challenges that the method successfully 

tackles by combining multi-objective optimization with dynamic parameter adaptation.  It has been 

found through experimental data that the enhanced ACO approach performs better than the 

conventional ACO in several key performance metrics. In particular, energy conservation was 

notably improved, with the enhanced ACO algorithm achieving a 19.6% higher residual energy 

compared to traditional ACO. The energy consumption rate also showed a marked reduction, with 

the proposed algorithm operating at a rate of 0.18 J/iteration, significantly better than the standard 

ACO's rate of 0.29 J/iteration. 

In terms of network lifetime, the proposed method extended the operational lifetime across various 

network topologies. For the 80-node configuration, the network operated for 120 iterations before the 

first node failure, maintaining over 90% connectivity until iteration 90. The performance was 

consistent even in larger configurations, such as the 160-node and 240-node networks, where the 

enhanced ACO ensured connectivity retention for a significant portion of the network lifetime, even 

with increased network size and more sparse connectivity. The logarithmic relationship between 

network size and lifetime further validated the scalability of the algorithm, confirming that the 

enhanced ACO is well-suited for large-scale deployments in WSNs. 

Overall, the enhanced ACO algorithm proves to be a promising solution for energy-efficient routing 

in WSNs, ensuring longer network lifetimes and higher energy conservation, which is crucial for the 

success of long-term deployments in real-world applications. The robustness of the algorithm, along 

with its flexibility in dynamic environments, makes it a strong candidate for implementation in both 

small and large-scale WSNs. 

4.2 Future Scope 

The future scope of this research lies in further refining the Enhanced ACO algorithm to address 

additional challenges such as scalability in highly dynamic and heterogeneous networks, where 

nodes exhibit varying energy consumption patterns and capabilities. Future research can also explore 

the integration of the Enhanced ACO with other advanced optimization techniques, using tools like 



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machine learning algorithms, to make dynamic predictions about things like network traffic and 

climate change.  In addition, vehicle or mobile ad hoc networks (MANETs) could benefit from 

energy-efficient routing if the algorithm were to be enhanced to accommodate sensor node mobility.  

Furthermore, QoS metrics like throughput and latency are incorporated in the multi-objective 

optimization process could further enhance the algorithm's applicability in real-time WSN 

applications. 

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[12] The Impact of Quality of Service (QoS) Parameters on IoT Application Performance  Volume 3,  

[13] Issue3, 2024, PP 1-20,  

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https://doi.org/10.1007/s11277-023-10434-z
https://journal.esrgroups.org/jes/article/view/1794
https://ijisae.org/index.php/IJISAE/article/view/6155
https://journal.inence.org/index.php/ijfiahm/article/view/363/263