A Fuzzy-Controlled Equilibrium Optimizer for Energy-Efficient and Reliable Multi-Level Data Aggregation in Wireless Sensor Networks

Wireless Sensor Networks (WSNs) appeared as a critical technology for real-life observing and monitoring in a wide apps’ range such as healthcare systems, military surveillance, environmental observation, and industrial automation [1]. Such networks include spatially distributed sensor nodes that collaboratively sense, process, and transmit data to a sink node/base station. Despite their versatility, WSNs are constrained by limited energy resources, redundant data transmission, and unstable wireless communication, which significantly affect network lifetime and performance. In addition, ensuring network security has become a critical challenge, motivating the use of intelligent approaches such as machine learning-based intrusion detection systems [2]. So, effective methods of data aggregation are important for reducing the use of energy, communication overhead, and developing the reliability of data beyond the network [3].

Traditional protocols of data aggregation, like Low Energy Adaptive Clustering Hierarchy (LEACH) [4, 5], Power Efficient Gathering in Sensor Information Systems (PEGASIS) [6], and Hybrid Energy Efficient Distributed (HEED) [7], have laid the foundation for WSNs’ clustering and routing. Although such algorithms basically depend on cluster heads’ static clustering/probabilistic selection, this makes them inappropriate for active and large-scale networks. Also, sometimes they neglect contextual parameters like data quality, node reliability, and residual energy, causing network instability and premature node death. Accordingly, algorithms of developed optimization and intelligent decision-making have been broadly investigated to consider such restrictions.

In the last few years, metaheuristic optimization mechanisms like Particle Swarm Optimization (PSO) [8], Grey Wolf Optimizer (GWO) [9], Firefly Algorithm (FA) [10], and Whale Optimization Algorithm (WOA) [11] have been used for WSN clustering and data aggregation issues. Such mechanisms effectively look for optimum solutions in complicated spaces; however often suffer from entrapment and convergence to premature local optima, particularly under active situations of a network where levels of node energy and topology change over time. So, obtaining a balance between local exploitation and global exploration is a main issue in designing strong optimization-based aggregation models.

Equilibrium Optimizer (EO) [12], inspired by models of control volume mass balance, has recently drawn attention as a robust metaheuristic with quick convergence and robust exploration ability. Against the traditional swarm-driven mechanisms, EO keeps an active equilibrium pool, which helps candidate solutions to global optima while maintaining diversity. However, its performance in active and resource-limited WSN areas could degrade when its parameters are weakly tuned/fixed.

To consider such issues, the present article presents a new Fuzzy-Controlled Equilibrium Optimizer (FCEO) framework for reliable and multi-level data aggregation in active WSNs. The offered framework combines fuzzy logic with the EO to adaptively monitor parameters of the algorithm and develop its convergence theory. The fuzzy system assesses hybrid contextual agents like communication distance, residual energy, and data reliability for choosing optimum aggregator nodes at every network level. The EO guarantees global cluster formation and routing ways’ optimization through keeping a balance between exploitation and exploration. This hybrid model not only avoids premature convergence but also guarantees effective and energy-aware data aggregation.

Also, the offered multi-level aggregation structure lets sensor data be progressively filtered and aggregated via hierarchical layers of gateways, sensor nodes, and cluster heads before reaching the node of the sink. This model decreases extra transmissions and considerably improves energy efficiency and network scalability. Simulation outcomes show that FCEO consistently performs better than popular baseline mechanisms, such as Fuzzy-LEACH, LEACH, and Enhanced Equilibrium Optimizer (EEO) [13], in terms of total network energy, packet delivery ratio (PDR), alive nodes, and medium residual energy. Fuzzy-controlled intelligence and equilibrium-driven optimization integration make the system able to actively adapt to topology shifts and keep high reliability under network situations’ fluctuation.

Briefly, this study's basic contributions include:

1.  A fuzzy-controlled optimization framework that combines fuzzy logic with the EO for enabling aggregator nodes’ intelligent selection and adaptive parameter tuning.

2.  A multi-level data aggregation scheme that improves communication reliability and energy efficiency also balances residual energy among nodes in active WSNs.

3.  The broad performance assessment compares the offered technique of FCEO with state-of-the-art algorithms, such as Fuzzy-LEACH, LEACH, and Firefly-driven strategies, showing greater performance in the case of PDR, alive nodes, total lifetime of network moderate energy, and entire network energy.

This study’s remainder is structured as follows: Part 2 shows relevant work and reviews present strategies for aggregating data in WSNs. Part 3 details the offered method of FCEO, such as the EO-driven optimization process, fuzzy decision model. Part 4 discusses the experimental setup, performance outcomes, and presents an in-depth results discussion. Part 5 concludes the study with further study directions.

This section provides the offered FCEO framework for reliable and multi-level data aggregation in active WSNs. The technique is structured into 4 basic elements (Figure 1): multi-level aggregation structure, fuzzy decision module, network model, and assumptions, as well as a combination with the EO.

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Figure 1. Flowchart of the proposed method

3.1 Network model and assumptions

WSN is schemed as a network of N sensor nodes randomly deployed within a geographical environment of size A × A. Every node is equipped with sensing, operating, processing, communication, and computational abilities under the restricted energy of a battery. Nodes communicate with cluster heads applying single/multi-hop links based on the topology of the network. Here, the dynamics of network basically arise from node failures as well as progressive energy depletion made by exhaustion of battery than physical node mobility. Accordingly, active nodes’ set changes over time, causing the dynamic cluster formation as well as routing decisions via simulation. Basically, whole nodes are assumed to be homogeneous in terms of abilities of communication, energy, and range of sensing.

Efficiency of energy refers to the crucial issue in WSNs, and to the scheme usage of energy for receiving and transmitting data, the first-order radio energy model is adopted. Particularly, the energy needed for transmitting a k-bit message beyond distance d is described as [24]:

$E_{t x}(k, d)=E_{\text {elec}} \cdot k+\varepsilon_{\text {amp}} \cdot k \cdot d^2$        (1)

That E_tx(k,d) (J) shows the energy of transmission needed to send a k-bit packet over a distance d (m), E_elec (J/bit) shows the energy used by the transmitter and receiver electronic circuitry, ε_amp (J/bit/m²) refers to the transmit amplifier energy coefficient. Here, the model of free-space propagation model (d²) is used because the distance of communication among nodes of sensor is relatively short. The energy needed to obtain the k-bit message is computed as [25]:

Fitness $=w_1 \cdot$ EnergyConsumption + $w_2 \cdot$ Delay $+w_3 \cdot(1-$ Reliability$)$         (2)

E_rx(k) (J) shows the energy needed to get a k-bit packet. As the reception of packet does not include signal amplification, just the electronic circuitry uses energy in this process.

Data aggregation is hierarchically carried out, beginning from sensor nodes to cluster heads, after that, gateways, and finally, the sink node. Channels of communication are taken to be error-prone, and light encryption is developed to ensure the safety of data. This network model basic aim is to decrease total usage of energy usage, extend the lifetime of the network, and guarantee safe and reliable data transmission over the network.

Against the WSN models based on mobility, the offered framework uses static locations of node via the simulation. Nonetheless, the network remains dynamic because node failures made by depletion of energy modify the topology of network, needing adaptive routing updates as well as periodic cluster-head reselection continuously.

3.2 Multi-level aggregation structure

To improve energy efficiency and reduce redundant transmissions, the proposed FCEO framework adopts a three-level hierarchical aggregation structure, as described below. The offered FCEO framework adopts a three-level hierarchical aggregation structure. At the first level, nodes of sensor gather environmental data and transmit them to their related cluster heads. At the second level, every cluster head does the local data aggregation and forwards the aggregated packets to a node of gateway. At last, the gateway runs a second-step process of aggregation and transmits the last aggregated data to the node of sink. Such strategy of hierarchical communication effectively balances consumption of network energy, develop scalability, and decreases extra transmissions. The whole the proposed multi-level aggregation framework way is briefed in Algorithm 1.

3.3 Fuzzy Decision Module

The Fuzzy Decision Module (FDM) is modelled for recognizing the most appropriate nodes for data aggregation at every level by taking hybrid variables at the same time, such as data reliability, residual energy, and distance to cluster heads. To obtain this, fuzzy logic is developed for controlling these parameters’ inherent uncertainty and variability, making a single Aggregation Suitability Score (ASS) for every node. This score could be mathematically stated as:

$A S S_i=f\left(E_i, D_i, R_i\right)$        (3)

The parameter R_i reliability is described as the node I communication reliability that is computed as the rate of successfully delivered packets to the total transmitted packets among the node and its related cluster head:

$R_i=\frac{P_i^{\text {success}}}{P_i^{\text {sent}}}, 0 \leq R_i \leq 1$        (4)

E_i shows node i's residual energy, D_i shows the distance from the node to its cluster head, and R_i shows the reliability of communication described by Eq. (4). The outcome ASS_i ranges from 0–1, where higher values show more appropriate nodes of aggregation. $P_i^{\text {success}}$ shows the number of successfully delivered packets and $P_i^{\text {sent}}$ shows the whole number of transmitted packets. A higher R_i value shows a more reliable link of communication and develops the related node’s aggregation priority. Nodes with higher residual energy, shorter distance to their cluster heads, as well as higher reliability of data, are determined to have higher ASS amounts, making them more probable to be chosen as nodes of aggregation. Conversely, nodes with lower energy/weak connectivity obtain lower scores.

In the proposed FCEO framework, the fuzzy inference system applies 3 variables of input such as distance to the cluster head (D_i), data reliability (R_i), and residual energy (E_i). Every variable of input is shown by 3 linguistic terms (Low, Medium, and High) applying triangular membership functions. The related membership functions are shown in Figure 2. ASS is the fuzzy system output that shows every candidate node’s aggregation priority.

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Figure 2. Membership functions of fuzzy inputs and Aggregation Suitability Score (ASS) output

The process of fuzzy decision pursues the Mamdani inference algorithm. A Mamdani-type fuzzy inference system was used due to its intuitive rule representation and suitability for decision-making issues in WSNs. In the process of inference, the min operator was applied for assessing every rule antecedent situation, while the max operator was used for aggregating all activated rules’ outcomes.

At last, the aggregated fuzzy output was transferred into a crisp ASS by applying the Centroid defuzzification technique that calculates the aggregated membership function gravity center.

The fuzzy rules assess the integrated effect of data reliability, communication distance, energy level. The fuzzy inference system uses 27 IF–THEN rules obtained from expert knowledge by considering whole feasible 3 linguistic input variables (Residual Energy, Distance, and Data Reliability) integrations. The whole fuzzy rule base is shown in Table 2. For instance, a node with short distance, high data reliability and high residual energy gets a high ASS value, when nodes with long distance, low communication reliability and low energy get lower aggregation priority. The final crisp ASS value is obtained using the centroid defuzzification method. The generated ASS is combined into the Equilibrium Optimizer Adaptive Selection (AS) Strategy approach. The gathered score dynamically impacts the candidate aggregation nodes’ selection probability and sets the process of optimization through developing the balance among exploration and exploitation. In the basic iterations of optimization, the approach keeps higher exploration ability to search different solutions of aggregation when in later iterations, exploitation is focused to refine the optimum aggregation structure.

Table 2. Fuzzy rule base for aggregation node selection

The fuzzy system lets the network actively adapt to shifting situations, guaranteeing that aggregation decisions balance communication cost, data reliability, and energy efficiency in a combined and context-aware manner.

3.4 Integration with Equilibrium Optimizer

EO [12] is a physics-inspired metaheuristic that presents strong abilities of global search to optimize routing ways, multi-level data aggregation, and cluster formation in WSNs. In the offered FCEO framework, fuzzy-generated ASS are applied to actively set EO exploration and exploitation parameters, helping the search process to more reliable and energy-efficient solutions. Basically, candidate solutions’ population showing assignments of cluster head and routing ways is made. Every candidate solution is assessed by applying a function of fitness which combines the usage of energy, data reliability, and communication delay that could be stated as:

Fitness $=w_1 \cdot$ Energy Consumption + $w_2 \cdot$ Delay $+w_3 \cdot(1-$ Reliability$)$        (5)

That w₁, w₂, and w₃ refer to weight coefficients reflecting every metric's relative significance. EC shows the normalized energy usage, Delay shows the normalized communication delay, Reliability is the packet delivery reliability, and w₁ + w₂ + w₃ = 1. Here, the weights were experimentally chosen as w₁ = 0.5, w₂ = 0.2, and w₃ = 0.3. The mechanism of EO updates the candidate solutions iteratively by moving them to optimum equilibrium situations while keeping diversity of population, so as to prevent premature convergence. By combining fuzzy logic with EO, the FCEO framework obtains the balanced trade-off among global exploration and local exploitation, guaranteeing that multi-level aggregation decisions and cluster head selection are reliable and energy-efficient under active situations of network situations. The radio energy model parameters’ values utilized in the simulations are briefed in Table 3.

Table 3. Notation used in Eqs. (1)-(5)

3.5 Algorithmic flow

The total FCEO framework starts with initializing a network that nodes of sensor nodes are used, and basic energy levels and data status are adjusted. The fuzzy decision module computes the Aggregation Suitability Score for every node, helping the cluster heads and aggregator nodes’ selection. Candidate solutions are made for EO that assesses every fitness of a solution given the data reliability, usage of energy, and delay. EO parameters are actively set by applying fuzzy scores to develop convergence to the global optimum. The best solutions assign the last cluster head assignments and multi-level aggregation ways. Data is aggregated and transmitted via a hierarchical network structure, and the process repeats iteratively till a termination situation, like max rounds’ number/exhaustion of network energy, is obtained. This combined strategy guarantees that the offered framework is energy-aware, adaptive, scalable able to present reliable data aggregation in active WSNs.