Research on the Energy-Efficient Non-Uniform Clustering LWSN Routing Protocol Based on Improved PSO for ARTFMR

Abstract

To address the challenges of improving energy balance and extending the operational lifetime of wireless sensor networks for Automated Railway Track Fastener Maintenance Robots (ARTFMR) along railways, this paper proposes an enhanced LEACH protocol incorporating Particle Swarm Optimization (PSO). Initially, network nodes are deployed, and their energy consumption is calculated to formulate a non-uniform deployment model aimed at improving energy balance, followed by network clustering. Subsequently, a routing protocol is designed, where the cluster head election mechanism integrates two critical factors—dynamic residual energy and distance to the base station—to facilitate dynamic and distributed cluster head rotation. During the communication phase, a Time Division Multiple Access (TDMA) scheduling mechanism is employed in conjunction with an inter-cluster multi-hop routing scheme. Additionally, a joint data-volume and energy optimization strategy is implemented to dynamically adjust the transmission data volume based on the residual energy of each node. Finally, simulations were conducted using MATLAB, and the results indicate that the proposed energy-balanced non-uniform deployment optimization strategy improves network energy utilization, effectively extends network lifetime, and exhibits favorable scalability.

1. Introduction

A Wireless Sensor Network (WSN) is an autonomous multi-node system in which a large number of low-power miniature sensor nodes cooperate through integrated sensing, wireless communication, and on-board data-processing capabilities. These networks can deliver secure and reliable communication and control services at a relatively low cost [1,2,3]. In recent years, WSNs have been widely applied in environmental monitoring, especially in chain-structured terrains such as railways, rivers, and mining areas [4,5]. In such chain-structured monitoring scenarios, sensor nodes are typically deployed in a linear arrangement, thereby forming Linear Wireless Sensor Networks (LWSNs). This type of network is susceptible to energy-consumption imbalance, a phenomenon commonly referred to as the “energy hole” problem. The issue is characterized by the significantly faster energy depletion of nodes located near the sink compared to those situated in remote areas [6,7,8]. Moreover, given the strong practical relevance of WSNs, the deployment of Linear Wireless Sensor Networks (LWSNs) for Automated Railway Track Fastener Maintenance Robots (ARTFMR) along railway lines necessitates full consideration of real-time data-transmission requirements [9]. Consequently, achieving efficient data transmission in railway-deployed LWSNs requires addressing two critical challenges: balancing node energy consumption and minimizing transmission delay.

To address the challenges of energy constraints in sensor nodes and the limited overall lifespan of WSNs [10], researchers have conducted extensive studies from multiple perspectives. These include dynamic adjustment of network topology [11] and the design of clustering routing protocols [12,13], aiming to achieve balanced resource allocation and improve network energy efficiency through hierarchical network structures, thereby extending network longevity. The current body of research encompasses a wide range of WSN clustering routing strategies, employing diverse methods such as deep reinforcement learning [14], fuzzy logic [15], swarm intelligence optimization algorithms [16,17,18].

Kasilingam Rajeswari et al. [19] introduced a genetic algorithm into the clustering routing process of WSNs. This approach first performs energy-efficient clustering of nodes, then applies the genetic algorithm with network coverage and node residual energy as key input parameters to optimize the selection of cluster head (CH) nodes. The strategy is designed with the dual objectives of minimizing both network communication overhead and node energy consumption, thereby significantly extending network lifetime. Mohammad Hossein Shafiabadi et al. [20] proposed an energy-efficient clustering routing protocol for WSNs based on a Self-Organizing Map (SOM). The protocol first constructs high-energy clusters through weight training and reorganization, and then integrates high-energy nodes with low-energy nodes to achieve inter-cluster energy balance, with the ultimate aim of prolonging network lifespan.

Yao et al. [21] developed a clustering routing protocol by applying an Improved Archimedes Optimization Algorithm (IAOA). Although this algorithm achieves efficient communication by integrating multiple swarm intelligence optimization strategies, its complex iterative process also leads to high computational complexity, undoubtedly increasing the additional burden on network nodes. Qi et al. [22] introduced an Energy-Efficient Non-Uniform Clustering Routing (E2NUCR) protocol. This protocol first uses the hybrid leapfrog optimization algorithm to complete the CH configuration, and then, considering factors such as the distance between nodes, communication energy consumption and hop count comprehensively, greedily builds the upper-layer backbone network through local broadcasting. Akhilesh Panchal et al. [23] proposed an Energy-Efficient Hybrid Clustering and Hierarchical Routing (EEHCHR) protocol. This protocol optimizes the clustering process by alternately employing random rotation and fuzzy clustering strategies, and introduces direct CHs and central CHs to serve as gateways for the upper-layer backbone network during the relay phase. Studies indicate that both the E2NUCR and EEHCHR protocols can substantially reduce network computational overhead while maintaining communication quality. Sunil Kumar Singh et al. [24] balanced energy consumption through periodic rotation of CHs; however, their protocol remained susceptible to the “energy hotspot” issue. This problem stems from the uneven distribution of CHs and network load, especially among CHs located near the sink node, which experience significantly imbalanced energy consumption—a key limitation for practical deployment of the protocol.

Gou et al. [25] developed an enhanced Energy-Efficient Uneven Clustering (EEUC) protocol, building upon the foundational LEACH architecture. This protocol comprehensively considers the residual energy of nodes and the load distribution among CHs during the clustering phase to balance CH energy consumption. However, its applicability in large-scale network scenarios remains limited. Li et al. [26] developed a reinforcement learning-based routing protocol, which effectively enhances the network’s adaptability to dynamic environments and prolongs the network lifespan by comprehensively considering the residual energy of nodes and link quality. However, in the later stage of network operation, the possible energy depletion of individual nodes may lead to data transmission interruption. Therefore, designing a reasonable alternative path update and routing maintenance mechanism is crucial for ensuring the continuous and stable operation of the network.

Although the above-mentioned algorithms can effectively extend the lifespan of WSN, they generally have the drawback of high algorithmic complexity, making them difficult to apply to LWSN deployed along railway lines in ARTFMR. In contrast to planar mesh topologies, LWSNs offer more constrained transmission paths. Consequently, CH nodes play a critically important role. A single CH failure can consequently lead to a complete collapse of data transmission across the entire network. The energy consumption of a CH is significantly higher than that of an ordinary member node. Without a reasonable energy consumption balancing strategy, CHs may fail due to premature energy depletion, which seriously affects the network lifespan [27,28]. To address the energy consumption balancing issue in chain-shaped areas, Ali [29] and Kong et al. [30] conducted routing optimizations for scenarios involving oil/gas pipelines and ultra-high voltage transmission lines, respectively. However, their research failed to address the challenges of load imbalance and real-time data transmission in monitoring networks, thus limiting their adaptability to railway monitoring environments. The generalizability of most existing LWSN routing algorithms for railway monitoring remains limited. This is primarily because they inadequately account for the impact of key parameters like CH load and spacing on energy balancing and network lifespan [31], in addition to a general scarcity of quantitative analysis on node energy consumption and transmission delay [32].

Based on the preceding analysis, this paper proposes LEACH-PSOI, an energy-efficient routing algorithm tailored for LWSNs deployed along railway lines for ARTFMR, addressing their specific operational characteristics and requirements. The proposed algorithm operates according to the following principles. First, in the initial deployment phase, sensor nodes are arranged non-uniformly along both sides and the central zone of the railway track to accommodate the inherently elongated and narrow topology of the monitoring area. Second, during the CH election process, nodes with higher residual energy are selected as initial particles. A linearly decreasing inertia weight strategy is incorporated to mitigate the traditional PSO’s tendency for premature convergence to local optima. Finally, a fitness function is formulated to balance node-level energy consumption, thereby optimizing CH selection. In addition, the LEACH-PSOI algorithm integrates intra-cluster Time-Division Multiple Access (TDMA) scheduling and inter-cluster multi-hop routing to improve both data transmission efficiency and network-wide energy performance. A dynamic adjustment mechanism is also introduced, which accounts for real-time data volume and residual energy. This mechanism achieves spatial balancing of communication load and temporal smoothing of energy expenditure by adaptively regulating the transmission load and energy distribution among nodes. Consequently, it effectively mitigates transmission interruptions that are frequently induced by the elongated, narrow structure of the railway environment, substantially extends the overall lifecycle of the ARTFMR-oriented LWSN, reduces network latency, and enhances communication reliability.

2. Wireless Sensor Network System Model

2.1. Network Model

The design and assessment of the proposed WSN routing protocol are predicated on the following assumptions concerning the sensor nodes and the underlying network model:

(1)

Base stations are assumed to possess unlimited communication and computational capabilities, whereas sensor nodes operate under constrained resources [33].

(2)

Sensor nodes are capable of autonomously adjusting their wireless transmission power [34].

(3)

Wireless communication links are assumed to be symmetric.

2.2. Energy Consumption Model

Data transmission between sensor nodes occurs over wireless channels, specifically free-space or multipath fading models, depending on the communication distance [35]. A complete communication process involves data transmission, reception and processing.

The data transmission module is composed of a signal transmission unit and a signal amplification unit. The corresponding energy consumption, denoted as $E_{TX}$, for transmitting k bits of data over a distance of dm, which is expressed by Equation (1).

$$E_{TX}(k,d)=\left\{\begin{array}{l}k{E}_{elec}+k{E}_{fs}{d}^2, d<d_0\\ k{E}_{elec}+k{E}_{mp}{d}^4, d\ge d_0\end{array}\right.$$

(1)

The energy consumption, denoted as $E_{RX}$, for receiving k bit data is given by Equation (2).

$$E_{RX}(k)=k{E}_{elec}$$

(2)

The data processing module serves to reduce data redundancy, thereby improving overall data quality. Its energy consumption $E_{DA}$ for processing k bit data is shown in Equation (3).

$$E_{DA}(k)=k{E}_{da}$$

(3)

In Equations (1)–(3), $E_{elec}$ signifies the energy consumption coefficient of the transceiver circuitry, whereas $E_{fs}$ and $E_{mp}$ designate the amplification circuit coefficients applicable to the free-space and multipath fading channel models, respectively (namely, the free-space channel model and the multipath fading channel model.); $d_0=\sqrt{E_{fs}/E_{mp}}$ is the communication distance threshold; and $E_{da}$ is the energy consumption per unit of data processing.

2.3. Network Node Model

This paper models the railway as a linear network of length D, based on the standard track gauge (1435 mm) and long-distance nature of railways. The network includes N ordinary nodes and one Sink node. The ordinary nodes share a common sensing radius r, initial energy, and communication capabilities, whereas the Sink node is energy-unconstrained. Operationally, sensor nodes in a cluster first collect and send data to their CH. After receiving the data, the CH aggregates it and then forwards the consolidated information to the Sink via multi-hop communication [36]. Figure 1 depicts the architecture of the linear network model adopted in this study.

3. LEACH Routing Protocol Based on Improved PSO Algorithm

3.1. Particle Swarm Optimization Algorithm

Particle Swarm Optimization (PSO) is a swarm intelligence algorithm widely adopted in WSN clustering routing protocols [37,38], noted for its ease of implementation and limited need for parameter adjustment, and rapid convergence. By using the collaboration and information sharing among individuals to search for local optimal values and obtain the global optimal value, it can effectively solve the WSN optimization clustering problem [39]. The mathematical formulation of the standard PSO algorithm is as follows: Suppose the particle swarm size is K, the search space is D-dimensional, the position of particle i ($1\le i\le K$) is $X_i=(x_{i1},x_{i2},x_{i3},\dots ,x_{iD})$, and it flies at a speed of $V_i=(v_{i1},v_{i2},v_{i3},\dots ,v_{iD})$. Suppose the current local optimal solution found by particle i is $P_i=(p_{i1},p_{i2},p_{i3},\dots ,p_{iD})$, and the global optimal solution obtained by all particles is $P_g=(p_{g1},p_{g2},p_{g3},\dots ,p_{gD})$. Throughout the iterative process, each particle continuously updates its velocity and position, guided by the parameters $P_i$ and $P_g$. In the railway line environment scenario, nodes are linearly distributed, and the search space of particles is reduced to one dimension. The expressions during the algorithm iteration are shown in Equations (4) and (5).

$$v_{id}(t+1)=\omega v_{id}(t)+{\phi }_1{r}_1(p_{id}(t)-x_{id}(t))+{\phi }_2{r}_2(p_{gd}(t)-x_{id}(t))$$

(4)

$$x_{id}(t+1)=x_{id}(t)+v_{id}(t+1),1\le i\le K$$

(5)

In Equation (4) and Equation (5), ${\phi }_1$ and ${\phi }_2$ are, respectively, the cognitive learning factor and the social learning factor, and $\omega$ is the inertia weight, $r_1, r_2\in (0,1)$.

3.2. Energy-Balanced Non-Uniform Clustering

Due to the distinctive linear topology of railway-deployed wireless sensor networks, the energy consumption of sensor nodes varies significantly depending on their geographical placement. In the proposed model, all ordinary nodes are homogeneous and static, possessing identical and non-replenishable initial energy. The sink node is fixed at one end of the network and is not subject to energy constraints. Sensor nodes are capable of autonomously adjusting their transmission power to improve efficiency, and all data packets are of a fixed size.

The cluster farthest from the sink exhibits the highest total energy consumption. This total includes the energy expended by member nodes to transmit sensed data to the CH, as well as the energy consumed by the CH for receiving, aggregating, and relaying the data. Specifically, the CH first receives and fuses the data, then forwards the aggregated result to the next hop. According to the energy model, the energy consumed by member nodes for data collection and transmission to the CH is expressed by Equation (6).

$$E_{TX-CH}=k{E}_{elec}+k{\epsilon }_{mp}{d}^4$$

(6)

The energy expenditure for data reception at the CH is defined by Equation (7).

$$E_{RX-CH}=k{E}_{elec}$$

(7)

The energy expenditure for a CH to relay the fused data is formulated as Equation (8).

$$E_{TX-CHi}=k{E}_{elec}+k{\epsilon }_{mp}{d}_i^4+E_{DK}(k),i=1,2,3,\dots ,n-1$$

(8)

In Equation (8), $d_i$ represents the distance from the i-th CH node to the (i-1)-th CH node within the network.

The total energy consumption within the farthest cluster is thus formulated as Equation (9).

$$E_n=3k{E}_{elec}+2k{\epsilon }_{mp}{d}_i^4+E_{DK}(k),i=1,2,3,\dots ,n-1$$

(9)

Addition to their own intra-cluster energy costs, non-farthest clusters must also forward data packets from preceding clusters. This additional relay responsibility means that a CH’s energy consumption is inversely proportional to its distance from the Sink, leading to a progressive increase for closer nodes. This total consumption is quantified by Equation (10).

$$E_i=3k{E}_{elec}+2k{\epsilon }_{mp}{d}_i^4+(n-i)(2k{E}_{elec}+k{\epsilon }_{mp}{d}_i^4+E_{DK}(k)),i=1,2,3,\dots ,n-1$$

(10)

A mathematical analysis of intra-cluster and inter-cluster energy consumption proves that the optimal configuration for minimizing total network energy consumption is an equal-spacing clustering strategy—where all clusters are dimensioned equally.

Using the energy model from Equation (1), the total energy consumption for inter-cluster data transmission is given by Equation (11).

$$E_n={\displaystyle \sum _{i=1}^{m}E(k,d)=(2n-1)}k{E}_{elec}+n{E}_{DK}+k{\epsilon }_{mp}{\displaystyle \sum _{i=1}^n{d}_i^4},{\displaystyle \sum _{i=1}^n{d}_i}\ge D$$

(11)

Theorem: Under constraint ${\displaystyle \sum _{i=1}^m{x}_i}\ge D$, the multivariate function $f(x_i)=x_1^m+x_2^m+x_3^m+\dots +x_i^m$, $m\ge 2$ (with $x_i$ as the independent variable) achieves a minimum value if and only if $x_1=x_2=x_3=\dots =x_i$. We adopt the Lagrange multiplier method to solve this constrained optimization problem for the multivariate function.

The theorem demonstrates that the total energy consumption $E_n$, given by Equation (11), achieves its minimum value under the condition that $d_1=d_2=d_3=\dots =d_n=D/n$. This condition is fulfilled when all sub-clusters have equal dimensions. By solving the derivative of Equation (11) set to zero, we obtain the optimal inter-cluster distance specified in Equation (12).

$$d_{ibest}={\displaystyle \frac{D}{n}}=\sqrt[4]{{\displaystyle \frac{2E_{elec}}{3{\epsilon }_{mp}}}}$$

(12)

A necessary condition for achieving a uniform average energy consumption rate among nodes is that the ratio of intra-cluster energy to the total node count remains as equal as possible, mathematically given by Equation (13).

$${\displaystyle \frac{E_i}{N_i}}={\displaystyle \frac{E_n}{N_n}}$$

(13)

In Equation (13), $N_i$, $N_n$ and $E_i$ are defined as the total number of nodes in the i-th cluster, the total number of nodes in the network, and the total energy consumption of nodes within the i-th cluster, respectively.

According to Equations (9), (11) and (13), consequently, the functional relationship between the number of nodes in the i-th cluster and the outermost cluster is mathematically expressed as Equation (14).

$$N_i={\displaystyle \frac{E_i}{E_n}}\cdot N_n=\left[1+{\displaystyle \frac{(2n-2i)E_{elec}+(n-i){\epsilon }_{mp}{d}_i^4}{3E_{elec}+2{\epsilon }_{mp}{d}_i^4}}\right]\times N_n$$

(14)

Using Equations (12) through (14), we obtain the total number of nodes for both the farthest cluster and the i-th cluster, yielding Equations (15) and (16), respectively.

$$N_n=\left[{\displaystyle \frac{13}{4n^2+9n}}\right]N$$

(15)

$$N_i=\left[{\displaystyle \frac{13+8(n-i)}{4n^2+9n}}\right]N$$

(16)

As shown in Figure 1, the closer to the convergence node the area is, the more sensor nodes are inside it. According to the node deployment strategy proposed above, the specific deployment form is to cover the nodes in the two sides and the middle of the track in an isosceles triangle coverage mode, forming multiple coverages, as shown in Figure 2. The schematic in Figure 2 uses individual blocks to represent distinct clustering intervals. The distance for each interval is derived from Equation (12), considering the specific scale of the network. Uniform nodal energy consumption can be achieved by deploying sensor nodes with unequal density in different clustering intervals. The design of this node deployment model is presented in Figure 3.

To accommodate the deployment constraints inherent in the linear topology of railway environments—where nodes must be positioned at predetermined sampling points along the track centerline and sides—this paper proposes an overlapping node coverage model (Figure 3). This model enhances system redundancy and robustness by deploying multiple nodes at each sensing point within a cluster. The total number of nodes per sub-cluster is determined by Equation (16) and can be adaptively adjusted in response to network load variations.

Under normal network operation, only one sensing node remains active, while the other overlapping sensing nodes are maintained in a dormant state. When the active node depletes its energy, one of the overlapping nodes is randomly activated. This process continues until all nodes within the coverage area cease to function. To accommodate spatial variations in sensing demand, a higher density of sensor nodes is deployed in clusters closer to the sink node, with a corresponding reduction in density for clusters farther away. The total number of nodes scales proportionally with the network size.

3.3. PSO-Optimized Cluster Head Election

This paper introduces a PSO-optimized clustering routing protocol to enhance energy efficiency and operational coordination in WSNs. The improvement addresses the traditional PSO’s susceptibility to local optima due to random particle selection by initializing the swarm with high residual-energy nodes. This optimized PSO is then applied to the CH election phase of the LEACH protocol. In LEACH, a node is elected as CH if a random number it generates falls below a threshold $T(n)$, given by Equation (17).

$$T(n)=\left\{\begin{array}{l}{\displaystyle \frac{p}{1-p(r\mathrm{mod}1/p)}} \hspace{1em}n\in G\\ 0\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em} n\notin G\end{array}\right.$$

(17)

In Equation (17), p represents the suggested percentage of expected CHs per round; r denotes the current round; mod indicates the modulo operation; rmod1/p is the number of nodes that have been elected as CHs in this round of the cycle, while G defined as the set of nodes that did not serve as cluster heads in the previous round.

The conventional LEACH protocol exhibits uneven nodal energy consumption in its CH election, resulting in most nodes retaining about 90% of their energy when the network expires, underscoring the critical need for optimizing the CH selection process.

In the improved scheme, PSO replaces this random process by optimizing the search for the CH node set. Each particle represents a CH combination scheme, thereby aiming to reduce overall network energy consumption, enhance energy balance, and boost the node survival rate.

The functioning CH bears the responsibility for intra-cluster and inter-cluster communication, resulting in a disproportionately high energy consumption relative to the cluster’s sensor nodes. The real CH is dynamically rotated to balance intra-cluster energy consumption, with the selection determined by the node’s residual energy as well as its distance to the base station. Within the validity period of each cluster, the real CH in the first round should be the sensor node closest to the base station, and in other rounds, it is selected through distributed calculation of the rotation function value of the sensor nodes. The rotation function is shown in Equation (18).

$$F_{net}(i)=\alpha F_{en}(i)+\beta F_{dis}(i)$$

(18)

In Equation (18), $\alpha$ represents the energy consumption coefficient, $\alpha \in (0,1)$, $\beta$ the distance coefficient, and $\beta \in (0,1)$, $\alpha +\beta =1$. Energy is the most significant challenge faced by sensor nodes [40]. The more residual energy a candidate sensor node has, the larger the value of its energy rotation function should be, as shown in Equation (19).

$$F_{en}(i)=E_{res}(i)/{\overline{E}}_{res}(i)$$

(19)

In Equation (19), $E_{res}(i)$ represents the remaining energy of sensor node i, and ${\overline{E}}_{res}(i)$ represents the average remaining energy of the cluster where sensor node i is located.

The distance factor is an important determinant of the wireless channel of sensor nodes [41]. The closer a candidate sensor node is to the base station, the larger the value of the corresponding distance rotation function should be. The distance rotation function to the base station is shown in Equation (20).

$$F_{dis}(i)={\overline{d}}_i(i)/d_i(i)$$

(20)

In Equation (19), $d_i(i)$ represents the distance between sensor node i and the Sink node, and ${\overline{d}}_i(i)$ the mean distance between the cluster containing node i and the Sink node.

As the disparity in nodal energy consumption widens over successive network cycles, the influence of the energy factor is progressively amplified, underscoring the need for adaptive weighting coefficients in the optimal CH selection process. This dynamic weight adjustment is formulated as Equation (21).

$$\alpha ={\displaystyle \frac{E_{\max }-E_{\min }}{E_{res}(i)}}$$

(21)

In Equation (21), $E_{\max }$ and $E_{\min }$ are defined as the maximum and minimum residual energy, respectively, within the set of surviving nodes located in the same cluster as sensor node i in the current round. $E_{res}(i)$ is defined as the aggregate residual energy of the cluster containing sensor node i in the current round.

Dynamically adjusting the weight coefficient using Equation (21) offers a significant benefit: it progressively amplifies the impact of residual energy on CH selection as the network operates, thereby mitigating the risk of a shortened network lifespan due to unbalanced node energy consumption.

After the initialization step, we calculate the particle fitness values based on Equation (18). During the iteration, particle positions are first updated via Equation (4). The corresponding velocities for the next iteration are then calculated using Equation (5). The particle possessing the minimum fitness value is identified as the optimal solution, thereby defining the final CH set from its candidate nodes.

Therefore, the updated threshold $T(n)$ is as shown in Equation (22).

$$T(n)=\left\{\begin{array}{l}{\displaystyle \frac{p{F}_{net}(i)}{1-p(r\mathrm{mod}1/p)}}\hspace{1em} n\in G\\ 0\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em} n\notin G\end{array}\right.$$

(22)

During the iterative calculation, the inertia weight $\omega$ in Equation (23) can adjust the search capability of this round based on the speed of the previous round. Parameter $\omega$ tunes the search focus: larger values emphasize global exploration, while smaller values emphasize local intensification. Addressing the tendency of the PSO algorithm to converge to local optima, a linearly decreasing inertia weight strategy [42] is implemented to dynamically tune $\omega$, which leads to a more balanced CH node distribution.

$$\omega =\left\{\begin{array}{l}{\omega }_{\min }+{\displaystyle \frac{({\omega }_{\max }-{\omega }_{\min })(f_i-f_{\min })}{f_{avg}-f_{\min }}}\cdot {\displaystyle \frac{{\overline{E}}_{res}(i)}{E_{res}(i)}}\hspace{1em}\hspace{1em}{f}_i\le f_{avg}\\ {\omega }_{\max }\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em} f_i>f_{avg}\end{array}\right.$$

(23)

In Equation (23), ${\omega }_{\min }$ and ${\omega }_{\max }$ represent the minimum and maximum inertia weights, respectively, while $f_{\min }$ and $f_{avg}$ are the minimum and average fitness values of the current round of the candidate CH of sensor node i. When the fitness value of the candidate CH at the initial moment has a large difference from the global optimal particle fitness $f_i$, the obtained $\omega$ is larger; conversely, when the candidate CH tends to be optimal, the speed at which $\omega$ approaches the global optimum decreases to conduct a fine search.

The search space is relatively small and the target function converges quickly. Parameter $c_1$ determines the intensity of the particles’ autonomous exploration, while $c_2$ determines the convergence speed of the group. If $c_1$ is too large, the particles will fluctuate greatly, converge slowly, and increase energy consumption. If $c_2$ is too large, the particles may prematurely gather around a few high-energy nodes, leading to concentrated energy consumption. Therefore, $c_1$ and $c_2$ need to be dynamically adjusted to make the search process adapt to energy changes and convergence stages. Through energy-aware dynamic adjustment, PSO can adaptively balance the exploration, convergence, and energy utilization processes at different stages, thereby significantly improving the energy efficiency and robustness of clustering and routing. The dynamic adjustment of $c_1$ and $c_2$ is shown in Equations (24) and (25).

$${\phi }_1=\left\{\begin{array}{l}{\phi }_{\min }^1+({\phi }_{\max }^1-{\phi }_{\min }^1)\cdot {\displaystyle \frac{{\overline{E}}_{res}(i)}{E_{res}(i)}}\hspace{1em}\hspace{1em}{f}_i\le f_{avg}\\ {\phi }_{\max }^1\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}{f}_i>f_{avg}\end{array}\right.$$

(24)

$${\phi }_2=\left\{\begin{array}{l}{\phi }_{\min }^2+({\phi }_{\max }^2-{\phi }_{\min }^2)\cdot {\displaystyle \frac{{\overline{E}}_{res}(i)}{E_{res}(i)}}\hspace{1em}\hspace{1em}{f}_i\le f_{avg}\\ {\phi }_{\max }^2\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}\hspace{1em}{f}_i>f_{avg}\end{array}\right.$$

(25)

In Equations (24) and (25), ${\phi }_{\min }^1$, ${\phi }_{\max }^1$, ${\phi }_{\min }^2$, and ${\phi }_{\max }^2$ respectively represent the minimum and maximum values of the cognitive learning factor ${\phi }_1$ and the social learning factor ${\phi }_2$.

3.4. Dispatch Improvement

Once the cluster head election is finalized, the network enters the communication stage. This stage is categorized into intra-cluster and inter-cluster communication. The intra-cluster communication is structured using a Time Division Multiple Access (TDMA) framework. The PSO controls the time slot allocation and the time slot length of the sensor node i within the cluster by outputting the reference parameters ${\mathit{\lambda }}_1$ and ${\mathit{\lambda }}_2$. The intra-cluster communication period is shown in Equation (26).

$$T_{frame}={\displaystyle \sum _{i=1}^{N_i}{s}_i}+(N_i-1)T_g$$

(26)

In Equation (26), $T_g$ represents the anti-collision guard interval, which is used to prevent time slot overlap caused by clock drift and signal propagation delay between nodes. The system reserves a segment of $T_g$ for adjacent nodes in each TDMA frame, and its value is adaptively set according to the network synchronization accuracy and the basic time slot length as shown in Equation (27); $s_i$ is the transmission time slot length of the i-th node within the cluster, as shown in Equation (28).

$$T_g=\eta \cdot s_{base},\eta \in [0.05,0.15]$$

(27)

In Equation (28), $\eta$ is the proportionality coefficient.

$$s_i=s_{base}\cdot {({\displaystyle \frac{V_i}{{\overline{V}}_c}})}^{{\lambda }_1}\cdot {({\displaystyle \frac{E_{res}}{{\overline{E}}_{res}}})}^{-{\lambda }_2}$$

(28)

In Equation (28), $V_i$ represents the data volume of sensor node i within the cluster; ${\overline{V}}_c$ is the cluster average; $s_{base}$ is the base time slot length, which is used to control the time granularity of TDMA scheduling within the cluster. At the beginning of each round, the system determines $s_{base}$ based on the load $V_i$ and energy state $E_{res}$ of each node in the network. Then, it adjusts the time slot length $s_i$ of each node by weighting based on this as a reference to achieve energy-balanced and load-adaptive time slot allocation. ${\lambda }_1$ and ${\lambda }_2$ are proportionality factors, which are dynamically adjusted through PSO to balance data priority and energy protection.

The CH broadcasts its own cost to the network. Each CH receives and retains only the broadcast from the CH with the lowest cost that is less than its own cost. If there is a broadcast message left on the built-in memory of the CH, the data within the cluster is sent to this relay CH; otherwise, the data within the cluster is sent to the base station.

4. Experimental Simulation and Analysis

The simulation setup consisted of an LWSN with nodes deployed along a railway line. The proposed energy-balanced non-uniform deployment model was validated using MATLAB2022b. To evaluate the performance of the LEACH-PSOI algorithm, we compared it with three benchmark protocols—LEACH, LEACH-C, and LEACH-PSO—across three key metrics: network lifetime, network throughput, and energy-consumption efficiency. This comparative analysis demonstrates the superiority of the proposed LEACH-PSOI algorithm.

4.1. Simulation Parameter Settings

The energy-balanced non-uniform node deployment model was evaluated through simulation experiments. The simulation parameters were configured as detailed in

Table 1. Simulation Parameters.

Parameter Symbol	Parameter Description	Value Assignment
$E_0$	Initial energy	$0.5 \mathrm{J}$
$E_{elec}$	data	$50 \mathrm{n}\mathrm{J}\cdot \mathrm{b}\mathrm{i}{\mathrm{t}}^{-1}$
${\epsilon }_{fs}$	Unit energy consumption	$10 \mathrm{p}\mathrm{J}\cdot {(\mathrm{b}\mathrm{i}\mathrm{t}\cdot {\mathrm{m}}^2)}^{-1}$
${\epsilon }_{mp}$	Power consumption coefficient	$0.0013 \mathrm{p}\mathrm{J}\cdot {(\mathrm{b}\mathrm{i}\mathrm{t}\cdot {\mathrm{m}}^4)}^{-1}$
l	Packet size	1024
$d_0$	Communication distance threshold	87 m
D	Length of railway track	180 m
N	Total nodes	300
$\omega$	Inertial weight	0.4~0.9
${\phi }_1$	Cognitive parameters	1.5~2.0
${\phi }_2$	Social parameters	1.8~2.2
$p_{size}$	Particle swarm size	30
$T_{\max }$	Maximum number of iterations	50
p	Expected proportion of cluster heads	0.05
r	Number of running rounds	2000

. To simplify the analysis, the energy cost associated with information sensing was neglected; only the energy consumption related to communication was considered. A working cycle was defined as the end-to-end process from data acquisition by a sensing node to its final relay to the sink node via the CH. Network lifespan was measured by counting the number of such cycles until the first node failed due to energy exhaustion.

4.2. Network Lifespan

The number of surviving nodes is defined as the quantity of sensor nodes with residual energy greater than zero at the end of each round. Figure 4 compares the proposed LEACH-PSOI protocol with LEACH, LEACH-C, and LEACH-PSO, illustrating the variation in surviving nodes as the number of network operation rounds increases.

Each simulation curve represents the average of 30 independent runs. As shown in Figure 4 for a 300-node network, network failure begins around the 184th, 212th, and 322nd operational rounds for the LEACH, LEACH-C, and LEACH-PSO protocols, respectively. In contrast, the LEACH-PSOI protocol exhibits a substantially longer operational lifetime, with network failure commencing only around the 679th round. Figure 4 further illustrates the relationship between the number of surviving nodes and the elapsed operational rounds. Node death first occurs around the 1466th, 1567th, and 1610th rounds for the LEACH, LEACH-C, and LEACH-PSO protocols, respectively, whereas the LEACH-PSOI protocol delays the onset of node death until approximately the 1976th round. Thus, the proposed protocol extends the network lifetime by 25.8%, 20.2%, and 18.5% compared to the three baseline protocols.

The LEACH protocol is limited to the clustering phase and lacks a relay mechanism, resulting in two principal shortcomings. First, the highly localized randomness in its CH rotation leads to an uneven distribution of network load and energy consumption. Second, the absence of relay transmission forces CHs to transmit data over long distances, incurring substantial energy costs and consequently delivering the poorest performance among the evaluated protocols. To address these inefficiencies and minimize unnecessary energy expenditure, the proposed LEACH-PSOI protocol refines the clustering procedure and establishes a stable operational phase. During this phase, a dynamic CH rotation scheme is implemented, which employs a composite function based on residual energy and distance to the base station. This strategy enhances the balance of network load and energy usage, thereby extending network lifetime and maintaining sustained service quality.

The proposed LEACH-PSOI protocol consistently outperforms other protocols in all evaluation metrics, as shown in

Table 2. Comparison of FND, HND and AND.

Routing	FND	HND	AND
LEACH	184	799	1466
LEACH-C	212	816	1577
LEACH-PSO	322	853	1610
LEACH-PSOI	679	1235	1976

. It significantly delays the First Node Death (FND) round by 72.9%, 68.8%, and 52.6%, and correspondingly extends the effective network lifespan, measured by the Half Node Death (HND) round, by 35.3%, 33.9%, and 30.9%, compared to the three baseline protocols. The experimental outcomes provide strong evidence for the protocol’s exceptional performance in network lifetime extension, stability improvement, and energy consumption balancing.

4.3. Network Throughput

Throughput is defined as the total amount of data (in bits) successfully transmitted by all nodes to the base station (sink) within each round. Figure 5 presents a comparative analysis of network throughput across operation rounds for the four protocols. The results show that network throughput increases steadily over time for all protocols, each reaching its respective maximum during normal network operation and peaking in the middle to later stages of the network lifecycle. The LEACH-PSOI protocol achieves relatively higher throughput, exceeding that of the LEACH, LEACH-C, and LEACH-PSO protocols by 15.8%, 11.1%, and 10.0%, respectively. Moreover, as the network scales, the throughput advantage of LEACH-PSOI becomes more pronounced. Each simulation curve represents the average of 30 independent runs.

4.4. Energy Consumption Efficiency

Figure 6 illustrates the relationship between the total network energy consumption and the number of operation rounds for the four protocols. In a network comprising 300 nodes, the LEACH, LEACH-C, and LEACH-PSO protocols deplete all node energy at approximately 1151, 1277, and 1335 rounds, respectively. In contrast, the LEACH-PSOI protocol sustains network operation beyond 1500 rounds, outperforming the other three protocols by 33.7%, 26.4%, and 23.1%, respectively, in terms of network lifetime.

Each simulation curve corresponds to the average of 30 independent simulation runs. Figure 6 plots the remaining network energy against the number of operation rounds for the four protocols. Analysis of the data indicates that LEACH exhibits the lowest energy consumption efficiency, followed by LEACH-C and LEACH-PSO, whereas LEACH-PSOI achieves the highest efficiency, confirming its superior energy utilization performance.

5. Conclusions

To address the practical demands of chain-structured monitoring scenarios such as ARTFMR along railway lines, this study proposes a PSO-based clustering routing algorithm for LWSNs. Through non-uniform node deployment, the algorithm constructs clusters and enhances the conventional PSO method. By comprehensively considering node energy consumption and distance factors, it optimizes the formation of non-uniform clusters. In the communication phase, the algorithm introduces a time-division multiple access (TDMA)- based inter-cluster multi-hop path-scheduling mechanism, coupled with a joint data-volume and energy optimization strategy, to effectively mitigate the “energy hole” problem. Experimental results demonstrate that the LEACH-PSOI protocol outperforms benchmark protocols, including LEACH, LEACH-C, and LEACH-PSO in terms of network lifetime, throughput, and energy efficiency. The proposed protocol effectively balances energy-consumption distribution across the network, extends operational duration, and improves energy-utilization efficiency.

Future research may further optimize the topological structure of the algorithm using reinforcement learning methods to accelerate convergence during the clustering stage and reduce routing overhead. Additionally, although the effectiveness of the proposed improvements has been validated through comparisons with the LEACH series in this study, an important direction for future work involves systematically evaluating LEACH-PSOI against more advanced protocols designed for LWSN or energy-efficient WSNs—such as those based on non-uniform clustering, hybrid heuristics, or deep reinforcement learning—within a unified simulation platform and on real-hardware testbeds. Such comparative analysis will more comprehensively elucidate the performance advantages and limitations of the proposed protocol under various network conditions and facilitate its adoption in practical railway monitoring systems.