A Nature-Inspired Hybrid Approach for Energy-Efficient Lifetime Extension in Wireless Sensor Networks

The current work aims to enhance the lifespan of WSNs by combining techniques such as evolutionary algorithms, particle swarm optimization (PSO) and GA. Because energy consumption is proportional to data transmission frequency, the collection of repeated data reduces energy consumption [24-30]. Make effective use of the power usage of sensor nodes to overcome this drawback. Since sensors are non-rechargeable battery-based, they consume energy for three main reasons: path finding, data processing and communications. Recently, many efficient algorithms have been created for path planning. The general algorithmic adaptability of meta-heuristic algorithms to various optimization problems is noteworthy. Existing algorithms may exhibit lower performance than meta-heuristic algorithms in solving complex optimization problems due to their limited ability to adapt to diverse problem characteristics. To solve the above-mentioned issues with awareness, we used meta-heuristic algorithms like PSO, grey wolf optimization (GWO), bat algorithm (BA), etc. Therefore, it has been imperative to work over the past year to develop a path-planning routing system. In this paper, we propose a hybrid meta-heuristic algorithm to improve the drawbacks faced by sensor nodes. The goal of hybridization is to reduce any significant drawbacks while simultaneously combining the benefits of each algorithm to create a hybrid algorithm. Hybridization generally yields results that can be improved in terms of accuracy or computational speed. The initial energy for each sensor is the same for all nodes. The features of each routing protocol include path-finding, reliability, scalability, etc.

The proposed method divides the network into three types of sensor nodes, assigning specific roles for sensing, data transmission, processing, and reception. This division distributes the workload among different nodes, reduces the burden on individual sensors, and improves energy efficiency and network lifetime. Otherwise, the nodes will die prematurely. Here, we propose three types of sensors: 1. Tx/Rx sensor; 2. normal sensor; 3. aggregate sensor. The path-finding is done using a natural method called bat-finding prey. The BA finds the best route to reach the nearby base stations. To further enhance the energy of each sensor node, consider the following example: sensor s1 transmits the data along the path [s2, s6, s9] to reach the base station, and again, if sensor s1 wants to transmit the data, then the data will travel in the same direction as [s2, s6, s9]. By doing so, the energy will drain soon. Therefore, to balance the issue, we need to find out the number of iterations of data transmission. Based on the analysis, the computation of iterations is done by the ant colony algorithm. The iterations are calculated using an artificial pheromone deposited in the regular path. In Step 4, when the number of iterations exceeds the threshold value, the data is divided equally and transmitted in two directions.

2.1 Water flow algorithm

The suggested algorithm starts with fundamental processes such as a strong water flow striking a mud surface, water splitting, merging, and finally settling down when the water flow is decreased. The natural evolution rule serves as the foundation for evolutionary algorithms. The pressure is estimated from one spot to another. The water travels through small particles like stones and mud, but once it crosses a number of iterations, the path is cleared to reach the destination in a short period. While the current topology does not support scalability or network restoration, the water flow method aids in the creation of the artificial topology network. Using the pressure flow formula, a node will be created in each iteration of the water flow to move the water from one side to the other. Here, water flow is thought of as an iteration; it covers a certain area as it moves from high to low space. In the combat field application, a dynamic network link is crucial for extending the network's lifespan. The topology creation and node elevations are displayed in Figures 2 and 3, respectively.

In the algorithm, V is the sensor-node set; E is the edge set; G is the graph; θ is the WFA parameter set; connected is a Boolean connectivity flag; r is the repair-attempt counter; and R_max is the maximum number of repair attempts. Function names and Boolean keywords are upright text; mathematical variables are italicized in the manuscript typesetting.

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Figure 2. Nodes with elevations

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Figure 3. Mathematical design and network link generation based on the water flow algorithm (WFA) topology

The starting flow is initialized with the basic parameters: iteration limit N, initial mass M, velocity Y and the limit of sub-flow, as Table 1 describes the mapping of WFA variables to WSNs.

Table 1. Mapping of water flow algorithm (WFA) variables to wireless sensor networks (WSNs) topology parameters

Assume N is the number of water flows in the pipe in the current iteration; it is assigned as i = {1, 2, 3, …, N}.

$n=\min \left\{\max \left\{1, \operatorname{int}\left(\frac{M_i Y_i}{T}\right)\right\}\right\}$       (1)

where, T is the time.

$Y_2=\sqrt{\frac{2\left(l_2-l_1\right)}{\rho}+Y_1^2+2 g\left(h_2-h_1\right)}$       (2)

where, l₂, l₁ are the pressures at points 1 and 2; g is gravity; h₂, h₁ are the heights at points 1 and 2; and ρ is fluid density.

$Y_i=\sqrt{Y_i^2+\frac{2 g h}{A}}$       (3)

Formula to calculate the coverage area of water as:

$r=\frac{A_{\text {pipe}} \times Y^2}{g}$       (4)

where, A is the cross-sectional area of the pipe, g is acceleration, and Y is velocity.

2.2 Bat algorithm

The node separation process is completed by meta-heuristic algorithms and they will guide the search process by nature and are used as one of the important techniques to solve many composite optimization problems. Among many nature-inspired algorithms, the BA is one of the algorithms introduced by Yang [31]. Because microbats are small to medium-sized bats that feed on insects, the BA is based on the echolocation behavior of microbats. It uses sonar, called echolocation, to detect prey. For example, if one microbat produces a high-pitched sound and it bounces back, it can determine the distance to prey and also the size. So the distance is measured using the following parameters: frequency, pulse rate, loudness, and position of each bat. The expression to calculate all the parameters is given below:

Step 1:

$p_i=p_{\text {min}}+\left(p_{\text {max}}-p_{\text {min}}\right)$       (5)

where, p_i is the bat frequency value, pmax is the maximum frequency, and pmin is the minimum frequency. The bat will automatically adjust the frequency and frequency value depending on the size of the area.

Step 2:

$y_i^t=y_i^{t-1}\left(y_i^t-x_{\text {gbest}}^t\right) y_i$        (6)

Step 3:

$z_i^t=z_i^{t-1}+y_i^t$       (7)

where, $y_i^t$, $z_i^t$ velocity and location of the i-th bat at the period of time t.

Step 4:

$l_i^{t+1}=\alpha l_i^t$        (8)

Step 5:

$r_i^t=r_i^0\left[1-e^{-\gamma t}\right]$        (9)

where, $l_i^{t+1}$, $r_i^t$ denotes loudness and the pulse rate at the time.

2.3 Enhanced bat algorithm

An artificial bat moving in a certain direction finds the optimum answer; nevertheless, the bat's speed has a significant impact on the algorithm's accuracy and rate of convergence. Here, we are going to combine local and global search; initially, by having a higher speed, we can find the optimal solution, and at a lower speed, we can find the local solution. Based on the above analysis, the equation has been refined to solve an early problem that occurred in the basic algorithm.

Step 1

The velocity update formula:

$y_i^t=s y_i^{t-1}+\left(\left|x_i-x_j\right|+\left|y_i-y_j\right|-x_{\text {gbest}}^t\right) y_i$        (10)

By selecting the optimal sound from among the other artificial bats, the updated formula for determining the ideal position is furthered. The random walk probability distribution function is the optimal position that was determined with the use of the Levy Fly method. By substituting the Levy flight for local searching for a single bat's ideal position, the global search process is able to produce more matching and optimization iterations, which enhances both the algorithm's convergence and accuracy. Comparative evaluation of the improved BA against baseline algorithms is illustrated in Table 2, while Figure 4 presents the corresponding convergence comparison between the standard BA and the improved BA over iterations.

Table 2. Comparative evaluation for improved bat algorithm (BA)

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Step 2

Position update equation:

$\mu=L_b+(1-c f)\left(\frac{L_b}{U_b}\right)+\left(1-\frac{\operatorname{Min}_{\text {iter}}}{\operatorname{Max}_{\text {iter}}}\right)$       (11)

$z^{i+t}=z^t \bigotimes l(\mu)$        (12)

where, L_b and U_b represent the lower bound and upper bound of frequency, and cf denotes a constant factor.

2.4 Fitness function

The proposed work requires the shortest path to reach the base station, so here the objective function is considered as distance. In this work, an artificial topology network is assigned, which further helps to search for a local optimum. The random value (rv) is initialized to a large value. By allowing the bats to move at random, it improves the algorithm's capacity for exploration and enables it to more fully explore the search space. When the iterative process comes to a conclusion, the value of w_i drops, which narrows the search region surrounding the optimal solution and improves the algorithm's exploitation potential. The distance is calculated using the following formula;

$d_k=r+\frac{U b-L b}{n} * r v$        (13)

Fitness function $=\sum_{k=1}^3 \frac{d_k}{3}$        (14)

where, r is the radius of the network, n is the number of waves and rv is the random vector.

When d_k is divided by 3, we can find the nearest artificial bat value. Using the above equation, we need to select the Tx/Rx among the deployed sensors and sensor nodes located at shorter distances are selected as Tx/Rx nodes, while nodes located farther away from the Tx/Rx nodes are designated as aggregator nodes based on the predefined distance criteria. Usually, a WSN is considered a group of sensor nodes. The nodes are deployed randomly. Consider a WSN with n nodes (where i = 1, 2, 3, …, n). Among these nodes, a set of Tx/Rx nodes is selected based on Eq. (1) and is responsible for data transmission. When choosing Tx/Rx, factors such as energy and node distance among the nodes are also taken into account. By considering the net optimal solution, we assume it is an aggregator node, and the rest of the nodes are considered normal nodes.

There is a requirement for data processing techniques or methodologies because the sensed data must be processed effectively to increase network performance. Hence, transmitting a larger amount of data to the base station requires more energy. Eliminating duplicate data is an aggregation technique used in WSNs that helps them use less energy. The aggregator sensor collects the data from a nearby node, aggregates the data by removing the replicated data, and finally transmits unique data to the Tx/Rx node. Every aggregation point compresses redundant data. When multiple packets are merged into a single packet using data loss aggregation, the quantity of data that is sent out is often less than what was received. When energy conservation is required and the communication load is beyond the system's capacity, this method can be helpful. When a sensor node receives duplicate copies of the same data, it has two options for processing the information: it can treat the data as duplicate and process each copy separately, or it can treat the data as one copy. The way these two functions vary is because aggregation only yields a single representative value—such as MIN, MAX, or MEDIAN—out of all the values in the dataset.

Steps for data aggregation:

Step 1: Collecting data from nearby sensors.

Step 2: Removing redundant data and sending only useful information to the Tx/Rx sensor.

Step 3: Calculating the amount of data transmitted.

The Tx/Rx sensor will collect all the data from the aggregator sensor and transmit it to the next Tx/Rx sensor.

$E_{t x}=k E_{\text {elec}}+E_{\text {amp}} d^2$        (15)

$E_{r x}=K E_{\text {elec}}$        (16)

where, E_elec represents the electronics energy, E_amp represents amplifier energy, k is bits and d is meters. Total energy consumed by this node E = E_tx + E_rx.

2.5 Calculation of route cost using ant colony

Following the conclusion of phase 1, nodes begin transmitting data from one Tx/Rx node to another. The travel cost between the nodes needs to be calculated for each iteration. The ant colony algorithm is used to compute the path cost. The ant finds the path based on semiochemicals, which are secreted by the ants themselves. The first ant starts travelling and will drop chemical substances on the ground; subsequently, another ant follows the same path. Consider the following example: The following list of ants (S1, S2, S3, S4, and S5) will find the food. Each ant goes in a different direction, and each lays a trail of pheromone where it goes. Using the meta-heuristic algorithm, each ant completes an iteration. The final ant chooses the path where it finds the highest pheromone levels. Figure 5 illustrates the overall architecture of the proposed work.

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Figure 5. Architecture diagram for the proposed work

Generally, if the sensor (S1) transmits the data using the same path again and again, then the particular set of sensors will lose their energy soon compared to other sensors. The measurement has been made using the pheromone intensity value. In the optimized BA and ant colony algorithm, path planning has been done, and here we need to initialize the artificial pheromone value for all the Tx and Rx nodes. The trail from the Tx/Rx node i to the next Tx/Rx node j is created by an artificial ant placed in each Tx/Rx. Once the transmission is completed, the level of pheromone is updated on both, depending on the formula:

$\Delta \mu_{i j}=\sum_{k=0}^n \Delta \mu_{i j}$        (17)

$\mu_{i j}=(1-\alpha) \mu_{i j}+\Delta \mu_{i j}$         (18)

The route cost is calculated in the given equation.

$C=d T_x / R_{x i}-T_x / R_{x j}+\Delta \mu_{i j}$        (19)

The overall fitness functions can be expressed as follows:

$\begin{gathered}F=w_1 \frac{E_{\text {cons}}}{E_{\max}}+w_2 \frac{D_{\text {path}}}{D_{\max}}+w_3-\frac{E_{\text {res}}}{E_{\text {init}}}+w_4 \frac{\text { Delay }}{\text { Delay}_{\text {max}}}+w_5 \frac{1}{\text { Lifetime}}\end{gathered}$        (20)

where, $E_{\text {cons}}=$ total energy consumption, $D_{\text {path}}=$ routing path distance, $E_{\text {res}}=$ residual energy, $E_{\text {init}}=$ initial energy, Delay = end-to-end delay, Lifetime = network lifetime, and $w_1 w_2 w_3 w_4 w_5$ = weighting coefficients.

2.6 Data decomposition

In this section, the sensor nodes divide the original data into separate shares that are placed into a sub-array using a Vandermonde matrix [32]. Subsequently, in order to improve the reliability of perceived data transmission in WSNs, the sensor networks are utilized to send these data shares appropriately to the source node and attempt to pre-process the perceived original data using a matrix decomposition algorithm. The information that was first interpreted is expanded upon and divided into many information exchanges.

Convert these Z1 bits to Z2 y-ary digits using the following equation: Z1 = Z2 · log₂y, where y represents the number of data elements.

Step 1: A = {a₁, a₂, ..., a_d} is the result of dividing A into d vectors. Each vector can be expressed as ad={a_d,1, a_d,2, …, a_d,m}, where m represents the number of y-ary digits contained in each subarray.

Step 2: Build an m × n y-ary Vandermonde matrix B using the set of indices b₁, b₂,..., and b_n.

Step 3: According to Steps 1 and 2, the total number of data will be divided into n subparts, each of which is represented as a y-ary sub-array t_k·t_d = [a_d,₁, a_d,₂, a_d,₃, …, a_d,_m], where t_k = [t_k,₁, t_k,₂, t_k,₃, …, t_k,_n] includes n q-ary digits, and the symbol “·” denotes the multiplication operator in the q-ary notational system.

The Vandermonde matrix decomposition is executed at the Tx/Rx, which possesses greater computational capability than individual sensor nodes. Therefore, the additional computational cost does not increase the energy consumption of ordinary sensor nodes. The primary effect is a reduction in communication overhead through smaller or less redundant transmissions.

Since the proposed water flow algorithm (WFA), Improved BA, and ant colony optimization (ACO) algorithms are stochastic in nature, each simulation scenario was executed 30 independent times using different random seeds. The reported results correspond to the mean and standard deviation of the obtained performance metrics.

mean $=\frac{1}{n} \sum_{i=0}^n x_i$        (21)

where, $x_i$ is the performance metric obtained in the i^th run; n is the total number of independent runs.

standard deviation $=\sqrt{\frac{1}{n-1} \sum_{i=1}^n\left(x_i- mean\right)^2}$        (22)

To account for the stochastic behavior of the proposed heuristic optimization framework, each simulation scenario was executed 30 independent times using different random seeds. Each simulation scenario was executed for a fixed set of network parameters, and the results reported in this study represent the performance obtained under these configurations for each corresponding network size.

2.7 Computational complexity analysis

Since the modules are executed sequentially, the overall complexity is:

$T_{\text {total}}=O\left(Q_w N+Q_b B N+Q_a A N+N\right)$        (23)

where, B represents the number of bat-algorithm agents or bats, A represents the number of ant-colony agents or ants, N the number of sensor nodes, $Q_w$ number of water flow iterations, $Q_b$ number of bat iterations, and $Q_a$ number of ant colony iterations. The simulation parameters used in this study are summarized in Table 3.

Table 3. Parameters used in MATLAB simulation