1. Introduction
With the continuous development of internet technology, artificial intelligence, and 5G technology, the Internet of Things has become a hot research topic in the current technology field. As one of the core supporting technologies of the Internet of Things, wireless sensor networks play a supporting role in the Internet of Things. Wireless sensor networks (WSNs) are networks in which multiple homogeneous sensor nodes are interconnected and communicate for information transmission [
1,
2]. They use wireless communication to complete the target monitoring and information transmission of the environment. WSNs are widely used in aviation [
3], environmental [
4], medical [
5], industrial [
6], and other fields due to their advantages of low cost, versatility and easy deployment. In recent years, the fields of smart transportation [
7], smart homes [
8], and smart cities [
9] have also achieved large-scale applications. However, the traditional random deployment method can lead to large-scale node coverage gaps and high-density overlapping coverage in the target area, which directly affects the detection quality of the target area and causes resource waste. Therefore, investigating ways to adaptively deploy sensor nodes in WSNs and make the distribution of sensor nodes more uniform and the coverage of nodes higher is of great significance for reducing the cost of constructing WSNs and improving the quality of network services.
In recent years, researchers have proposed many metaheuristic algorithms inspired by the behaviour of natural biological groups and the laws of physical phenomena. These algorithms are widely used in the node deployment optimization problem of WSNs because of their simple principles, few parameters, and easy implementation. The metaheuristic algorithms commonly used to solve WSN coverage problems include the bee algorithm (BA) [
10], whale optimization algorithm (WOA) [
11], particle swarm optimization (PSO) [
12], grey wolf optimization algorithm (GWO) [
13], black hole algorithm (BHA) [
14], butterfly optimization algorithm (BOA) [
15], genetic algorithm (GA) [
16], etc. In addition, to improve the coverage rate of WSNs, many scholars have proposed improved metaheuristic algorithms. Hu et al. proposed an improved grey wolf optimization algorithm (IGWO) to enhance the WSN coverage rate [
17]. Zhu et al. proposed a hybrid strategy weed algorithm (LRDE_IWO) to solve the problem of the dense and sparse distribution of nodes in the monitoring area [
18]. Wang et al. proposed a virtual force-Lévy-embedded grey wolf optimization (VFLGWO) algorithm to effectively solve uneven WSN coverage problems [
19]. He et al. optimized the deployment of WSN nodes by using the improved sine–cosine optimization algorithm, and the coverage rate was improved compared with the original sine–cosine algorithm [
20]. The above research shows that it is feasible to use a metaheuristic algorithm to optimize WSN node deployment, but the node coverage still needs to be improved.
The marine predator algorithm (MPA) is a new metaheuristic algorithm proposed by Faramarzi et al. in 2020 [
21]. The algorithm is inspired by the movement of marine predators and their prey, that is, marine predators search for food sources through Lévy motion or Brownian motion. The MPA has been successfully applied in many fields due to advantages such as its simple operation, few parameters to be adjusted, and strong stability. For example, Abd-Elaziz et al. applied the MPA to the multilevel image segmentation problem and obtained satisfactory segmentation results [
22]. Abdel-Baset et al. used the MPA to improve the parameter estimation of photovoltaic models [
23]. Eid et al. used the MPA to optimize active and reactive power resources in distribution networks, to minimize the total losses and total voltage deviations, and to improve the distribution system’s overall performance [
24]. However, few scholars have proposed an improved MPA to solve the WSN coverage optimization problem. Hence, this paper proposes an improved MPA to solve the WSN coverage optimization problem. The proposed algorithm uses the dynamic inertia weight adjustment strategy to balance the exploration and exploitation capabilities of the algorithm. In addition, the improved algorithm uses the multi-elite random leading strategy to enhance the information exchange rate between population individuals. In summary, the main contributions of this paper are as follows:
An improvement in the efficiency of a powerful metaheuristic method named MPA is investigated to solve the WSN coverage optimization problem.
An improved marine predator algorithm (IMPA), combined with a dynamic inertia weight adjustment strategy and multi-elite random leading strategy, is developed to improve the ability of the standard MPA to handle complex problems. The performance of the IMPA is evaluated on 11 benchmark test functions and part of the CEC2014 test functions.
The proposed IMPA is applied to solve the WSN coverage optimization problem. The results are compared with those of other metaheuristic algorithms and improved algorithms in the literature.
The remainder of the paper is organized as follows:
Section 2 describes the WSN coverage problem mathematically.
Section 3 describes the details of the proposed IMPA, along with the mathematical model and computational process.
Section 4 analyses the experimental results of the proposed IMPA.
Section 5 analyses the effectiveness and feasibility of the proposed IMPA in solving the WSN coverage problem. The conclusion of this work is provided in
Section 6.
2. WSN Coverage Model
Assume that WSN randomly deploys
N isomorphic sensor nodes on a two-dimensional plane sensing field with a size of
M =
×
, and each sensor node has the same sensing radius
and communication radius
. The wireless sensor node set is positioned as
L = {
,
, …,
}, and the coordinates of
are (
,
),
i∈{1, 2, …,
N}. To better calculate the node coverage, the two-dimensional plane
M is discretized into
m ×
n grid points to be covered, and the geometric center of the grid is the coverage target point
= (
,
),
j∈{1, 2, …,
m ×
n}. If the distance between grid point
and any node in the target area is less than or equal to the perception radius
, the grid point is considered to be completely covered by the WSN. The Euclidean distance between sensor node
and grid point
is as follows:
The probability that grid node
is covered by sensor node
is defined as:
where
is the perceptual error radius, and
λ is the perceptual attenuation coefficient.
In this area, any grid can be covered by multiple sensor nodes at the same time. The mathematical model of the joint coverage probability is as follows:
where
L is the set of all sensor nodes in the target area. The total coverage of the target area is defined as the ratio of the number of grids covered by the node set
L to the total number of grids in the area. Therefore, the mathematical model of coverage
is defined as:
Formula (4) shows that the WSN coverage optimization goal is to deploy a certain number of sensor nodes in a reasonable area to achieve the maximum . Therefore, this paper applies the proposed improved marine predator algorithm to obtain the optimal value of to improve the coverage of the WSN.
5. Coverage Optimization in Wireless Sensor Networks (WSNs)
To verify the feasibility and effectiveness of the proposed IMPA for WSN node coverage optimization, two experiments were performed. Experiment 1 compares the effect of the IMPA with EO, SCA and the original MPA. Experiment 2 compares the IMPA with the improved grey wolf optimization (IGWO) [
17], invasive weed algorithm (IWO) [
18], improved hybrid strategy weed algorithm (LRDE_IWO) [
18], Lévy-embedded grey wolf optimization (LGWO) [
19] and virtual force-Lévy-embedded grey wolf optimization (VFLGWO) [
19]. In the experiments, the parameters are set the same as in the literature [
17].
Assume that 40 sensor nodes are deployed in the sensing field of the target area
M = 50 × 50 m, the perceived radius
= 10 m, the communication radius
= 20 m, and the maximum number of iterations
= 500. The specific parameters are shown in
Table 8.
5.1. Comparison with Other Standard Metaheuristics
To verify the effectiveness of IMPA in solving the WSN coverage problem, the IMPA, EO algorithm, SCA and the original MPA are simulated. The experimental data are shown in
Table 9.
Figure 5 shows the node coverage graph of the proposed IMPA, random deployment, and optimization of each algorithm.
As seen from
Table 9, the coverage rate optimized by the IMPA reaches 93.72%. At the same time, the coverage rate of the IMPA is improved by 19.10%, 4.28%, 16.84%, and 4.91% compared with the random deployment, EO algorithm, SCA algorithm, and the original MPA, respectively. From
Figure 5a,c, the middle region optimized by random deployment and the SCA algorithm has a large range of coverage blank phenomena.
Figure 5b,d show that the upper left region optimized by the EO algorithm and the MPA has a serious overlap phenomenon. In
Figure 5e, the regional node coverage optimized by the IMPA is more uniform and less redundant, and the full coverage of the target area is approximately achieved, which effectively improves the random deployment node coverage vulnerability and the MPA-optimized node coverage aggregation defect.
To further explore the influence of the number of sensor nodes on the WSN-optimized node coverage, simulation experiments were carried out on different sensor nodes for each algorithm (random deployment, MPA and IMPA) in the target area. The number of isomorphic sensor nodes is set to 35, 40, 45, 50, and 55, and the other parameters are consistent with
Table 8. The variation trend of the coverage ratio of different algorithms with the number of nodes is shown in
Figure 6.
As shown in
Figure 6, the proposed algorithm is superior to the random deployment and the MPA in the coverage rate of wireless sensor network nodes with different numbers of nodes, and the IMPA almost approaches a 100% coverage rate when there are 55 nodes. This shows that the two strategies of the IMPA can effectively improve the probability of escaping from a local optimum and balance the ability of global exploration and local exploitation, thereby improving the effective coverage rate of the WSN nodes.
5.2. Comparison with the Latest Improved Algorithm
To highlight the competitiveness of the IMPA in solving the WSN coverage problem,
Table 10 depicts the comparison results of the IMPA with other algorithms in the literature, including IGWO [
17], IWO [
18], LRDE_IWO [
18], LGWO [
19], and VFTGWO [
19].
Table 10 shows that the coverage rate of the IMPA is slightly inferior to the LRDE_IWO algorithm. However, compared with other four algorithms, the IMPA still has an advantage. Therefore, the IMPA has certain practicability for improving the WSN coverage problem.
6. Conclusions
To effectively improve the node deployment coverage rate of wireless sensor networks, an improved marine predator algorithm, termed IMPA, was proposed. It combines a dynamic inertia weight adjustment strategy and a multi-elite random leading strategy to better improve the coverage rate of WSNs in monitoring areas and the reduction of resource waste. Eleven benchmark functions with different features and partial CEC2014 test functions were tested and compared with existing metaheuristics and improved algorithms. The experimental results demonstrated that the IMPA had better stability and optimization performance than other algorithms. Finally, the IMPA was applied to a WSN coverage optimization problem. The simulation results showed that the IMPA coverage was higher than that of IGWO, IWO, LGWO, VFTGWO, and other metaheuristic algorithms.
In future research, we aim to consider additional optimization objectives based on the WSN coverage optimization problem; for example, predicting the energy consumption of nodes. In other words, we intend to investigate how to effectively adjust the size of the perceived radius of sensor nodes in order to reduce the sensing redundancy of the monitored area, thereby achieving the objective of extending the network life cycle.