Energy supply is one of the most critical challenges of wireless sensor networks (WSNs) and industrial wireless sensor networks (IWSNs). While research on coverage optimization problem (COP) centers on the network’s monitoring coverage, this research focuses on the power banks’ energy supply coverage. The study of 2D and 3D spaces is typical in IWSN, with the realistic environment being more complex with obstacles (i.e., machines). A 3D surface is the field of interest (FOI) in this work with the established hybrid power bank deployment model for the energy supply COP optimization of IWSN. The hybrid power bank deployment model is highly adaptive and flexible for new or existing plants already using the IWSN system. The model improves the power supply to a more considerable extent with the least number of power bank deployments. The main innovation in this work is the utilization of a more practical surface model with obstacles and training while improving the convergence speed and quality of the heuristic algorithm. An overall probabilistic coverage rate analysis of every point on the FOI is provided, not limiting the scope to target points or areas. Bresenham’s algorithm is extended from 2D to 3D surface to enhance the probabilistic covering model for coverage measurement. A dynamic search strategy (DSS) is proposed to modify the artificial bee colony (ABC) and balance the exploration and exploitation ability for better convergence toward eliminating NPhard deployment problems. Further, the cellular automata (CA) is utilized to enhance the convergence speed. The case study based on two typical FOI in the IWSN shows that the CA scheme effectively speeds up the optimization process. Comparative experiments are conducted on four benchmark functions to validate the effectiveness of the proposed method. The experimental results show that the proposed algorithm outperforms the ABC and gbestguided ABC (GABC) algorithms. The results show that the proposed energy coverage optimization method based on the hybrid power bank deployment model generates more accurate results than the results obtained by similar algorithms (i.e., ABC, GABC). The proposed model is, therefore, effective and efficient for optimization in the IWSN.
With the rapid development of modern manufacturing, there is a shift from simple production to intelligent production. Since the factory has its complexity and needs to keep its originality of guaranteeing the running of the production line, adding a traditional cable network is not advisable. The wiring could interfere with the existing process and require the production line to be transformed into a new factory. Thus, there is a high demand for IWSNenabled intelligent production, which helps monitor the manufacturing process and sets actual databases for future upgrades. Various IWSN applications require deploying different sensor devices to monitor the production line for other purposes. Since the sensor devices must operate and monitor continuously, the power supply becomes a limitation; powering the sensor devices with batteries requires future replacement, recharging, and maintenance, which is not convenient and may miss the detection of some typical parameters. With the booming expansion of efficient printing circuits and the fabrication of highlyintegrated devices, the application of powering devices by radiofrequency (RF) is essential for inspiring the use of RFenabled sensor devices in industries.
Regarding energy harvesting, the sensor devices can only harvest energy within a certain distance from the power banks. The power banks are equipped with grid power and can send RF signals at a fixed capacity. The hybrid power bank operates on RF and uses it to propagate energy to the devices in the deployment area. Many existing works in the literature assumed the range as a circle with a fixed radius, ignoring the influence of the ambient environment and deviating from reality. In contrast, we propose a probabilistic model which improves the accuracy of the harvest range, taking into consideration the influence of obstacles in the environment. Particularly in terms of the geometric plane distance, we focus on the interference of the RF signal from the threedimensional(3D) surface. Generally, there exist machines, semifinished products, carrier boxes, pieces of furniture, and operators in the production line, and they all interfere with the RF signal to the degree that cannot be ignored.
The topic of energy supply coverage has quickly become one of the most attractive variables determining the quality of service in IWSNs. The power bank can serve the sensor devices within their coverage range while all current sensor devices, FOI, and coverage areas are known. Due to the dynamic nature of IWSN, and the sensor devices being selfconfigurable and able to be online automatically and opportunistically, it is possible to target the overall energy supply coverage. Because the power banks are always online and the interference of the RF signal is dynamic, the coverage rate of a particular point is not deterministic but based on presumptions. However, once a sensor device of the IWSN is deployed, the coverage probability can be determined according to its physical location following the hybrid power bank deployment model. The purpose of studying the energy supply coverage is to find the optimal least number of power banks which not only powers the current sensor devices but also reserve redundancy for the future development of IWSN while guaranteeing the operation of the IWSN.
In the IWSN, coverage, connectivity, and routing are the typical factors to be considered. We focus on the power supply coverage of the IWSN in this research work. The minimum number of power banks and their deployment locations is determined before the deployment of the sensor devices and running the IWSN. If any sensor device fails to be under the coverage area of the power banks, it will not function properly and be disconnected from its application network. Thus the IWSN fails to accomplish its task. In this research work, we first plot the 3D surface of the application FOI, and then deploy some of the power banks and check the power supply coverage rate of each point on the FOI. Because there exist coverage cavities, there is a need to add more power banks to fill them and calculate the power supply coverage of each point. The newly added power banks cover the coverage cavities and enhance the coverage rate of the areas around the cavities.
With all the analyses above, two critical issues arise. 1) How to mimic the real FOI and compute their coverage rate. 2) How to find the coverage cavities and fill them. First, we propose establishing a 3D projecting model and the probabilistic model to better reflect RF signal status at the point on the 3D surface. Second, the wavelet subband energy entropy is utilized with metaheuristics methods to find the cavities and decide where to deploy the new power banks, thus improving the overall coverage.
This research work lies in artificial intelligence, modelling, and systems engineering, focusing on the coverage rate of the specific targets or the target areas but expanding the scenarios in work to a broader range. The presumable coverage rate of every point on the FOI and the coverage rate of the targets or the target areas can be derived accordingly. While much of the existing research treats the FOI as a 2D plane or 3D space, we draw from practice that it is a 3D surface, the power banks can only be deployed on the surface, and the RF signals cannot penetrate the surface. As illustrated in
In
The main contribution of this research work is given as follows:
Design and implementation of a hybrid metaheuristics algorithm for coverage optimization.
The FOI settings in the model are tunable, and the interferences are transferred to obstacles of the 3D surface, which fluctuate the terrain.
The traditional 2D Bresenham’s algorithm [
The traditional artificial bee colony (ABC) algorithm is employed with a dynamic search strategy (DSS) for the NPhard deployment problem. It balances the global and local search ability and cellular automata to accelerate the convergence speed, thus resulting in a better and quicker solution for power bank deployment locations.
The comparative experiments on numerical benchmark function optimization are carried out for the artificial bee colony with a dynamic search strategy (ABCDSS) algorithm compared to the ABC and GABC algorithms, verifying that the proposed algorithm is competitive.
The overall flow of the hybrid power bank deployment model is given in
Wireless sensor networks (WSN) are currently used in several applications, such as environmental monitoring, military surveillance, and smart cities [
In this paper, we study the COP of IWSN. Since the birth of the IWSNs, the network performance has been tied closely to the ambient environment or the ambient wireless conditions, especially in industrial applications. Precisely, we deploy the power banks on a 3D surface, which not only takes the shape of the geometry terrain but also appends the interference from the ambient environment to the 3D surface. Approximation algorithms are efficient algorithms that find approximate solutions to optimization problems (in particular NPhard problems) with provable guarantees on the distance of the returned solution to the optimal one [
Several approximation algorithms and methods have been utilized in the literature for the covering models. The sensing models can be either deterministic or probabilistic. We assume the average covering range is
Some other generally adopted probabilistic models are summarized in
Name  Functions  Descriptions 

Elfes model [ 

Li model [ 

Ahmed multilayer model [ 

Tsai shadowfading model [ 

Akbarzadeh sigmoid model [ 
Finally, for the coverage issue, the power banks are omnidirectional to supply as many sensor nodes as possible, and the FOI is established as a 3D surface with considering obstacles making it more adaptive for IWSN applications compared to other works in this field [
The rest of the research work is organized as follows; Section two illustrates the methodology employed and discusses the proposed algorithm, general method, and other strategies employed. The experiment conducted is further discussed in section three with comparison experiments, and section four presents the results and analysis. Section five outlines the conclusion of the research work.
The main objective of this research is to design and implement a hybrid power bank deployment model for energy supply coverage optimization in IWSN, which helps prepare the powering supplement of incoming installation of RFenabled sensor tags. To closely mimic the practical industry environment, the 3D surface with obstacles is addressed. Although the coverage rate of a particular point is not deterministic once a sensor device of the IWSN is deployed, the coverage probability can be determined according to its physical location and ambient environment. Thus, a combination of the probabilistic coverage model and the lineofsight algorithm is typically utilized to accurately compute the covering probability of each point on the FOI, which is divided into the covered and uncovered regions accordingly. The critical point is to achieve the optimum coverage of the FOI with a minimum number of power banks, forming the NPhard deployment problem. While addressing the NPhard COP, a dynamic search strategy is deployed to balance the ABC algorithm’s exploration and exploitation ability, inspired by the differential evolution algorithm. The cellular automata mechanism is further introduced to solve the drawbacks of the proposed heuristic algorithm, simplify the convergence process and accelerate the convergence speed when generating the power bank deployment locations. The research is conducted to achieve optimum coverage of the FOI with a minimum number of power banks operating on RF technology, serving as the source of energy for the installation in the deployment region and minimizing the chances of fires and power outages from direct power sources. The limitation of this paper is that the RF signals are set to operate on the same spectrum. This can be improved upon in future works by expanding the spectrum of propagation to satisfy the various installations in the deployment area. The energy supplied by the RF is of the same capacity, irrespective of the required capacity needed by the installed systems in the deployment area. Future works would look at satisfying the energy requirement of each installation in the deployment area. The energy of the hybrid power banks can be in a given range from which each device can be powered according to its corresponding capacity.
Physical obstacles like machines and manufacturing materials in the deployment area all impact electromagnetic waves’ propagation. Instead of ignoring this, we add their interference to the 3D surface as part of the ambient environment parameter. The 3D surface model with fluctuation is utilized to mimic the actual environment in the industry as close as possible, as shown in
Due to the existence of obstacles, such as machines and carrier boxes in the production line, the RF energy sent by the power bank can be blocked. In the LOS method, either no obstacles reside between the antenna and the system, or there is a partial obstruction. However, in NLOS, there is a full obstruction between the antenna and the system. For indoor wireless network installations, it is important to consider obstacles such as walls, ceilings, and furniture affecting LOS since these all play a role in wireless signal reception. The utilization of the LOS method is illustrated in
A point on the surface is covered only when it is within the range of one or more power banks’ coverage. To determine whether each point is on the surface, a probabilistic covering model is utilized to form a mathematical formula considering the characterization of the point coverage rate as a function of distance and other ambient environmental objects.
First, the average coverage range is defined as
Bresenham’s algorithm is extended from 2D to 3D to differentiate between the node
Assuming the point at
Next, the optimal location choice for the point
These calculations are conducted recursively for each
As mentioned earlier, the above calculations assume that
After all the above calculations, the FOI is divided into the covered and uncovered regions. The covered area refers to the points covered by one or more power banks, while the uncovered area refers to the points beyond all the power banks’ covering range. The uncovered can be visualized as the cavities on the surface and in the quality of network coverage (QoNC) matrix. The DB6 wavelet is adopted to decompose the separable into an approximation image and three detailed images in finding the coverage cavities. Then, by taking the matrix’s discrete wavelet transform (DWT) iteratively, the overall QoNC indicates the coverage probability provided by the corresponding power banks at each point.
The QoNC for the FOI can be formulated as:
Since many points may be under several nodes’ covering range, a scheme is defined when nodes cover a point to modify the probabilistic covering model further to be more accurate. The modified probabilistic covering model is given as:
After all the computations, the probabilistic coverage index is formed for each point as a matrix. For the QoNC matrix, the values of the element with an index
This research aims to optimize the energy supply coverage regarding the power bank deployment strategy. After the first round of deployment of the power banks, some coverage cavities arise. The problem relates to where the extra power banks can be deployed to fill the cavities while balancing the number of power banks and the overall energy supply coverage rate. The NPhard problem that forms can be solved by the heuristic algorithm, simulating the natural swarm’s working mechanism.
Since we have the model for power net coverage, it is natural that some efforts are made to complete the power net by implementing as few power banks as possible. To better determine the locations of the power banks, the hybrid ABCDSS with the CA method is adopted to perform the placement optimization.
Illuminated by the natural bee swarm’s working flow, which mimics the honey bee swarm’s forgetting mechanism, Karaboga formulated the ABC algorithm to optimize the numerical functions. The ABC algorithm is a selforganized system with four outstanding characteristics: positive feedback, negative feedback, fluctuations, and multiple interactions, which makes it an attractive group optimization algorithm. A general description of the ABC algorithm is given in Algorithm 2.
For the ABC algorithm, there is only one employed bee for each food source. The starting point is set as onehalf employed bees and the other half onlookers. Each employed bee is randomly nominated to one source for the first solution. Then by selecting a new candidate solution for each employed bee according to function
When a solution cannot be further improved within a limit parameter, the scout comes out, and a new key will be randomly generated.
For group optimization algorithms, the exploration and exploitation ability is vital to the quality of the generated solutions. The former refers to finding the optimum solution in the unknown areas in the solution domain. In contrast, the latter refers to utilizing the experiences gained from previous reasonable solutions to investigate better solutions. However, the exploration ability and the exploitation ability usually conflict with each other in practice. Balancing the two capabilities is essential in achieving a reasonably good optimization.
In the ABC algorithm, as mentioned earlier, the parameter
Illuminated by the DE algorithm [
Analyzing the modified ABC algorithm with
To form the dynamic balancing process during the iterations, a selftuning factor
Then the balancing factor
To avoid premature while escalating the process of convergency, the ABCDSS is proposed:
Note that when λ = 1,
However, the problemsolving process is not relatively smooth and quick, leading to finding highorder solutions to resolve the problem further. Inspired by the mapping of cellular networks, the FOI is cut into small cells allowing each cell to form the FOI solution accordingly.
The cellular automata (CA), a discrete problemsolving model, is capable of dealing with complex problems while cutting extensive mathematic computations. Since the FOI is a continuous surface in engineering, it is practical to approximate it with discrete space or discrete values. Typically, the CA consists of a regular grid of cells, each assigned a finite number of states, and the grid can be assigned any finite number of dimensions. The four fundamental elements of CA are lattice structure, cell variables, the concept of neighbourhood, and updating rules. In this study, the cells are distributed in each lattice structure, and the neighbouring cells are connected. Adding that the form of the cellular space is the immediate reflection of the physical dimensions, and the rectangular lattice structure is adopted rather than other commonly used triangular and hexagonal lattice structures as the edge shape of the FOI is rectangular. Each cell of the lattice is a joint of parameters that will be updated over the iteration process. The solving process is by defining a set of neighbourhood cells for the specific cell and assigning a random state for each cell to set the initial state. Thus, a new generation is born with the mathematical function that determines the latest state of each cell related to its current state and the states of its neighbouring cells. The cell variables at the time
The neighbouring cells
The configuration of neighbouring cells is a description of the nature of the application, which is vital to the system. The traditional Moore neighbourhood structure [
Based on the values needed in the iterations for the updating rules, the updating strategy is:
The primary purpose of the ABCDSS is to seek optimized nectars by exchanging information about the food source position and nectar amount. ABCDSSbased CA model is introduced to accelerate the convergence speed and derive optimized network topology for WSNs, thus determining the locations of the power banks. In this article, CA is introduced to specify the neighbour solution
The proposed cellular velocity update equation acts on the design variables and combines available information at the central site; thus, for every discrete time step, the updating equation generates a new design at each site using the related information as follows:
The iteration process is repeated until a stopping criterion is met. The inner and outer loops are regarded as convergent when the limited number of generations in each loop is satisfied.
With all the above modifications, the hybrid power bank deployment model for energy supply coverage optimization is settled, and the optimum power bank deployment locations of a specific FOI are generated.
To validate the proposed algorithm and model the COP, the performance of the three algorithms is tested on numerical benchmark function optimizations as was performed in [
Function name  Functions  Initial range 

Sphere  
Griewank 


Rastrigin 


Ackley 


Schwefel 


Rosenbrock 


A set of comparative experiments on the above numerical benchmark function optimizations was conducted to compare the performances of the three algorithms. The dimensions of solution space were set to 30 and 100 for the benchmark function to generate the statistical experiment’s means and standard deviation parameters and repeated them 50 times. The population size was set to 80 for all three algorithms, and the maximum generation times were set to 5000.
The performance of the proposed hybrid power bank deployment model in the industrial environment is evaluated, and the accessibility of powering the energy harvesting in IWSNs is verified in comparative experiments performed on the semireal 3D surface. First, to generate the 3D surface with as many features as the natural manufacturing environment, the surfacegenerate program is coded in MATLAB to represent different environments by setting the parameters at different values. In this paper, the surface models utilized are terrains with narrow and winding canyons, towering and steep mountains named even and uneven plants, as shown in
After the generation of the 3D surfaces, the axis of the surface is extracted discretely as the 3D surface is continuous. Bring our assumption to the semiextreme situation, and the FOI is defined as 2560 meters long and 2560 meters wide, which is a super sizeable single plant according to industry standards. The parameter values set in the simulation are shown in
Parameter  Quantity  Unit 

0.1  
2  
2560  m  
2560  m  
55  m  
10  m 
Simulation experiments were performed using MATLAB 2022B software to evaluate the proposed algorithm’s performance. Six wellknown benchmark functions were employed to compare the performance of the ABC, GABC and the ABSDSS algorithms. Since an absolute 0 may not be reported in practice, and the results below
Function name  Dimension  Algorithm  Mean best fitness  Standard deviation 

Sphere  30  ABC  7.1935 
3.403 
GABC  4.7661 
1.802 

ABCDSS  1.2338 
1.532 

100  ABC  2.9227 
3.128 

GABC  1.8921 
1.782 

ABCDSS  2.1339 
3.957 

Griewank  30  ABC  1.5230 
2.071 
GABC  2.9103 
5.220 

ABCDSS  0  0  
100  ABC  2.6538 
5.360 

GABC  3.9138 
2.993 

ABCDSS  0  0  
Rastrigin  30  ABC  1.4181 
7.731 
GABC  6.2551 
3.949 

ABCDSS  2.1073 
2.268 

100  ABC  1.9422 
1.305 

GABC  3.3099 
1.257 

ABCDSS  4.0285 
2.138 

Ackley  30  ABC  4.1664 
5.610 
GABC  3.0730 
2.951 

ABCDSS  2.4857 
2.874 

100  ABC  3.4512 
1.031 

GABC  2.8841 
6.163 

ABCDSS  1.0008 
9.131 

Schwefel  30  ABC  4.0112 
7.9893 
GABC  3.8730 
9.1651 

ABCDSS  0  2.9878 

100  ABC  3.4512 
1.7905 

GABC  2.2463 
2.9121 

ABCDSS  2.0114 
4.6071 

30  ABC  6.4079 
5.7493 

GABC  2.0761 
3.2097 

Rosenbrock  ABCDSS  1.1761 
0  
100  ABC  2.1307 
8.6301 

GABC  3.9603 
3.0814 

ABCDSS  1.8702 
2.2483 
From
Three strategies are utilized to derive the power bank deployment schemes to address the COP: the ABCDSS scheme with enabled CA, the ABCDSS scheme, the GABC scheme, and the ABC scheme. The number of sensors deployed utilizing each scheme is shown in
3D surface  Scheme  The number of power banks  

160 m × 160 m grid size  320 m × 320 m grid size  480 m × 480 m grid size  
I  ABCDSS scheme with enabled CA  1082  916  909 
ABCDSS scheme  1060  918  913  
GABC scheme  1071  920  914  
ABC scheme  1059  921  917  
II  ABCDSS scheme with enabled CA  929  903  882 
ABCDSS scheme  926  910  894  
GABC scheme  927  906  889  
ABC scheme  922  911  901 
The initial artificial bee number is set as the number of cell grids, and the required QoNC of each cell grid is set to 0.9. The QoNC of each scheme is shown in
3D surface  Scheme  The number of power banks  

160 m × 160 m grid size  320 m × 320 m grid size  480 m × 480 m grid size  
I  ABCDSS scheme with enabled CA  0.913879399  0.897543949  0.887221532 
ABCDSS scheme  0.906251598  0.873535161  0.871670837  
GABC scheme  0.904162738  0.872298720  0.866325168  
ABC scheme  0.903991704  0.871887210  0.859026512  
II  ABCDSS scheme with enabled CA  0.974321732  0.941289353  0.909659437 
ABCDSS scheme  0.931759837  0.918976599  0.868093241  
GABC scheme  0.930637629  0.917089427  0.867021317  
ABC scheme  0.926214201  0.917056492  0.865903673 
The grid size of cells was set at three different degrees to conduct the evaluations; one is 160 meters long plus 160 meters wide, the second is 320 meters long plus 320 meters wide, and the third is 480 meters long plus 480 meters wide. The power bank deployment scheme generating consumption time of each scheme is shown in
3D surface  Scheme  The number of power banks  

160 m × 160 m grid size  320 m × 320 m grid size  480 m × 480 m grid size  
I  ABCDSS scheme with enabled CA  7.3 min  77.4 min  104.7 min 
ABCDSS scheme  7.5 min  81 min  131.2 min  
GABC scheme  7.7 min  86 min  142 min  
ABC scheme  8.2 min  88.7 min  147.3 min  
II  ABCDSS scheme with enabled CA  6.4 min  67.3 min  97.6 min 
ABCDSS scheme  6.7 min  69.8 min  119 min  
GABC scheme  7.5 min  71.9 min  128 min  
ABC scheme  7.7 min  79.6 min  136.9 min 
Comparing
Comparing the ABCDSS scheme with enabled CA and the ABCDSS scheme to the ABC scheme in
Comparing the ABCDSS scheme with enabled CA and the ABCDSS scheme or ABC scheme from
Since the expected QoNC of the region is 0.9, which was reached by the schemes mentioned above in most cases, the three schemes are verified. However, considering all factors, the ABCDSS scheme with enabled CA generates better results. Thus, the proposed hybrid power bank deployment model for IWSN is effective and efficient. That is, the FOI is covered as expected, and the energy web can support the operation of the function of the IWSN. The FOI is not defined as the whole area but as the specified targets or target areas in practice; thus, the QoNC is far beyond 0.9 and could power the entire IWSN.
For the COP of WSN and IWSN, traditional research has mainly considered the monitoring coverage of the network and treated the FOI as in a 2D plane or 3D space. However, with the booming expansion of printing efficient circuits and fabrication of highlyintegrated devices, the application of powering devices by RF is enabled. RFenabled sensor devices are generally used in industries. Illuminated by the raised issue of widely spreading RFenabled sensor devices, we focus on the power banks’ energy supply coverage in this work. The FOI is not simplified but has considered the obstacles for a more practical 3D surface. In addressing the NPhard and COP, modifications were made to the ABC algorithm to generate better and quicker convergence results. A DSS was proposed to modify the ABC and balance the exploration and exploitation ability for better convergence. Further, the CA was utilized to enhance the convergence speed and establish the ABCDSS with enabled CA. Comparative experiments were carried out for benchmark functions and case studies. The results show that the proposed hybrid power bank deployment model for energy supply coverage optimization in IWSN is effective and efficient.
Based on the limitation of this paper, future works would require that the spectrum of propagation by the RF be expanded to satisfy the various installations in the deployment area. The energy distributed by the power banks can also be varied in the deployment area to satisfy the requirement of each installation.
This work was partly supported by the China Scholarship Council.
The authors declare they have no conflicts of interest to report regarding the present study.