Optimization of wireless sensor network deployment based on desert golden mole optimization algorithm
0 Abstract
The deployment of wireless sensor networks (WSNs) in extreme environments such as nuclear fusion devices and the aerospace industry is crucial for real-time monitoring of critical parameters. However, it faces many challenges. In this paper, we propose the desert golden mole optimization algorithm (DGMOA), a novel algorithm inspired by the survival strategy of the desert golden mole and combined with the Dingo optimization algorithm (DOA). DGMOA addresses these challenges through two core mechanisms: the sand swimming strategy enhances the global search capability, and the hiding strategy is used for fine-grained local optimization. Through simulation tests, DGMOA shows excellent performance. It can quickly explore a large range of solution space in the initial search phase and adjust the position of individuals to avoid local optimal traps, resulting in a more uniform sensor layout and higher coverage. In convergence speed, it outperforms existing algorithms with faster convergence. Regarding energy consumption, the reasonable node layout reduces unnecessary waste and prolongs the service life of the sensor network. The results show that DGMOA is a highly effective solution for sensor layout in complex and extreme environments, with significant improvements in performance and energy consumption over traditional methods.
Keywords
1. INTRODUCTION
In high-tech equipment and experimental facilities, vacuum vessels, as a key component, are widely used in nuclear fusion devices, semiconductor manufacturing, and aerospace industry[1, 2]. Since these vessels are required to operate in extreme environments, such as high temperatures, strong radiation, and complex pressure variations, real-time monitoring of their status is crucial[3]. Wireless sensor network (WSN) layout is one of the core means to achieve this goal, and by reasonably arranging multiple types of sensors, the temperature, pressure, stress, leakage, and other key parameters of the vacuum vessel can be comprehensively monitored to ensure its stability and safety.
The WSN layout should not only consider the geometry and operating environment of the vacuum vessel, but also need to incorporate its material properties and operating conditions. Complex geometries may lead to stress concentrations and localized hotspots, while weld points and seams in the vessel are often the key areas for monitoring[4]. Figure 1 shows the simulated structure of the vacuum vessel. In addition, the non-magnetic materials and high vacuum conditions of vacuum vessels present technical challenges for sensor selection and installation. Therefore, the type, number, location, and signal processing methods of the sensors must be carefully designed and optimized in order to minimize interference with the internal environment of the vacuum vessel while ensuring monitoring accuracy.
Figure 1. The simulated structure of the vacuum vessel.
WSN is a network consisting of a large number of sensor nodes distributed in space that collaborate to collect, process and transmit environmental data through wireless communication[5]. Wireless sensors provide strong support for applications such as environmental monitoring, security, and smart agriculture[6-8]. In practical applications, the deployment of wireless sensors needs to address several key issues, including how to maximize coverage, ensure image resolution and quality, optimize energy consumption, and cope with changes in complex environments[9]. In WSNs, due to the wide distribution of nodes, limited resources, and uncertainty of network topology, it becomes a challenge to effectively solve the problems of node placement, routing, and energy management[10, 11]. Optimization algorithms are widely used in WSNs as an effective solution, such as genetic algorithms[12], particle swarm optimization algorithms[13], ant colony algorithms[14], etc., to improve the network coverage, energy utilization efficiency, and data transmission quality by optimizing the network topology and the node behaviors, so as to enhance the performance and reliability of WSNs.
In order to further improve the effectiveness of WSN deployment and coverage optimization, this paper proposes a new approach based on the desert golden mole optimization algorithm (DGMOA). DGMOA is a heuristic optimization algorithm inspired by the survival adaptations of the desert golden mole in extreme environments, which simulates its swimming and hiding behaviors in the sand and combines with the collaborative strategy of the Dingo optimization algorithm (DOA)[15] to search for the optimal solution. DGMOA is suitable for solving complex optimization problems due to its powerful global search capability and fast convergence. The following are the main contributions of this paper:
(1) Improved group synergy strategy: while retaining the group attack, chase, scavenger and survival rate strategies in DOA, DGMOA further enhances the inter-individual synergy, making the algorithm more efficient in global search and local optimization.
(2) Sand swimming strategy: the sand swimming behavior of desert golden mole rats shuttling in the desert is introduced, so that the algorithm can quickly explore a large range of solution space in the initial search phase to avoid falling into the local optimum too early. This strategy simulates the random search behavior of the golden mole when searching for food, which enhances the global search ability of the algorithm.
(3) Hiding strategy: this strategy simulates the hiding behavior of desert golden mole when encountering danger by adjusting the position of individuals to avoid dangerous regions or locally optimal traps in the search space. It improves the accuracy and adaptability of the algorithm in localized search and ensures that individuals are able to find more optimal solutions.
The remainder of this paper is organized as follows: Section 2 presents an overview of related work and the motivations behind our work. Section 3 describes the deployment model, sensor deployment and its steps based on the DGMOA algorithm. Section 4 details the experimental environment and discusses the experimental results. Finally, Section 5 concludes the paper.
2. RELATED WORKS
WSNs have been extensively studied due to their wide range of applications in areas such as environmental monitoring, security and smart agriculture. Deployment and optimization of sensor nodes in WSNs is crucial to maximize coverage, minimize energy consumption and ensure reliability of data transmission. Various optimization algorithms have been applied to address the challenges in WSN deployment. ZainEldin et al. proposed an improved dynamic deployment technique based on genetic algorithms (IDDT-GA), which aims to maximize the area coverage with a minimum number of sensor nodes, increasing the coverage and reducing the node overlapping area[16]. Deghbouch et al. proposed a hybrid bee colony algorithm and locust optimization algorithm (BAGOA) for optimizing node deployment in WSNs, which utilizes the advantages of each method and enhances the ability of local search, which improves the optimization accuracy and convergence speed[17]. Yao et al. proposed an optimization algorithm for node deployment in WSNs based on the improved moth flame optimization (MFO) algorithm, by introducing a variable spiral position update strategy and an adaptive inertia weighting strategy to enhance the global search capability of the algorithm, and combining with a virtual force interference strategy to optimize the deployment path of the nodes and improve the network coverage[18]. Wang et al. proposed an adaptive multi-strategy artificial bee colony algorithm (SaMABC) to optimize the coverage problem of WSNs[19]. The algorithm enhances the ability to jump out of local optimal solutions by designing a pool of policies and a fine-grained selection mechanism, combined with simulated annealing and dynamic search steps. Moreover, a hybrid approach combining multiple optimization techniques can achieve better results in WSN deployments. In terms of optimizing the performance of WSNs, Zhang et al. proposed a CERED active queue management method based on a priority scheduling policy to solve the congestion problem of WSN data packets[20]. Zhang et al. proposed adaptive N-strategy sleep scheduling for WSNs, which solves the high data packet delay problem of N-strategy sleep scheduling by introducing a wait state, while reducing energy consumption[21].
Heuristic algorithms have attracted significant attention due to their capacity to handle complex optimization challenges, and they have been widely applied in the context of WSN deployment. The DGMOA proposed in this paper is inspired by the survival adaptations of the desert golden mole. Similar nature-inspired algorithms, such as whale optimization algorithm (WOA)[22] and crayfish optimization algorithm (COA)[23], have shown remarkable success in diverse engineering optimization problems. They typically exhibit superior convergence speed and can often find high-quality solutions. For instance, the WOA models the unique hunting behavior of whales to search for optimal solutions effectively, while the COA emulates the behavior of crayfish in nature. However, these algorithms also have their limitations. They may not fully consider the specific characteristics and constraints of WSN deployment, such as the complex geometries and extreme operating conditions of the deployment environment, which could lead to suboptimal sensor placements. The DOA, proposed by Peraza-Vázquez et al., simulates the hunting and foraging behaviors of Dingoes[15]. It models strategies such as pack hunting, individual pursuit, and survival probability to solve optimization problems. While DOA has its strengths in certain scenarios, it may face challenges in adapting to the highly dynamic and constrained nature of WSNs. For example, in a WSN, the sensor nodes have limited resources and need to communicate wirelessly, which requires a more fine-grained optimization of node positions and energy consumption. In contrast, DGMOA is specifically designed to address the challenges in WSN deployment. It not only draws on the survival strategy of the desert golden mole but also integrates the collaborative strategies of DOA.
The desert golden mole lives under the sand dunes in the Namib Desert. To adapt to the extreme environment, it has evolved unique behavioral patterns. During the hot daytime, it digs holes under the sand dunes to avoid the high temperature, while at night, it needs to shuttle between the sand dunes in search of food and water. This movement behavior between the sand dunes inspired us to design the sand swimming strategy, which is incorporated into the DGMOA. Inspired by the desert golden mole's movement between sand dunes at night, in the initial search phase, this strategy allows the algorithm to quickly explore a large range of solution space. This is because it simulates the movement way of the desert golden mole between sand dunes, enabling the optimization algorithm to explore more flexibly in the search space and quickly traverse a large range of solution space, thus avoiding getting trapped in local optima too early and significantly enhancing the global search ability. When the desert golden mole encounters danger, it will use the surrounding environment to hide and choose the appropriate direction and position to avoid according to its relative position relationship with the danger source, the safe area and other individuals of the same kind. This hiding behavior is applied to the hiding strategy of DGMOA. This strategy adjusts the position of individuals to avoid dangerous regions or locally optimal traps in the search space, which improves the accuracy and adaptability of the algorithm in localized search and ensures that individuals can find more optimal solutions. By combining these unique strategies such as the sand swimming strategy and the hiding strategy, DGMOA is better able to meet the complex requirements of WSN deployment and optimize the coverage and energy consumption of the network more effectively than existing algorithms.
Effective sensor deployment strategies are essential to maximize coverage and ensure the reliability of WSNs. Various deployment models have been proposed, including deterministic, random, and hybrid approaches. Deterministic models place sensors at predetermined locations, while stochastic models randomly distribute sensors within the target area. Hybrid models combine the advantages of deterministic and random deployment to balance coverage and cost. The proposed DGMOA-based deployment strategy leverages the advantages of these models to maximize coverage by achieving optimal sensor placement through heuristic optimization.
3. METHODS
This section introduces the wireless sensor deployment model and the DGMOA, which combines the synergistic strategy of the DOA and simulates the sand swimming and hiding behaviors of the DGMOA to improve the convergence speed and coverage of the algorithm, and achieves a balance between global search and local optimization, and is applicable to the problem of optimizing the layout of a sensor network in a complex environment.
3.1. WSN deployment model
The WSN deployment problem can be converted into a constrained optimization problem, usually a nonlinear programming problem. Assuming that multiple wireless sensors are deployed in a two-dimensional planar area so that the area is well monitored, the deployment of sensors needs to be uniform and reasonable. The problem is expressed as follows:
Where
Assume that the monitoring area is a two-dimensional plane and digitize it into
In this paper, we use a binary perception model where the sensor node
The set of area points contained in the sensor
The goal of WSN coverage optimization is to achieve maximum coverage area using a minimum number of sensors, which is expressed in the form of a coverage ratio in order to facilitate the comparison of the coverage area of the sensors:
Which is used as an objective function, and an optimization algorithm is employed to find a set of sensor node combinations to maximize the coverage.
The model uses an optimization algorithm to reasonably deploy sensor nodes in the two-dimensional plane and maximize the coverage area of the monitoring area by introducing a coverage objective function. Through mathematical modeling and formula derivation, it can effectively describe and solve the deployment problem of WSNs.
3.2. DGMOA
In this paper, based on the research of Fielden et al., we deeply analyzed the behavioral patterns of the desert golden mole, proposed the sand swimming strategy and the hiding strategy, and implemented these strategies through code[24]. Meanwhile, combined with the DOA proposed by Peraza-Vázquez et al., the DGMOA shows significant advantages in terms of performance and flexibility[15]. Combining the sand swimming strategy and the hiding strategy, the DGMOA performs well in WSN coverage deployment, and is able to improve the network coverage and optimize the distribution of nodes more efficiently, thus significantly improving the overall performance of the WSN.
3.2.1. DOA
Dingoes usually hunt small animals, chasing them relentlessly until they capture them alone. The persecution strategy is modeled below:
Where
Dingoes usually hunt small prey, such as rabbits, alone, but when targeting larger animals such as kangaroos, they hunt in packs. Group Attack strategy is their most common hunting strategy where they surround their prey in a range and start chasing it until it tires. This strategy is modeled below:
Where
When Dingoes fail to find prey, they roam their habitat in search of carrion. The Scavenger strategy is modeled as follows:
Where
Australian Dingoes are at risk of extinction due to illegal hunting. Their probability of survival is modeled as follows:
Where
Where
3.2.2. Desert golden mole sand swimming strategy
In this paper, we introduce a sand swimming strategy for desert golden moles to optimize the search process by simulating the desert golden mole's behavior of shuttling between sand dunes at night. The desert golden mole is a small mammal living under sand dunes in the Namib Desert that survives in extreme environments with its unique behavior. During the hot days of the desert, they often shelter from the heat by digging holes under the dunes, but at night they need to travel between the dunes in search of food and water. Observing this behavior of desert golden mole inspired the design of an optimization strategy, the sand swimming strategy.
The sand swimming strategy is used to improve the global search capability of the optimization algorithm by simulating the way the desert golden mole moves between dunes at night. Assuming that
Where
In particle swarm optimization, the position update of particles mainly depends on their own historical optimal positions and the group's historical optimal positions. Consequently, the search direction is relatively concentrated around the known relatively good regions, and there is a high risk of getting trapped near the local optimal solution. In contrast, within the DGMOA's sand swimming strategy, the position update for the desert golden mole is expressed as
3.2.3. Desert golden mole hiding strategy
In this paper, we introduce the hiding strategy of the desert golden mole to optimize the search process by simulating the hiding behavior of the desert golden mole when encountering danger. In the optimization algorithm, the hiding strategy is used to adjust the exploration direction during the search process to avoid falling into unfavorable local optimal solutions or encountering dangerous regions in the search space as much as possible.
Suppose the position of the desert golden mole is a multi-dimensional vector
Where
The hiding strategy simulates the evasive behavior of the desert golden mole in the face of dangerous situations by using a multi-dimensional vector to represent the position of the desert golden mole and introducing a series of parameters to influence the evasive movement. By calculating the relative distances between the desert golden mole, the worst-positioned mole and the best-positioned mole, and considering the safe position and the random danger parameters, it realizes the intelligent adjustment of the exploration direction to avoid falling into the local optimal solution or encountering a dangerous area. The advantage of this strategy is that it can intelligently adjust the moving direction based on environmental conditions, enabling the algorithm to avoid dangers more effectively and find safer hiding places, thus improving the search efficiency and global search ability.
3.2.4. WSN coverage deployment with DGMOA
Firstly, the size of the sensor deployment area is set to
Figure 2. DGMOA application to WSN deployment modeling. DGMOA: Desert golden mole optimization algorithm; WSN: wireless sensor network.
Step 1: Initialize the position vector of the desert golden mole. The position of each desert golden mole represents a possible sensor deployment scenario. Initialize a vector of relative distances between the worst position mole and the best position mole to represent the distance of each desert golden mole from the current worst and best positions. Initialize a vector of safe locations to represent the level of safety at each location. Initialize a vector of random hazard parameters for adding randomness to the exploration process.
Step 2: Based on the current position vector of the desert golden mole, the fitness of each desert golden mole, i.e., the value of the objective function, is calculated.
Step 3: The DGMOA is used to update the position of the desert golden mole, adjusting its exploration direction and step size.
Step 4: During each periodic nighttime sand swimming event, the position vector of the desert golden mole is adjusted according to the mathematical model of the sand swimming strategy to simulate its movement through the desert. This strategy increases the randomness and exploration of movement directions by introducing velocity vectors and random deviations.
Step 5: With a probability of encountering a predator of
Step 6: Based on the WSN coverage deployment model, calculate the coverage ratio under the current desert golden mole location to assess the coverage effect of the sensor network. The coverage ratio indicates the proportion of the sensor deployment scenario that covers the entire area.
Step 7: Repeat steps 3 to 6 until a set number of iterations or convergence conditions are reached. In each iteration, the sensor deployment scheme is continuously optimized through the combination of position update, sand swimming strategy and hiding strategy to improve the coverage and deployment efficiency.
Step 8: Output the location vector of the optimal or near-optimal solution, along with the corresponding fitness value and coverage. The optimal solution represents the best deployment solution for the sensors that maximizes the coverage area and optimizes the energy consumption.
Through the above steps, the DGMOA is able to search the problem space intelligently, simulate the behavior of the desert golden mole in the natural environment by using the sand swimming strategy and the hiding strategy, so as to improve the algorithm's searching efficiency and global searching ability, and finally output the optimization results. The introduction of the shared optimal solution mechanism further enhances the optimization performance of the algorithm and makes it perform better in complex environments.
4. EXPERIMENTS
The experiments were conducted in a MATLAB R2023a environment on a standard PC equipped with a 3.20 GHz processor and 16 GB of memory. To test the performance of the proposed DGMOA for WSN deployment, we utilized simulated environments of 20 m
4.1. Ablation experiments
To evaluate the impact of the sand swimming strategy and the hiding strategy, we designed an ablation experiment. We compared the performance of the original DGMOA algorithm (with sand swimming strategy and hiding strategy), DGMOA with sand swimming strategy removed and DGMOA with hiding strategy removed. The experimental setups of the three algorithms are consistent in terms of simulated environment, sensor parameters and maximum number of iterations. The population size of the optimization algorithms is categorized as 500 and the maximum number of iterations is set to 1, 000. The simulated environment used for the deployment of the WSN is a 20 m
Under the same experimental setting, it can be seen from the convergence curve of the 20 m
Figure 3. Graphical representation of the results of the ablation experiment under the same experimental setup. (A) Convergence curve of experimental results for 20 m
4.2. Datasets
We set up different scenarios for the comparison of the experiments, 20 m
4.3. Experimental results and analysis
In a 20 m
Figure 4. Coverage performance of the proposed DGMOA algorithm in a 20 m
Figure 5. Statistical map of final coverage in a 20 m
Figure 6. Deployment diagram of WSN coverage in a 20 m
The performance results under different population sizes in a 50 m
Figure 7. Coverage performance of the proposed DGMOA algorithm in a 50 m
Figure 8. Statistical map of final coverage in a 50 m
Figure 9. Deployment diagram of WSN coverage in a 50 m
Through the results of the WSN coverage deployment simulation experiment, it can be seen that DGMOA shows significant excellence in sensor network deployment. The deployment of the sensor location is more uniform, the overlap and gap between the coverage area is less, achieving a higher coverage rate, and can effectively utilize the sensor resources to maximize the coverage area. Compared with other algorithms, DGMOA has significant advantages. It can quickly improve the coverage rate in a shorter time while maintaining the uniformity and efficiency of sensor deployment, proving that it outperforms the other compared algorithms in terms of global search, fast convergence, and final coverage effect. In summary, DGMOA has significant superiority in sensor network optimization and deployment and can quickly and efficiently achieve high coverage.
In terms of energy consumption, DGMOA deploys sensors to make the node layout more reasonable, reducing unnecessary energy waste, and thus improving the overall energy utilization efficiency. The unified sensor layout avoids the rapid energy consumption caused by too dense nodes, and also reduces the additional energy consumption that may be caused by coverage blind spots. Compared with other algorithms, DGMOA can maintain the effective operation of the network with lower energy consumption under the same monitoring tasks, prolonging the service life of the sensor network, especially suitable for complex and extreme environments with limited resources.
4.4. DGMOA algorithm analysis
In order to deeply explore the performance of the DGMOA algorithm, a systematic and multi-dimensional experiment and detailed analysis work was carried out. In the experimental planning, different scale simulation areas such as 20 m
Through the design of ablation experiments, the effectiveness of the two strategies of sand swimming and hiding is verified. As far as the sand swimming strategy is concerned, from the convergence curve of the experiment in the 20 m
Overall, the DGMOA algorithm has shown good performance in different scale regional experiments. The sand swimming and hiding strategies complement each other, and the combined efforts significantly enhance the comprehensive performance of the algorithm, which effectively confirms the important and effective position of the two algorithms in the algorithm system. This provides a solid theoretical and practical foundation for the algorithm to be deployed in complex WSNs.
5. CONCLUSIONS
This paper presents the DGMOA, which makes significant contributions. The sand swimming strategy, inspired by the desert golden mole's movement between sand dunes at night, allows the algorithm to quickly explore a large range of solution spaces in the initial search phase. This effectively avoids falling into local optima too early and greatly enhances the global search ability. The hiding strategy, simulating the desert golden mole's hiding behavior when encountering danger, adjusts the position of individuals to avoid dangerous regions or locally optimal traps in the search space. This improves the accuracy and adaptability of the algorithm in localized search and ensures more optimal solutions. These two strategies make DGMOA highly applicable in WSN deployment, optimizing the sensor layout and improving the network's performance and energy consumption.
Although DGMOA shows excellent performance, it still has some limitations. For example, in some extremely complex and dynamic environments, the algorithm may need to further adapt and optimize. Future research will focus on extending the algorithm to multi-objective optimization problems, considering multiple factors such as coverage, energy consumption, and latency simultaneously. Additionally, the application of DGMOA in real-world industrial scenarios will be explored, aiming to validate and improve its practical effectiveness and provide more valuable solutions for industrial applications.
DECLARATIONS
Authors' contributions
Made substantial contributions to conception and design of the study and performed data analysis and interpretation: Wang Z, Guo C
Performed data acquisition and provided administrative, technical, and material support: Sui J, Cui C
Availability of data and materials
The results of this study are obtained through machine-generated random data and algorithmic calculations. There is no applicable raw data to share. The details of the algorithms and the experimental process are described in the manuscript to ensure the reproducibility of the research.
Financial support and sponsorship
This work was supported in part by the Technology Innovation Guidance Program of Shandong Province (Grant No. YDZX2023030).
Conflicts of interest
All authors declared that there are no conflicts of interest.
Ethical approval and consent to participate
Not applicable.
Consent for publication
Not applicable.
Copyright
© The Author(s) 2025.
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Wang, Z.; Guo, C.; Sui, J.; Cui, C. Optimization of wireless sensor network deployment based on desert golden mole optimization algorithm. Intell. Robot. 2025, 5, 1-18. http://dx.doi.org/10.20517/ir.2025.01
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