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RETRACTED ARTICLE: Hierarchical energy-saving routing algorithm using fuzzy logic in wireless sensor networks

This article was retracted on 13 May 2024

This article has been updated


Currently, sensor energy assembly in wireless sensor networks is limited, and clustering methods are not effective to improve sensor energy consumption rate. Thus, a hierarchical energy-saving routing algorithm based on fuzzy logic was constructed by considering three aspects: residual energy value, centrality, and distance value between nodes and base stations. The remaining sensor nodes selected by fuzzy logic algorithm have a longer time to live and greater residual energy than those selected by low-power adaptive clustering hierarchical protocol algorithm, fuzzy unequal clustering algorithm, and fuzzy logic cluster head election algorithm. For network life cycle, the number of rounds in which the first dead node appears, in descending order, is studied: energy-saving routing algorithm (400 rounds) > new geographic cellular structure algorithm (300 rounds) > virtual grid based dynamic routes adjustment algorithm (100 rounds). Under the same experimental round, energy-saving routing algorithm’s remaining energy curve always reaches its maximum. The energy-saving routing algorithm by fuzzy logic constructed by this research institute can significantly improve network energy utilization, which has certain reference value.

1 Introduction

Wireless sensor networks (WSN), as a distributed network, is a structure that combines many sensor nodes in a freely organized form through wireless communication technology. Sensor devices perceive environment or situation changes of different physical objects in daily life by connecting them. Then, the corresponding state data was transmitted to the Internet, which helped people better understand and analyze the physical environmental changes corresponding to a certain sensor. There are two connection methods for WSN: wireless communication and wired internet connection. Due to the more flexible network settings of sensors connected through wireless communication in WSN, they can prevent creators from being affected by environment and time, making them more widely applicable compared to other sensors. However, due to dense distribution of wireless sensor nodes at WSN end, the assembled micro batteries’ energy supply is limited, which cannot better meet nodes working needs in WSN. In addition, the dynamic update of network topology caused by environmental changes in sensor location requires significant energy consumption, further exacerbating sensor energy consumption. Currently, a commonly used method to solve sensor energy issues in WSN is clustering. However, when using the clustering method for cluster head selection, it will consume more energy due to random allocation [3]. When collecting and forwarding data from cluster heads located at cluster edge, it will further consume more energy [4]. Since traditional routing algorithms often do not adequately take into account the energy state of the nodes, which leads to a significant reduction in the network lifetime, in order to solve the problem of energy consumption in WSNs, the energy consumption of the nodes is optimized by introducing fuzzy logic algorithms, which prolongs the effective lifetime of the entire network. A hierarchical energy-saving routing algorithm (HESRA) by fuzzy logic (FL) can improve node energy consumption problem in WSN. By utilizing fuzzy logic algorithm (FLA) to improve cluster head selection method, the routing algorithm was improved, and the most suitable router algorithm for the current sensor was identified. This optimized node energy loss and extended sensor service life. The study consists of four parts. Firstly, the relevant work in recent years was discussed. Secondly, a FL-based HESRA was proposed in the experiment, and the algorithm proposed in the study selected cluster head with the highest priority. Then, performance testing was conducted on the proposed algorithm. The final section draws conclusions.

2 Related works

Many scholars have made corresponding achievements and contributions in WSN energy-saving. Sredharan et al. proposed a cluster head selection and hybrid routing protocol algorithm based on fuzzy multi-attribute decision-making to improve WSN performance and demonstrated its performance in subsequent experiments [5]. Pattnaik et al. proposed an algorithm combining fuzzy clustering and other optimization methods to achieve efficient routing assembly in WSN. Simulation experiments have confirmed that this algorithm has certain advantages in energy utilization and system lifespan [6]. PANKAJ et al. proposed a new clustering algorithm to extend network lifespan by reducing sensor nodes battery loss and verified algorithm effectiveness in simulation experiments [7]. Nosratian et al. proposed a fuzzy trust prediction model by shortest path and node information to monitor malicious nodes in WSN, thereby extending network service life [8]. Ahmed et al. proposed a load balancing clustering and FL coyote optimization algorithm to balance load gateways with less energy, thereby extending network lifespan [9]. Mittal et al. proposed a fuzzy enhancement algorithm to overcome the limitations of clustering-based hierarchical algorithms in WSN, stabilize network performance, and extend network lifespan [10]. Manev et al. proposed an algorithm based on FL controller to calculate the most reliable energy-saving link between sensor nodes and routers in WSN and verified the proposed algorithm effectiveness through experiments [11]. Singh et al. proposed a system algorithm by fuzzy rules to avoid dangerous intrusions in WSN, thereby ensuring network lifespan [12]. Zulaikha et al. proposed an energy-saving routing protocol algorithm using a genetic FL system to solve low-power links and verified the proposed algorithm performance in experiments [13]. Mittal et al. proposed a clustering neural network optimization algorithm based on fuzzy type 2 to reduce energy constraints in WSN. This algorithm can effectively extend network lifespan [14].

In the application of virtual technology to WSN, Prajapati et al. proposed a new multi hop virtual multi-input multi-output communication protocol algorithm to extend WSN service life. Asher et al. proposed a multi-input multi-output system algorithm to improve WSN performance and conducted detailed experiments on network energy conservation research [16]. Sun et al. proposed a wireless network model for content-based image retrieval and sustainable computing to improve WSN’s ability to resist shortcut key attacks and verified this model’s accuracy and robustness through experiments [17]. Md et al. proposed an improved load balancing clustering algorithm to address the limitations of battery life, memory limitations, and computing power in WSN. This algorithm has been verified to have certain reference value in experiments [18].

In summary, FLA and virtual network technology (VNT) have made many achievements in the research of WSN, but there is relatively little data on combining the two to further extend the lifespan of WSN. Based on this, a FL-based HESRA can reduce WSN energy consumption and extend its life cycle.

3 Cluster head selection of HESRA By FL

This study first uses FLA to select a cluster head with the highest priority and considers extending WSN lifecycle from three aspects: residual energy value, centrality, and distance value between nodes and base stations. Then, by integrating VNT, HESRA is constructed to further reduce WSN’s energy consumption and extend its lifespan.

3.1 Clustering selection of energy-saving routers based on FLA construction

Fuzzy rules are constructed based on “if–then” statements. For example, if a node has a high residual energy and a short distance from the base station, then the likelihood of that node being selected as a cluster head increases. Membership functions are used to quantify these fuzzy inputs, e.g., using trigonometric or Gaussian functions. FLA was proposed by Azerbaijani scientist Lotfi Zadeh in 1965. FL uses membership to represent the transition state between true and false relationship values. Membership represents the degree. When its value increases, the degree to which the corresponding ordinary set U belongs to the mapping set A within its value range increases. The representation methods of fuzzy sets include Zadeh representation and order pair representation. In Zadeh representation, when discrete set’s universe \(U\) is discrete sets, formula (1) stands for a fuzzy set.

$$\underset{\sim}{A}=\sum_{u\in U}\frac{u\underset{\sim}{A\left(u\right)}}{u}$$

In Eq. (1), \(\underset{\sim}{A}\) stands for a fuzzy set. \(u\) is an element in set \(U\). \(u\underset{\sim}{A\left(u\right)}\) stands for the mapping of element \(u\) in fuzzy set \(\underset{\sim}{A}\). When domain \(U\) is a continuous set, formula (2) is a fuzzy set.


The ordinal pair representation is mainly applicable to a domain fuzzy set representation of known elements and their membership degrees in formula (3).

$$\underset{\sim}{A}=\left\{u,\;u_{\underset{\sim}{A}}\left(u\right)\left|u\in U\right.\right\}$$

Membership functions are used to quantify fuzzy input and output variables. In the study, triangular membership functions are used to represent fuzzy sets. Specifically, there are (1) membership functions for the residual energy of nodes: three fuzzy sets “low,” “medium,” and “high” are defined, corresponding to the energy ranges of [0, 0.3 J], [0.2 J, 0.8 J], and [0.7 J, 1 J] energy ranges; (2) membership function for distance to the base station: three fuzzy sets, “short,” “medium,” and “long” are defined that correspond to the distance ranges of [0, 30 m], [20 m, 70 m], and [60 m, 100 m], respectively; (3) membership function for the possibility of being a cluster head: three fuzzy sets “low,” “medium,” and “high” are defined three fuzzy sets corresponding to the possibility ranges of [0, 0.3], [0.2, 0.8], and [0.7, 1], respectively. These membership functions were derived based on observation and analysis of experimental data and optimized through several iterations of experiments. WSN area containing N sensor nodes is set as a given rectangle, and in the selected local WSN, these sensor nodes’ positions remain unchanged. Each node has same properties and type, and the initial state is a normal node with same initial energy. The mobile aggregation node can directly connect and communicate with the cluster points without fixing its position (that is, mobile aggregation node can move freely). Corresponding data collection was conducted based on a round of changes in the position of mobile aggregation nodes as a reference. Figure 1 shows the structure of WSN.

Fig. 1
figure 1

Schematic diagram of wireless sensor network structure model

From Fig. 1, WSN consists of three parts: nodes, mobile aggregation nodes, and cluster heads. The cluster head node mainly collects information from various environments, and the cluster head collects the collected data information and then transmits it to mobile aggregation node. There is a certain correlation between the energy consumed by sensors during data collection and transmission in WSN and transmission distance. By comparing transmission distance and boundary distance, the corresponding node’s transmission energy consumption mode is obtained. Formula (4) calculates the energy consumed by a sensor that transmits \(k\) bytes.

$$E_{tx}\left(k,d\right)=\left\{\begin{array}{l}E_{elec}\ast k+\varepsilon_{fs}\ast k\ast d^2,\;d<d_0\\E_{elec}\ast k+\varepsilon_{mp}\ast k\ast d^4,\;d<d_0\end{array}\right.$$

In Eq. (4), \({E}_{elec}\) is the energy consumed by the sensor when transmitting 1 bit of data. \({\varepsilon }_{fs}\) is wireless amplifier’s energy consumption under free transmission model. \(d\) is the distance between the sending and receiving nodes. \({d}_{0}\) is a boundary between free and multipath transmission modes. \({\varepsilon }_{mp}\) is the energy consumption of the wireless amplifier in multipath transmission model. Formula (5) is the energy consumed by sensor to receive \(k\) bytes.

$$E_{rx}\left(k\right)=E_{elec}\ast k$$

Formula (6) calculates the boundary between two transmission modes.


Based on the number and distance of transmission nodes, the energy required for transmission can be determined. When \(d\ge {d}_{0}\), a free transmission mode spatial channel will be selected for data transmission to determine energy consumption. When \(d\ge {d}_{0}\), a multi-path transmission mode will be selected to ensure data volume’s speed and energy consumption during data transmission. The traditional cluster head selection method to extend WSN lifecycle is not effective. Therefore, this study utilized FLA to optimize cluster heads selection, considering three aspects: residual energy value, centrality, and distance value between nodes and base stations. Figure 2 shows the cluster head selection optimization.

Fig. 2
figure 2

Flowchart for optimizing cluster head selection

From Fig. 2, before selecting and optimizing cluster heads, the node’s remaining energy will be calculated first. The location information of all cluster node members is judged by the residual energy, and the cluster centroid location is obtained. Then, the distance between each cluster node member and cluster centroid is compared, and the centrality data is calculated. This experiment incorporated node’s remaining energy, node centrality, and node gateway distance into FL system. According to these corresponding rules, the node with the highest priority is obtained. The data collection was completed by aggregating and fusing the data at the highest priority node. Formula (7) is based on the Mamdani rule of FLA for selecting the highest priority.


In Eq. (7), \({x}_{1}\) stands for node’s remaining energy, \({x}_{2}\) stands for node centrality, and \({x}_{3}\) stands for node and gateway’s distance. The highest priority node is used as cluster head to collect and upload perceptual information within the cluster. The cluster head selected through FL can achieve maximum network load balancing, thereby extending WSN service life.

3.2 WSN energy-saving routing algorithm integrating VNT

Due to WSN’s composition characteristics, its network performance largely depends on sensor nodes efficiency. Based on sensor nodes’ energy assembly characteristics, further research is being conducted to consider reducing entire WSN energy consumption and extending its service life by improving sensor nodes working efficiency [19]. According to VNT, there is no need to install physical network devices, and it can run multiple non-interfering logical networks on the same physical network device simultaneously, which can be an effective data collection strategy in WSN. Therefore, this study considers combining FLA and VNT to construct an energy saving routing algorithm (ESRA) for exchanging data channel information. WSN set in Sect. 2 was also used as researching premise. And mobile aggregation node’s running direction in WSN was given to be counterclockwise and running at a uniform speed along WSN region’s boundary. The data transmission path is dynamically adjusted according to mobile aggregation node’s position changes. ESRA constructed by the research was used to partition the cell head nodes twice, so that only half of the cell head nodes were used to participate in new routing path reconstruction during each routing process. This in turn saves energy consumption caused by dynamic path adjustment, improves WSN energy utilization, and extends network lifespan. Figure 3 is a schematic diagram of the ESRA model for adjusting network routing paths.

Fig. 3
figure 3

Schematic diagram of a model for adjusting network routing paths using energy-saving routing algorithms

From Fig. 3, the routing energy-saving algorithm divides the cell head nodes into two types: direct communication and indirect communication. The main function of indirect communication node is to select the nearest direct communication node as the next hop node to transmit data, without considering routing path’s dynamic programming design. This direct communication node mainly collects data perceived by sensors within the cell and forwards the data information of adjacent indirect cell header nodes. The mobile aggregation node mainly travels in a counterclockwise direction to collect information collected by all cell header nodes. A certain communication conversion frequency was set to ensure that mobile aggregation node can connect to direct communication cell header node at the shortest distance near the next cell. Anda conversion period between direct and indirect cell header nodes was set. When routing path’s transition time reaches transition cycle, the direct and indirect cell head nodes exchange their states and functions. Figure 4 shows the process of adjusting entire WSN routing path.

Fig. 4
figure 4

Routing path adjustment process

From Fig. 4, before collecting the perception data of cell head nodes, it is first determined whether conversion cycle satisfies mutual conversion between inter and direct communication cell head nodes. If it can be met, ESRA will first transpose the type and function of intermediate and direct nodes. If it cannot be met, the existing nodes will be considered for data collection and aggregation first, and then the conversion cycle will be determined and adjusted.

4 Performance analysis of HESRA based on FL

All experiments were conducted in an environment as close as possible to realistic conditions, including parameters such as network size, node energy, and communication range. Possible external factors such as environmental noise and signal interference were also considered and adjusted accordingly in the experimental design to minimize their effects. Matrix&Laboratory (MATLAB) is a powerful mathematical software that can meet experimental testing needs. Therefore, MATLAB was chosen to test FLA performance on clustered ESRA. A rectangle with a network coverage range of 100 × 100 m2 was set up, and 100 sensor nodes with the same initial energy value were randomly placed. Within the set network coverage range, the mobile aggregation node can freely move to collect information and data perceived and uploaded by cluster head nodes. Table 1 shows the specific parameter settings.

Table 1 Specific parameter settings

MATLAB was used to test the performance of the FL clustering algorithm constructed in the study. And its WSN life cycles were compared with low-energy adaptive clustering hierarchy (LEACH), cluster head election mechanism using fuzzy logic (CHEF), and fuzzy unequal clustering algorithm (EAUCF) in the same testing environment. Figure 5 shows the experimental results.

Fig. 5
figure 5

Comparison of network life cycles of four algorithms in the same experimental environment

From Fig. 5, as rounds increase, the surviving nodes in rectangular network of all four algorithms show a decreasing trend. And after a certain round, the surviving nodes in four algorithms decrease at different rates. After 600 rounds of cluster heads selected by LEACH algorithm, the surviving node is almost zero, and node survival number decreases the fastest. The reason for this phenomenon is that when LEACH protocol selects cluster heads, it only considers cluster head’s random number and does not pay attention to the remaining energy value. Therefore, sensor has the fastest dead time and entire network cycle’s shortest survival life. At around 650 rounds, the surviving node in EAUCF is also almost zero. Around 900 rounds, the surviving node under CHEF algorithm is almost zero. Due to CHEF algorithm focusing on node’s centrality and residual energy value, EAUCF algorithm focuses on residual energy and the distance between nodes and base stations. Therefore, node’s living time under EAUCF algorithm is longer than node’s living time under CHEF algorithm. Around 1300 rounds, the surviving nodes in the same network under FLA constructed by this research institute decrease to 0, which significantly prolongs network’s service life compared to other three algorithms. The reason may be that the FLA constructed in this study focuses on node’s remaining energy, the centrality of nodes, and the distance between nodes and mobile gateways. This design experiment compared four algorithms’ energy consumption under the same network with same surviving nodes in Fig. 6.

Fig. 6
figure 6

Comparison of four algorithms for remaining energy at the same node in the same network

From Fig. 6, under the same rounds, the total remaining energy of nodes is ranked in descending order as LEACH < EAUCH < CHEF < FLA in this study. Under the same total remaining energy of nodes, the sustainable number of rounds for sensor nodes is ranked in descending order as LEACH < EAUCH < CHEF < FLA in this study. After 1300 rounds, the remaining energy of node based on FLA is 0, which is at least 500 more persistence time for the same node compared to other three similar algorithms. Under the same network conditions, the proposed algorithm saves about 30% energy over LEACH and about 15% over CHEF. Unlike the LEACH algorithm, the fuzzy logic algorithm proposed in the study considers not only the randomness of the nodes but also the residual energy of the nodes and the distance from the base station in a comprehensive manner while selecting the cluster heads. This comprehensive consideration leads to a significant optimization of the algorithm in terms of energy consumption. Using MATLAB software to test ESRA performance, the entire experiment includes two parts: determining the parameter values that maximize network performance and verifying ESRA performance. Table 2 shows the experimental parameter settings.

Table 2 Detailed setting of experimental parameters

Mobile aggregation node’s moving speed was set to 10 m/s, and the surviving nodes are tested when the exchange cycles of direct and indirect cell head nodes were 5 s, 10 s, 20 s, and 40 s, respectively. Figure 7 shows the experimental results.

Fig. 7
figure 7

Comparative diagram of the first node death in cell head nodes under different exchange cycles

From Fig. 7, when the direct and indirect cell head nodes’ exchange periods are 5 s, 10 s, and 20 s, respectively, the maximum surviving nodes are 300. When node exchange cycle is 40 s, the maximum surviving nodes are 298. When swap cycle is 5 s, the remaining nodes’ living time is the longest, 345 rounds. After 350 rounds, the survival nodes decrease to 298. At this point, the corresponding WSN has the longest node life under four exchange cycles at a mobile convergence node speed of 10 m/s. When the remaining energy value of sensor node is 0, it is determined that it cannot continue with data collection and forwarding work. This current routing algorithm determines WSN’s lifecycle based on the time when the first dead node (DN) appears. That is, from the time when all nodes survive to the first node dying, it is of WSN’s lifecycle. To further evaluate WSN’s performance comparison under different conditions, experimental tests were designed to test round number during the first DN, half DN, and all DN exchange cycles of different cell head nodes at a mobile convergence node speed of 10 m/s in Fig. 8.

Fig. 8
figure 8

Record of the number of rounds with dead nodes under different exchange cycles

From Fig. 8, the earliest occurrence of the first dead node round number (DNR) has an exchange period of 40 s, followed by exchange periods of 20 s, 10 s, and 5 s, respectively. The first DNR under four exchange cycles is 257, 293, 327, and 345 rounds, respectively. When DN reaches half, the minimum wheel with an exchange cycle of 10 s is 775. The maximum exchange period for the remaining node’s survival round is 40 s, corresponding to 819 node survival rounds. When all nodes die, the longest duration of the rotation cycle is 40 s, and it will not be until 1435 rounds before all nodes die. When exchange period is 5 s, all nodes will die in the 1322nd round. It can be considered that when exchange period is 40 s, this node will run 100 more rounds than when exchange period is 5 s. Therefore, the remaining nodes in WSN with swap cycles of 5 s and 40 s are calculated in Fig. 9.

Fig. 9
figure 9

Network life cycle changes under different interchange cycles

From Fig. 9, around 1100 rounds, there were fewer remaining nodes with a cell head node exchange cycle of 5 s, and the corresponding WSN consumed more energy. Before the experiment number reached 1100 rounds, the remaining nodes number under two exchange cycles were roughly the same, and the energy consumed was also relatively equivalent. After 1100 experimental rounds, the remaining sensor nodes number in WSN under two exchange cycles is below 50, which no longer meets the data information monitoring requirements of WSN detection area set by the research institute under rectangular area. WSN sensor nodes with a swap cycle of 40 s will only exhibit good performance when round is large (after 1100 rounds). When the exchange cycle is 5 s, the first DN appears with a longer number of rounds, so research has determined to set exchange cycle to 5 s. Three hundred wireless sensor nodes were selected for simulation experiments, and mobile aggregation node’s running speed was set to 10 m/s, and cell head node’s conversion period was set to 5 s. This experiment tested the remaining nodes number and network energy consumption in VNT under this setting. Figure 10 compares the remaining nodes number and network energy consumption of currently performing WSN routing algorithms such as new geographic cellular structure algorithm (GCA) and virtual grid-based dynamic routes adjustment (VGDRA) in the same experimental environment.

Fig. 10
figure 10

Comparison of the number of remaining nodes and network energy consumption between different algorithms

In Fig. 10a, for WSN life cycle, the first DNR of ESRA constructed by this research institute is longer than GCA and VGDRA algorithms’, with a value of 400 rounds. The first DNR under VGDRA algorithm is 100 rounds, and the GCA is 300 rounds. As experiment increased, the remaining nodes number under all three algorithms showed a decreasing trend. But the ESRA constructed by this research institute has the largest number of remaining nodes under the same experimental rounds. From Fig. 10b, sensor nodes’ initial energy values are the same for three algorithms. As experimental rounds increase, the remaining nodes’ energy decreases. However, under the same experimental rounds, the studied ESRA node’s residual energy curve remained at the top and lasted for the longest experimental round, with a value of 1400 rounds. The ESRA constructed by this research institute has better energy-saving effects compared to GCA and VGDRA algorithms and can extend WSN nodes’ lifecycle.

5 Conclusion

FLA was used to select and optimize cluster heads from three aspects: residual energy value, centrality, and distance value between nodes and base stations and combined with VNT to construct ESRA. So, it can construct a more efficient energy consumption scheme for sensor nodes and extend wireless networks’ lifespan. Compared to algorithms such as LEACH and CHEF, the algorithm proposed in the study introduces fuzzy logic, which adds some computational complexity. However, this complexity is valuable as it leads to higher energy efficiency and longer network lifetime. Compared with LEACH, EAUCH, and CHEF algorithms, the remaining sensor nodes based on FLA selection have a longer time to live. When experimental rounds are 1300, its survival node will approach 0. Under the same experimental rounds, the remaining energy of nodes in descending order is as follows: FLA constructed by this research institute > CHEF > EAUCH > LEACH, more than 500 cycles longer than nodes under the same algorithm. In the experiment, different exchange periods of direct and indirect cell head nodes were compared. When the exchange cycle is 5 s, the first DNR is the longest, with 345 rounds. After determining exchange period and mobile aggregation node’s running speed, the remaining nodes’ number and network energy consumption of GCA and VGDCA algorithms were compared in the same experimental environment. For WSN lifecycle, the first DNR in descending order is ESRA (400 rounds) > GCA (300 rounds) > VGDRA (100 rounds) studied. In the network energy consumption experiment, under the same experimental rounds, the remaining energy curve of ESRA always lies above GCA and VGDCA energy consumption curves. When experimental rounds are 1400, the remaining energy of ESRA constructed by this research institute approaches 0. Unlike the LEACH algorithm, the fuzzy logic algorithm proposed in the study considers not only the randomness of the nodes but also the residual energy of the nodes and the distance from the base station in a comprehensive manner while selecting the cluster heads. This comprehensive consideration leads to a significant optimization of the algorithm in terms of energy consumption. The FL-based ESRA constructed by this research institute can significantly improve network energy utilization and extend network lifecycle in WSN, which has certain reference significance. The algorithm proposed in the study is highly scalable and can be adapted to different network scenarios and requirements through parameter tuning or module replacement. The algorithm is particularly suitable for wireless sensor network scenarios that require a high degree of energy efficiency and long lifetime, such as smart agriculture, health monitoring systems, and environmental monitoring. In these application scenarios, energy efficiency and network lifetime are critical. The research foresees that data sensing and collection efforts will also focus primarily on areas such as environmental monitoring, health monitoring, and industrial automation. However, the study only explores the fixed mobility speed of mobile aggregation nodes, does not consider frequent route reconfiguration, and has not further investigated the data-aware collection of aggregation nodes within the network area. The results may be affected if different node speeds or dynamic movement patterns are considered. Dynamic movement patterns may lead to more frequent route reconfigurations, which may affect the performance and practical applicability of the algorithm. Frequent route reconfiguration means that in dynamic or unstable network environments, routing paths may need to be recalculated and updated frequently. Such frequent changes not only increase the control overhead of the network but may also lead to several problems: (1) increased energy consumption: each route reconfiguration requires additional communication between nodes, which consumes more energy; (2) data transmission delay: route reconfiguration may lead to an increase in the transmission delay of data packets in the network, which affects the performance of real-time applications; (3) network stability degradation: frequent path changes may lead to network stability degradation, which affects the reliability of data transmission. To mitigate these effects, future research should explore how to optimize algorithms for highly dynamic network environments without sacrificing energy efficiency and network lifetime. In addition, although the research focuses on network lifetime and energy efficiency, there are other performance metrics and practical challenges, such as network throughput, end-to-end latency, or security, that warrant further study. These additional metrics will be able to provide a more comprehensive assessment of the effectiveness of the algorithms in real-world deployments.

Availability of data and materials

The datasets generated during and/or analyzed during the current study are available from the corresponding author on reasonable request.

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Dan Wang: writing—original draft preparation; Qing Wu: methodology; Ming Hu: writing—review and editing.

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Wang, D., Wu, Q. & Hu, M. RETRACTED ARTICLE: Hierarchical energy-saving routing algorithm using fuzzy logic in wireless sensor networks. EURASIP J. on Info. Security 2023, 9 (2023).

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