A Clustering Method for Wireless Sensor Network Nodes Based on an Improved Harris Eagle Algorithm

Abstract

This invention discloses a node clustering method for wireless sensor networks based on an improved Harris Eagle algorithm, including cluster head election and node joining mechanisms. The base station collects the remaining energy and location information of nodes, and uses the improved Harris Eagle algorithm to predict network lifetime, optimizing the optimal weight coefficients and network partition radius, and broadcasting the parameters to all nodes in the network. Nodes participate in cluster head election by calculating a comprehensive weight based on remaining energy, density, and distance from the base station. A load penalty factor and a near-field cluster head size control mechanism are introduced. An energy variance threshold is set to trigger the Harris Eagle algorithm to re-optimize the weight coefficients. The beneficial effects of this invention are: by improving the Harris Eagle algorithm, dynamic global optimization of clustering parameters is achieved; the cluster head election mechanism is improved; and by combining non-uniform clustering and a load penalty mechanism, network load is effectively balanced, and network lifetime is extended.

Description

Technical Field

[0001] This invention relates to the technical field of wireless sensor networks, and in particular to a method for clustering nodes in wireless sensor networks based on an improved Harris Eagle algorithm. Background Technology

[0002] Wireless sensor networks (WSNs) are formed by a large number of wireless sensor nodes through self-organization. They are capable of real-time monitoring and collaborative sensing of a work area, and of collecting and processing information on monitored objects and the work area. Node clustering is a key technology for optimizing topology management and improving energy efficiency in WSNs, and is fundamental to ensuring stable and reliable network operation. An excellent clustering scheme is a prerequisite for ensuring efficient operation and a long lifespan of WSNs in the work area.

[0003] Clustering weights for nodes in wireless sensor networks often rely on static, empirical settings, failing to adapt to dynamic network energy consumption and topology changes, resulting in poor algorithm generalization. Existing strategies fail to effectively coordinate the coupled effects of multi-dimensional network characteristics (such as node load history and regional node density), focusing only on single-factor optimization, leading to biased cluster head election and uneven energy consumption. Furthermore, cluster heads near base stations bear a huge data forwarding load, a problem neglected by traditional uniform clustering mechanisms, causing critical nodes to die prematurely and significantly shortening the network lifespan.

[0004] Patent No. CN112672396A describes a mobile node clustering method for wireless sensor networks based on an improved whale algorithm. The scheme first constructs a mobile node model of the wireless sensor network. Based on the remaining energy, location, and number of times a mobile node has been selected as a cluster head node, an improved whale algorithm is used to select the cluster head node, avoiding rapid node death and improving the overall network lifetime. However, this method is prone to getting trapped in local optima and does not consider the problem of excessive load caused by data aggregation and forwarding of nearby cluster heads.

[0005] Patent No. CN114531665A describes a method and system for clustering nodes in wireless sensor networks based on Lévy flight. This method incorporates Lévy flight's particle swarm optimization algorithm into the election process of cluster head nodes, thereby saving node power consumption and extending node lifespan. However, this method does not consider the issues of non-cluster head nodes joining the cluster and cluster head rotation.

[0006] Therefore, designing a clustering scheme for wireless sensor network nodes that extends network lifetime, balances network load, and has fast convergence speed and strong search capability is a problem that needs to be solved.

[0007] The information disclosed in this background section is intended only to enhance the understanding of the overall background of the invention and should not be construed as an admission or in any way implying that the information constitutes prior art known to those skilled in the art. Summary of the Invention

[0008] The purpose of this invention is to provide a node clustering method for wireless sensor networks based on an improved Harris Eagle algorithm. By constructing a cluster head node selection and non-cluster head node inclusion mechanism, the improved Harris Eagle algorithm is used to find the optimal node clustering scheme, thereby overcoming the defects in the prior art.

[0009] The objective of this invention is achieved through the following technical solution: a node clustering method for wireless sensor networks based on an improved Harris Eagle algorithm, comprising the following steps: S01. Construct a cluster head node selection and non-cluster head node inclusion mechanism; S02. The base station collects parameters such as the remaining energy and location information of all nodes in the network, and uses the improved Harris Eagle algorithm to optimize the optimal weight coefficient and network partition radius with the predicted network lifetime as the target. S03. Broadcast the optimized cluster parameter set to all network nodes via the downlink; S04. After receiving the parameters, the node calculates a comprehensive weight value based on its remaining energy, node density, and distance from the base station, and participates in the cluster head election. S05. By introducing a load penalty factor and a near-cell cluster size control mechanism, non-uniform clustering is achieved to protect near-cell nodes of the base station.

[0010] S06. Preset energy variance threshold and establish Harris Eagle algorithm triggering mechanism to dynamically optimize weight coefficients; Preferably, in step S01, the cluster head node election mechanism comprehensively considers the node's remaining energy, local node density, and the distance from the node to the base station, as well as the node's own comprehensive weight value. The calculation formula is: ; in, Let be the current remaining energy of node i. Let be the initial energy of the node. Let be the number of neighboring nodes of node i. This represents the maximum number of neighbors for all nodes in the network. This represents the average distance from all nodes in the network to the base station. Let be the distance from node i to the base station. These are the weighting coefficients.

[0011] Preferably, in step S02, the improved Harris Eagle algorithm dynamically optimizes the weight coefficients and network partition radius. The process is as follows: 2.1. Set initial parameters and establish the target optimization model; 2.2. Initialize the population using a Logistic mapping to generate an initial population that is more widely and evenly distributed in the solution space and has extremely high diversity; 2.3 Calculate the initial fitness value and set the position of the individual with the best fitness as the current prey position; 2.4. Execute the exploration and development phases based on the prey's escape energy, and update the individual Harris Eagle locations; 2.5 Calculate the individual fitness value after the location update and compare it with the prey fitness value. If the individual fitness value after the location update is better than the prey fitness value, then the location of the individual with the better fitness value is taken as the new prey location. 2.6. Simulated annealing is introduced to avoid the Harris Eagle algorithm getting trapped in local optima; 2.7 Determine if the number of iterations has reached the preset parameter. If not, repeat steps 3.4-3.6. If yes, terminate the algorithm and output the current optimal Harris Eagle individual position.

[0012] Preferably, in step 3.1, the initial parameters include the Harris Eagle population size and the maximum number of iterations. In the Harris Eagle algorithm, each Harris Eagle is represented as: ; in Each weighting coefficient has a value range of [0.1, 0.8]. The range of values ​​is , It is the network radius. The radius used to define the "near zone" is the distance between the node and the base station. The area marked as "near zone" is the area marked as "far zone". Construct a fitness function with the goal of maximizing network lifetime: ; Where FND is the predicted number of rounds of death for the first node when using the weight combination X for clustering; This represents the initial total energy of the entire network. This is the predicted total energy consumption of the entire network when using the weight combination X.

[0013] Preferably, in step 3.2, a set of random number sequences is generated using a Logistic mapping, and its iterative formula is as follows: ; Where r is the control parameter and t is the iteration time step. This represents the proportion of the population at time t to the maximum possible population size.

[0014] Preferably, in step 3.4, the specific processes of the Harris Eagle algorithm exploration and development phases are as follows: Harris eagles roost widely and randomly within their search area, observing and monitoring prey with two equally probable random distributions. The mathematical model is as follows: ; Where k represents the current iteration number of the optimization process, Indicates the position of the search agent in the next iteration. This indicates the location of the search agent randomly selected from the current population. This indicates the location of the optimal solution found so far. This indicates the position of the current iterative search agent, where Ub and Lb represent the upper and lower bounds of the variable, respectively. q is a random number between 0 and 1, representing The average position of all search agents in the current population is calculated using the following formula; ; in, This represents the position of the i-th search agent in the k-th iteration, and N represents the total number of search agents in the population; During the development phase, the HHO algorithm simulates the hunting behavior of the Harris Eagle, determining four update mechanisms based on two variables: probability r and escape energy E. Here, r < 0.5 indicates the prey has a chance to escape, and r ≥ 0.5 indicates the prey has no chance of escape. The development update mechanisms are as follows: When r≥0.5 and |E|≥0.5, the prey has sufficient energy but no chance to escape successfully, and the Harris Eagle will engage in soft encirclement behavior. ; ; ; Where J represents the positional difference between the current optimal solution and the search agent at the k-th iteration in the optimization process; J is used to simulate the jump intensity when the prey escapes. It is a random number between -1 and 1; When r ≥ 0.5 and |E| < 0.5, the prey does not have enough energy and has no chance of escaping successfully; the Harris Hawk then engages in a hard encirclement behavior. ; When r < 0.5 and |E| ≥ 0.5, the prey has sufficient energy and a chance to escape successfully, and can use more deceptive maneuvers during the escape. At this time, the Harris Hawk will adjust its position and direction according to the prey, and execute a gradual dive-and-encircle maneuver. ; ; In this strategy, the Levi flight is used to simulate the feigned escape maneuvers made by prey in a real-world scenario, and the formula is as follows: ; Where S is a denoted by ... The random vector, where D represents the dimension of the problem, and LF represents the Lévy fly operator; ,b is a parameter with a default value of 1.5; Therefore, during the soft encirclement phase with a gradual dive, the final strategy for the Harris Eagle to update its position is shown in the following formula: ; When r < 0.5 and |E| < 0.5, the prey has a chance to escape successfully but lacks sufficient escape energy. The Harris Eagle attempts to reduce the distance to the prey through a gradual, rapid dive and establish a hard encirclement behavior before killing the prey in a surprise attack: ; ; Therefore, during the hard encirclement phase with a gradual dive, the final strategy for the Harris Eagle to update its position is shown in the following formula: ; Preferably, in step 3.6, the simulated annealing operation update formula is introduced as follows: ; Where T represents temperature, and its variation is controlled by the number of iterations. Represents a random number between 0 and 1. This is a sign function, taking the value 1 or -1; A probability is calculated using the Metropolis criterion to decide whether to accept or reject a new solution. The calculation formula is as follows: ; in, This represents the difference in target fitness between the new solution and the current solution.

[0015] Preferably, in step S05, the introduction of the load penalty factor and the near-zone cluster size control mechanism specifically involves: ; in, This is the penalty coefficient, used to adjust the severity of the penalty. As a load penalty factor, if a node has served as cluster head in the most recent k rounds, then ,otherwise, ; In the cluster head election and cluster formation process, a differentiated strategy is adopted for near-field nodes and far-field nodes. When the candidate cluster head in the near-field receives member nodes, its maximum number of member nodes is limited so that the cluster size formed in the near-field is smaller than that in the far-field, thus achieving non-uniform clustering.

[0016] Preferably, in step S06, the base station continuously monitors the standard deviation of the remaining energy of all nodes in the network. When the standard deviation exceeds a preset threshold, it indicates that the energy imbalance between nodes has intensified, and the HHO needs to readjust the weights. When the base station finds that a node in the network has failed due to energy depletion, it means that the network topology and energy distribution have undergone significant changes, and immediately triggers the HHO to recalculate the parameters.

[0017] The present invention has the following advantages: By using the Harris Eagle algorithm to dynamically optimize clustering parameters with the goal of maximizing network lifetime and employing a non-uniform clustering mechanism to balance the load, the death time of nodes is effectively delayed, and the overall lifespan of the network is fundamentally extended.

[0018] 2. Overcoming the limitation of traditional clustering methods where weight coefficients depend on empirical settings, the Harris Eagle algorithm can optimize online based on the real-time network status, ensuring that the clustering strategy always maintains optimal performance and possesses strong environmental adaptability.

[0019] 3. By introducing partition radius optimization and load penalty factor, a non-uniform clustering structure is intelligently constructed, which reduces the data forwarding burden of the cluster heads in the near area and fundamentally avoids the problem of the failure of nodes in the middle of the network due to excessive energy depletion. Attached Figure Description

[0020] Figure 1 This is a flowchart illustrating the overall process of optimizing cluster head election and non-cluster head clustering mechanisms in this invention. Figure 2 This is a flowchart of the improved Harris Eagle algorithm in this invention. Detailed Implementation

[0021] The present invention will be further described below with reference to the accompanying drawings. The scope of protection of the present invention is not limited to the following description: like Figure 1 As shown, a method for clustering nodes in a wireless sensor network based on an improved Harris Eagle algorithm includes the following steps: S01. Construct a cluster head node selection and non-cluster head node inclusion mechanism; the cluster head node election mechanism comprehensively considers the node's remaining energy, local node density, and distance from the node to the base station, as well as the node's own comprehensive weight value. The calculation formula is: ; in, Let be the current remaining energy of node i. Let be the initial energy of the node. Let be the number of neighboring nodes of node i. This represents the maximum number of neighbors for all nodes in the network. This represents the average distance from all nodes in the network to the base station. Let be the distance from node i to the base station. These are the weighting coefficients; S02. The base station collects parameters such as the remaining energy and location information of all nodes in the network, and uses the improved Harris Eagle algorithm to optimize the optimal weight coefficients and network partition radius with the predicted network lifetime as the objective; the improved Harris Eagle algorithm dynamically optimizes the weight coefficients and network partition radius. The process is as follows: 2.1. Set initial parameters and establish the target optimization model; 2.2. Initialize the population using a Logistic mapping to generate an initial population that is more widely and evenly distributed in the solution space and has extremely high diversity; 2.3 Calculate the initial fitness value and set the position of the individual with the best fitness as the current prey position; 2.4. Execute the exploration and development phases based on the prey's escape energy, and update the individual Harris Eagle locations; 2.5 Calculate the individual fitness value after the location update and compare it with the prey fitness value. If the individual fitness value after the location update is better than the prey fitness value, then the location of the individual with the better fitness value is taken as the new prey location. 2.6. Simulated annealing is introduced to avoid the Harris Eagle algorithm getting trapped in local optima; 2.7 Determine if the number of iterations has reached the preset parameter. If not, repeat steps 3.4-3.6. If yes, terminate the algorithm and output the current optimal Harris Eagle individual position.

[0022] like Figure 2 As shown, the improved Harris Eagle algorithm is used to dynamically optimize the cluster head weight parameters and network partition radius, including the following steps: The initial parameters include the Harris Eagle population size and the maximum number of iterations. In the Harris Eagle algorithm, each Harris Eagle is represented as: ; in Each weighting coefficient has a value range of [0.1, 0.8]. The range of values ​​is , It is the network radius. The radius used to define the "near zone" is the distance between the node and the base station. The area marked as "near zone" is the area marked as "far zone". Construct a fitness function with the goal of maximizing network lifetime: ; Where FND is the predicted number of rounds of death for the first node when using the weight combination X for clustering; This represents the initial total energy of the entire network. The predicted total energy consumption of the entire network when using the weight combination X; The Logistic mapping is used to generate an initial population that is more widely and evenly distributed in the solution space and has a high degree of diversity. The iterative formula is as follows: ; Where r is the control parameter and t is the iteration time step. This represents the proportion of the population at time t to the maximum possible population size. The specific process of the Harris Eagle algorithm's exploration and development phases is as follows: Harris eagles roost widely and randomly within their search area, observing and monitoring prey with two equally probable random distributions. The mathematical model is as follows: ; Where k represents the current iteration number of the optimization process, Indicates the position of the search agent in the next iteration. This indicates the location of the search agent randomly selected from the current population. This indicates the location of the optimal solution found so far. This indicates the position of the current iterative search agent, where Ub and Lb represent the upper and lower bounds of the variable, respectively. q is a random number between 0 and 1, representing The average position of all search agents in the current population is calculated using the following formula: ; in, This represents the position of the i-th search agent in the k-th iteration, and N represents the total number of search agents in the population; During the development phase, the HHO algorithm simulates the hunting behavior of the Harris Eagle, determining four update mechanisms based on two variables: probability r and escape energy E. Here, r < 0.5 indicates the prey has a chance to escape, and r ≥ 0.5 indicates the prey has no chance of escape. The development update mechanisms are as follows: When r≥0.5 and |E|≥0.5, the prey has sufficient energy but no chance to escape successfully. The formula for calculating the soft encirclement behavior of the Harris Eagle in this case is as follows: ; ; ; Where J represents the positional difference between the current optimal solution and the search agent at the k-th iteration in the optimization process; J is used to simulate the jump intensity when the prey escapes. It is a random number between -1 and 1; When r ≥ 0.5 and |E| < 0.5, the prey does not have enough energy and has no chance to escape successfully. The formula for calculating the Harris Eagle's hard-surround behavior is as follows: ; When r < 0.5 and |E| ≥ 0.5, the prey has sufficient energy and a chance to escape successfully, and can use more deceptive maneuvers during the escape. At this time, the Harris Eagle will adjust its position and direction according to the prey. The formula for calculating the Harris Eagle's gradual dive and soft encirclement behavior is as follows: ; ; In this strategy, the Levi flight is used to simulate the feigned escape maneuvers made by prey in a real-world scenario, and the formula is as follows: ; Where S is a denoted by ... The random vector, where D represents the dimension of the problem, and LF represents the Lévy fly operator; ,b is a parameter with a default value of 1.5; Therefore, during the soft encirclement phase with a gradual dive, the final strategy for the Harris Eagle to update its position is shown in the following formula: ; When r < 0.5 and |E| < 0.5, the prey has a chance to escape successfully but lacks sufficient escape energy. The Harris Eagle attempts to reduce the distance to the prey through a gradual, rapid dive and build a hard encirclement before killing the prey in a surprise attack. The calculation formula for this behavior is as follows: ; ; Therefore, during the hard encirclement phase with a gradual dive, the final strategy for the Harris Eagle to update its position is shown in the following formula: ; To avoid the Harris Eagle algorithm getting stuck in local optima, a simulated annealing operation is introduced, and the updated formula is as follows: ; Where T represents temperature, and its variation is controlled by the number of iterations. Represents a random number between 0 and 1. This is a sign function, taking the value 1 or -1; A probability is calculated using the Metropolis criterion to decide whether to accept or reject a new solution. The formula is as follows: ; in, This represents the difference in target fitness between the new solution and the current solution.

[0023] S03. Broadcast the optimized cluster parameter set to all nodes in the network via the downlink; if there is an isolated node that has not received any message, set that node directly as the cluster head to avoid disconnection from the network; S04. After receiving the parameters, the node calculates a comprehensive weight value based on its remaining energy, node density, and distance from the base station, and participates in the cluster head election. S05. By introducing a load penalty factor and a near-cell cluster size control mechanism, non-uniform clustering is achieved to protect near-cell nodes of the base station; the calculation formula after introducing the load penalty mechanism is as follows: ; in, This is the penalty coefficient, used to adjust the severity of the penalty. As a load penalty factor, if a node has served as cluster head in the most recent k rounds, then ,otherwise, This parameter directly protects nearby nodes and all recently active nodes, preventing them from having excessively high weights and being elected consecutively. In the cluster head election and cluster formation process, a differentiated strategy is adopted for near-field nodes and far-field nodes. When receiving member nodes, the maximum number of member nodes for candidate cluster heads in the near-field is limited, so that the cluster size formed in the near-field is smaller than that in the far-field, thus achieving non-uniform clustering. This cluster head selection mechanism encourages the nodes near the base station to become cluster heads in the first round and undertake more data forwarding tasks, while prioritizing the protection of far-field base station nodes with huge energy consumption. However, in a multi-layer cluster tree network, the cluster heads close to the base station are not only the aggregation point of their own cluster data, but also the relay station when distant clusters send data to the base station. Nodes close to the base station may die early due to excessive load. The non-uniform clustering plus load penalty mechanism can ensure more frequent cluster head rotation and protect the cluster head nodes in the near-field. S06. Set a preset energy variance threshold and establish a Harris Eagle algorithm triggering mechanism to dynamically optimize the weight coefficients; the base station continuously monitors the standard deviation of the remaining energy of all network nodes. When the standard deviation exceeds a preset threshold, it indicates that the energy imbalance between nodes has intensified, and the HHO needs to readjust the weights; when the base station finds that a node in the network has failed due to energy depletion, it means that the network topology and energy distribution have undergone significant changes, and immediately triggers the HHO to recalculate the parameters.

[0024] Finally, it should be noted that the above descriptions are merely preferred embodiments of the present invention and are not intended to limit the present invention. Although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art can still modify the technical solutions described in the foregoing embodiments or make equivalent substitutions for some of the technical features. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the protection scope of the present invention.

Claims

1. A method for clustering nodes in a wireless sensor network based on an improved Harris Eagle algorithm, characterized in that: Includes the following steps: S01. Construct a cluster head node selection and non-cluster head node inclusion mechanism; In step S01, the cluster head node election mechanism comprehensively considers the node's remaining energy, local node density, and distance from the node to the base station, as well as the node's own comprehensive weight value. The calculation formula is: ； in, Let be the current remaining energy of node i. Let be the initial energy of the node. Let be the number of neighboring nodes of node i. This represents the maximum number of neighbors for all nodes in the network. This represents the average distance from all nodes in the network to the base station. Let be the distance from node i to the base station. These are the weighting coefficients; S02. The base station collects the remaining energy and location information of all nodes in the network, and uses the improved Harris Eagle algorithm to optimize the optimal weight coefficient and network partition radius with the predicted network lifetime as the target. In step S02, the improved Harris Eagle algorithm dynamically optimizes the weight coefficients and network partition radius. The process is as follows: 2.

1. Set initial parameters and establish the target optimization model; 2.

2. Initialize the population using a Logistic mapping to generate an initial population that is more widely and evenly distributed in the solution space and has extremely high diversity; 2.3 Calculate the initial fitness value and set the position of the individual with the best fitness as the current prey position; 2.

4. Execute the exploration and development phases based on the prey's escape energy, and update the individual Harris Eagle locations; 2.5 Calculate the individual fitness value after the location update and compare it with the prey fitness value. If the individual fitness value after the location update is better than the prey fitness value, then the location of the individual with the better fitness value is taken as the new prey location. 2.

6. Simulated annealing is introduced to avoid the Harris Eagle algorithm getting trapped in local optima; 2.7 Determine if the number of iterations has reached the preset parameter. If not, repeat steps 2.4-2.

6. If yes, terminate the algorithm and output the current optimal Harris Eagle individual position. S03. Broadcast the optimized cluster parameter set to all network nodes via the downlink; S04. After receiving the parameters, the node calculates a comprehensive weight value based on its remaining energy, node density, and distance from the base station, and participates in the cluster head election. S05. By introducing a load penalty factor and a near-cell cluster size control mechanism, non-uniform clustering is achieved to protect near-cell nodes of the base station. In step S05, the introduction of the load penalty factor and the near-zone cluster size control mechanism is specifically as follows: ； in, This is the penalty coefficient, used to adjust the severity of the penalty. As a load penalty factor, if a node has served as cluster head in the most recent k rounds, then ,otherwise, ; In the process of cluster head election and cluster formation, a differentiated strategy is adopted for near-field nodes and far-field nodes. When the candidate cluster head in the near-field receives member nodes, its maximum number of member nodes is limited so that the cluster size formed in the near-field is smaller than that in the far-field, thus achieving non-uniform clustering. S06. Preset energy variance threshold and establish Harris Eagle algorithm triggering mechanism to dynamically optimize weight coefficients; In step S06, the base station continuously monitors the standard deviation of the remaining energy of all nodes in the network. When the standard deviation exceeds a preset threshold, it indicates that the energy imbalance between nodes has intensified, and the HHO needs to readjust the weights. When the base station finds that a node in the network has failed due to energy depletion, it means that the network topology and energy distribution have undergone significant changes, and immediately triggers the HHO to recalculate the parameters.

2. The wireless sensor network node clustering method based on the improved Harris Eagle algorithm according to claim 1, characterized in that: In step 2.1, the initial parameters are set, including the Harris Eagle population size and the maximum number of iterations. In the Harris Eagle algorithm, each Harris Eagle is represented as: ; in Each weighting coefficient has a value range of [0.1, 0.8]. The range of values ​​is , It is the network radius. The radius used to define the "near zone" is the distance between the node and the base station. The area marked as "near zone" is the area marked as "far zone". Construct a fitness function with the goal of maximizing network lifetime: ; Where FND is the predicted number of rounds of death for the first node when using the weight combination X for clustering; This represents the initial total energy of the entire network. The predicted total energy consumption of the entire network when using weight combination X.

3. The wireless sensor network node clustering method based on the improved Harris Eagle algorithm according to claim 1, characterized in that: In step 2.2, a sequence of random numbers is generated using the Logistic mapping, and its iterative formula is as follows: ; Where r is the control parameter and t is the iteration time step. This represents the proportion of the population at time t to the maximum possible population size.

4. The wireless sensor network node clustering method based on the improved Harris Eagle algorithm according to claim 1, characterized in that: In step 2.4, the specific processes of the Harris Eagle algorithm's exploration and development phases are as follows: Harris eagles roost widely and randomly within their search area, observing and monitoring prey with two equally probable random distributions. The mathematical model is as follows: ; Where k represents the current iteration number of the optimization process, Indicates the position of the search agent in the next iteration. This indicates the location of the search agent randomly selected from the current population. This indicates the location of the optimal solution found so far. This indicates the position of the current iterative search agent, where Ub and Lb represent the upper and lower bounds of the variable, respectively. q is a random number between 0 and 1, representing The average position of all search agents in the current population is calculated using the following formula: ; in, This represents the position of the i-th search agent in the k-th iteration, and N represents the total number of search agents in the population; During the development phase, the HHO algorithm simulates the hunting behavior of the Harris Eagle, determining four update mechanisms based on two variables: probability r and escape energy E. Here, r < 0.5 indicates the prey has a chance to escape, and r ≥ 0.5 indicates the prey has no chance of successfully escaping. The development update mechanisms are as follows: When r≥0.5 and |E|≥0.5, the prey has sufficient energy but no chance to escape successfully. The formula for calculating the soft encirclement behavior of the Harris Eagle in this case is as follows: ; ; ; Where J represents the positional difference between the current optimal solution and the search agent at the k-th iteration in the optimization process; J is used to simulate the jump intensity when the prey escapes. It is a random number between -1 and 1; When r ≥ 0.5 and |E| < 0.5, the prey does not have enough energy and has no chance to escape successfully. The formula for calculating the Harris Eagle's hard-surround behavior is as follows: ; When r < 0.5 and |E| ≥ 0.5, the prey has sufficient energy and a chance to escape successfully, and can use more deceptive maneuvers during the escape. At this time, the Harris Eagle will adjust its position and direction according to the prey. The formula for calculating the Harris Eagle's gradual dive and soft encirclement behavior is as follows: ; ; In this strategy, the Levi flight is used to simulate the feigned escape maneuvers made by prey in a real-world scenario, and the formula is as follows: ; Where S is a denoted by ... The random vector, where D represents the dimension of the problem, and LF represents the Lévy fly operator; ,b is a parameter with a default value of 1.5; Therefore, during the soft encirclement phase with a gradual dive, the final strategy for the Harris Eagle to update its position is shown in the following formula: ; When r < 0.5 and |E| < 0.5, the prey has a chance to escape successfully but lacks sufficient escape energy. The Harris Eagle attempts to reduce the distance to the prey through a gradual, rapid dive and build a hard encirclement before killing the prey in a surprise attack. The calculation formula for this behavior is as follows: ; ; Therefore, during the hard encirclement phase with a gradual dive, the final strategy for the Harris Eagle to update its position is shown in the following formula: 。 5. A method for clustering nodes in a wireless sensor network based on an improved Harris Eagle algorithm according to claim 1, characterized in that: In step 2.6, the simulated annealing operation update formula is introduced as follows: ； Where T represents temperature, and its variation is controlled by the number of iterations. Represents a random number between 0 and 1. The sign function takes the value 1 or -1; a probability is calculated using the Metropolis criterion to accept or reject the new solution. The calculation formula is as follows: ； in, This represents the difference in target fitness between the new solution and the current solution.

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