Wireless sensor network clustering routing based on improved beluga optimization algorithm

Abstract

The application discloses a wireless sensor network clustering routing based on an improved beluga whale optimization algorithm and relates to the field of Internet of Things.The technical scheme of the application improves the beluga whale optimization algorithm through student t distribution and cosine boundary strategy, which is called tCBWO.BWO algorithm is in the local development stage most of the time during the algorithm execution process; a DPR heuristic algorithm is proposed and applied to WSN; a new hierarchical routing scheme of WSN is proposed.The stability of the BWO algorithm is improved, and the Prim algorithm is improved in combination with a transmission energy consumption model of WSN, and is named as tCBWO-DPR algorithm.The algorithm can provide high-quality data transmission service in each round and can effectively improve the balance of the network.

Description

Technical Field

[0001] This invention relates to the field of the Internet of Things (IoT), and in particular to cluster routing for wireless sensor networks based on an improved white whale optimization algorithm. Background Technology

[0002] In wireless sensor networks (WSNs), the main idea of ​​traditional hierarchical routing is to divide sensor nodes into multiple clusters, with each cluster forwarding data to the base station via a cluster head. This cluster-based data transmission reduces energy consumption and extends network lifespan. However, cluster head nodes bear relatively higher network energy consumption when forwarding data, affecting network stability. Existing hierarchical routing often uses nodes closer to the base station as cluster heads, but the number of such nodes is often limited, leading to excessive burden on neighboring nodes. Previous research on small-scale hierarchical routing typically employed single-hop node transmission. If the distance between a node and the base station exceeds a certain threshold, node communication costs increase dramatically. Therefore, selecting suitable cluster head nodes and establishing efficient data transmission paths remains an optimization challenge for WSNs. Summary of the Invention

[0003] To address the aforementioned technical problems, this invention provides a wireless sensor network clustering routing based on an improved white whale optimization algorithm.

[0004] The technical solution adopted by this invention to solve its technical problem is: wireless sensor network clustering routing based on the improved Whale optimization algorithm. The wireless sensor network clustering routing based on the improved Whale optimization algorithm is characterized by including a network model: a hierarchical routing model divides the network into multiple clusters and uses cluster head rotation to ensure balanced energy utilization and improve the efficiency of the WSN; the nodes are divided into multiple units, and the nodes in each unit fuse the data within the unit through the cluster head node and then send it to the base station.

[0005] First-order radio transmission model: During the operation of the wireless sensor, the data transmission energy consumption only considers the data transmission energy consumption;

[0006] Energy consumption expression for the transmitting unit:

[0007]

[0008] E elec E represents the energy consumed by the transmitting circuit to process each bit of data. amp Where is the amplification factor of the transmitting amplifier, k is the size of the transmitted data packet, and d is the transmission distance of the data packet. Maximum transmission distance;

[0009] Energy consumption expression for receiving unit:

[0010] E RX (k)=kE elec

[0011] Where E elec The energy consumed by the receiving circuit to process each bit of data.

[0012] Preferably, the beluga whale optimization algorithm:

[0013] Initialization of the whale pod:

[0014] Initially, an initial whale population X is generated randomly:

[0015]

[0016] Where n is the population size of beluga whales, d is the dimension of the variable space, and for all beluga whales, the corresponding fitness value is:

[0017]

[0018] Whether a whale enters a phase of global exploration or localized development depends on the balance factor B. f B f The expression is as follows:

[0019]

[0020] Where t is the current iteration number, T is the maximum iteration number; B0 is a random number in the interval (0, 1); when B f When the value is greater than 0.5, the whale enters the global development stage; otherwise, it enters the local development stage.

[0021] Global exploration:

[0022] The position update strategy for global search defined in this algorithm is as follows:

[0023]

[0024] in, Let p be the new coordinates of the i-th beluga whale in the j-th dimension. j (j = 1, 2, 3, ..., d) is a random number selected in d dimensions; r1 and r2 are random numbers in the interval (0, 1);

[0025] Partial development:

[0026] To improve the convergence performance of the algorithm, a Levy flight strategy is employed, where the position update formula during the local development phase is as follows:

[0027]

[0028] in, Let i represent the next generation individual of the i-th solution. This represents the current optimal solution. The solution is randomly selected. This represents the i-th solution, where r3 and r4 are random numbers within the interval (0,1), and C1 is the adaptive balance factor, where C1 = 2r4(1-T / T) max );L F Indicates the Levy flight factor;

[0029] Whale fall phase:

[0030] The position of the whale after it falls is as follows:

[0031]

[0032] Where r5, r6, and r7 are random numbers within the interval [0, 1]. step This represents the step size during the beluga whale's fall, and its value depends on the number of iterations.

[0033]

[0034] Where C2 is the step size factor between the probability of whale pod crashes and the population size, bwo sets C2 = 2nW f ub and lb represent the upper and lower bounds of the variable space, respectively. The probability of a whale pod crashing.

[0035] Preferably, the algorithm is improved and optimized by utilizing a cosine factor boundary strategy; the optimized B f The calculation formula is as follows:

[0036]

[0037] Among them, CB f This is a balance factor based on the cosine factor. `max` and `min` are the maximum and minimum values ​​of the balance factor, respectively; in this paper, `max` = 0.9 and `min` = 0.1.

[0038] When random number B0 > CB f When the random number B0 ≤ CB, the algorithm enters the global exploration phase; f At this point, the algorithm enters the partial development stage;

[0039] Random perturbation factor based on t-distribution

[0040] During the local development of this algorithm, the student t-distribution was introduced to optimize the algorithm from getting trapped in local optima;

[0041] When the degrees of freedom df are small, the distribution curve is flatter. When the degrees of freedom df equals 1, the t-distribution curve can approximate the Cauchy distribution curve. The greater the degrees of freedom of the t-distribution, the closer its distribution curve is to the standard normal distribution curve. The probability density of the student t-distribution Z~t(n) with n degrees of freedom is as follows:

[0042]

[0043] Where Γ(x) is the gamma function,

[0044] By utilizing the influence of degrees of freedom on the t-distribution, a new local exploitation strategy was established:

[0045]

[0046] in, Let i represent the next generation individual of the i-th solution. This represents the current optimal solution. The solution is randomly selected. This represents the i-th solution, where r3 and r4 are random numbers within the interval (0,1), and C1 is the adaptive balance factor, where C1 = 2r4(1-T / T) max ). t(T) follows the student distribution Z~t(T).

[0047] Preferably, a fitness function is established by combining node energy and node position relationship, and the tCBWO algorithm is used to select the node more suitable to be elected as the cluster head; the prim algorithm is improved by using a distance factor; ordinary nodes are added to the cluster by judging their position relationship with the cluster head;

[0048] Based on the remaining energy information of the nodes and the positional relationships between the nodes, and combined with the optimization algorithm, the cluster head for the next stage is selected. The optimization function established for cluster head election is as follows:

[0049] Fitness = αg1(x) + (1-α)g2(x)

[0050] Where α is the weight parameter of each variable, g1 is the energy model, and g2 is the node position model;

[0051] The energy model g1 expression is as follows:

[0052]

[0053] Among them, E n Let r be the remaining energy of the nth node, and r be the current round number.

[0054] The network is made more balanced by assessing the coverage of network nodes by cluster heads. The expression for node position g2 is as follows:

[0055]

[0056] Among them, dist(CH) i ,n) is the distance from cluster head j to neighboring node i, and d0 is the effective coverage area of ​​the cluster head node's signal, which is set to in this paper. N is the number of cluster heads, and M is the number of network nodes. This represents the number of nodes that the cluster head can effectively cover.

[0057] Preferably, inter-cluster transmission:

[0058] The relationship between path hop count and distance: When the transmission distance is less than 104.4m, direct data transmission can effectively reduce network energy consumption; when the node distance is between 104.4 and 192.6m, single-hop transmission is suitable; when the physical distance between nodes is greater than 192.6m, multi-hop transmission is suitable.

[0059] Preferably, during the inter-cluster communication phase, cluster head nodes less than 104.4 km from the base station communicate directly with the base station; in subsequent phases, the Dprim algorithm is continued to be used to construct inter-cluster communication, and the specific implementation process is as follows:

[0060] Let s be the base station, and A, B, C, E, and D be the candidate cluster heads; the execution flow of its Dprim algorithm is as follows:

[0061] a) Construct candidate cluster heads C = {A, B, C, E, D, S}, visited set V = {}, and path R = {};

[0062] b) Starting from base station S, remove base station S from candidate set C and add it to V. C = {A, B, C, E, D}, V = {S}, R = {};

[0063] c) Find candidates whose distance s is less than d from the candidate set. max Nodes A and C are selected, and paths (A, S) and (C, S) are constructed with S respectively. These paths are then added to R. A and C are removed from the candidate set C and added to the visited set V. Figure 5 As shown in (b). C = {B, E, D}, V = {S, A, C}, R = {(A, S), (C, S)};

[0064] d) Starting from the visited set V, the paths to the candidate set C are (A, B), (C, D), and (A, D). Among them, the path (C, D) is the shortest and can form a minimum spanning tree. Therefore, (D, C) is added to the path R, D is removed from the candidate set C, and D is added to V; C = {B, E}, V = {S, A, C, D}, R = {(A, S), (C, S), (D, C)};

[0065] e) Starting from the visited set V, the paths to candidate set C are (A, B), (D, B), and (E, D). Among them, the path (A, B) is the shortest and can form a minimum spanning tree. Therefore, (B, A) is added to path R, B is removed from candidate set C, and B is added to V. Figure 5 (d) is shown. C={E}, V={S, A, B, C, D}, R={(A, S), (C, S), (D, C), (B, A)};

[0066] f) Starting from the visited set V, there are paths (B, E) and (D, E) to reach the candidate set C. Among them, the path (B, E) is the smallest and can form a minimum spanning tree. Therefore, (E, B) is added to the path R, and E is removed from the candidate set C and added to V. C = {}, V = {S, A, B, C, D, E}, R = {(A, S), (C, S), (D, C), (B, A), (E, B)};

[0067] g) After the above operations, all elements in C have been moved to V, and (A, S), (C, S), (D, C), (B, A), (E, B) form a spanning tree.

[0068] Preferably, intra-cluster transmission: a strategy of directly connecting nodes that have not joined the CH set to the nearest CH; or a method of directly connecting nodes that have not yet joined the cluster head set to the nearest cluster head node.

[0069] The beneficial effects of this invention are:

[0070] 1. Based on the White Whale Optimization (BWO) algorithm, a t-distributed cosine optimization algorithm (tCBWO) is proposed. tCBWO enhances the global exploration capability of BWO by introducing a cosine dynamic boundary strategy, enabling a broader exploration of the search space. Furthermore, SAOA enhances the local exploitation capability of BWO through a t-distributed dynamic factor, which helps the algorithm converge to the optimal solution faster and more accurately. The improved algorithm is tested using CEC2017 under different dimensions. The test results show that SAOA improves convergence and stability compared to other algorithms across different functions and dimensions.

[0071] 2. This invention proposes a novel WSN clustering routing algorithm, tCBWO-DPR. During cluster head election, a fitness function based on node capacity and location relationships is introduced, and the tCBWO algorithm is used to select the cluster head. Furthermore, considering the energy consumption characteristics of WSNs, a distance threshold is introduced to improve the performance of the Prim algorithm. Ablation and comparative experiments verify the algorithm's performance, showing that the tCBWO-DPR algorithm outperforms other algorithms in terms of stability and convergence during the cluster head election process. This algorithm has certain practical application value and can provide new ideas and methods for WSN research and application.

[0072] The improved algorithm comprehensively considers multiple factors such as the positional relationships between clusters and node energy to construct a clustering model; the data transmission stage comprehensively considers computational complexity and the positional relationships of nodes. However, relying solely on traditional heuristic algorithms results in long running times and excessive computational resource consumption. To address this issue, future research will explore deep learning techniques, such as GNN and CNN, to reduce the overall computational load and thus improve network reliability. Attached Figure Description

[0073] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments will be briefly introduced below. Obviously, the drawings described below are only 10 of the drawings in the present invention. For those skilled in the art, other drawings can be obtained from these drawings without creative effort.

[0074] Figure 1 This is a schematic diagram of clustered routing according to an embodiment of the present invention;

[0075] Figure 2 This is a schematic diagram illustrating the effect of the degree of freedom df on the t-distribution according to an embodiment of the present invention;

[0076] Figure 3 This is a flowchart of the tCDWO-DPR algorithm according to an embodiment of the present invention;

[0077] Figure 4 This is a schematic diagram illustrating the relationship between energy consumption per bit of data transmitted by a node in an embodiment of the present invention and distance and hop count;

[0078] Figure 5 This is a schematic diagram illustrating an improved DPR algorithm according to an embodiment of the present invention;

[0079] Figure 6 This is a schematic diagram of the node distribution according to an embodiment of the present invention;

[0080] Figure 7 This is a schematic diagram of node survival in an embodiment of the present invention ((a) ablation experiment, (b) comparative experiment);

[0081] Figure 8 The diagram shows the change in the remaining energy of the node in an embodiment of the present invention ((a) ablation experiment, (b) comparative experiment);

[0082] Figure 9 This is a schematic diagram of the nodal energy variance in an embodiment of the present invention ((a) ablation experiment, (b) comparative experiment);

[0083] Figure 10 This is a schematic diagram of the data reception volume in an embodiment of the present invention ((a) ablation experiment, (b) comparative experiment); Detailed Implementation

[0084] To enhance understanding of the present invention, the invention will be further described in detail below with reference to the accompanying drawings and embodiments. These embodiments are only used to explain the invention and do not limit the scope of protection of the invention.

[0085] Example

[0086] 1. Model Declaration

[0087] 1.1. Network Model

[0088] In wireless sensor networks, sensor nodes are typically deployed within a designated monitoring area, communicating with each other through an ad-hoc network and forwarding data to a base station. The base station then transmits the received data to a data center via the internet. Over long distances, long-distance transmission consumes more energy from sensor nodes, leading to a decrease in network lifetime. A hierarchical routing model, as shown in the figure, divides the nodes within the monitoring area into clusters. Nodes within each cluster forward information to the base station through a cluster head node, thereby achieving balanced energy consumption and extending the network's lifespan.

[0089] Clustering routing model for wireless sensor networks, such as Figure 1 As shown, hierarchical routing divides the network into multiple clusters and uses cluster head rotation to ensure balanced energy utilization and improve WSN efficiency. Nodes are divided into multiple units, and nodes within each unit merge data within the unit through the cluster head node before sending it to the base station, thereby reducing the overall network energy consumption.

[0090] In this invention, the sensor network model is defined as follows: ① The monitoring area is a regular rectangular planar area; ② Nodes are static nodes, randomly deployed, and each node has a unique ID; ③ All nodes communicate wirelessly and can autonomously control their transmission power; ④ The energy of the base station is infinite. 1.2. First-order radio transmission model

[0091] During the operation of a wireless sensor, the energy consumption for data transmission is much greater than that for data acquisition. For ease of later calculation, only the energy consumption for data transmission will be considered. During data transmission, the wireless sensor's radio unit directly consumes the sensor's energy. Its radio transmission unit is divided into a data transmitting unit and a data receiving unit. In the transmitting unit, the transmission energy consumption is related to the distance, and its energy consumption expression is as follows:

[0092] During wireless sensor operation, the energy consumed for data transmission is typically much higher than that for data acquisition. For ease of subsequent calculations, we will only consider the energy consumption for data transmission. During data transmission, the radio unit directly consumes the sensor's energy. This radio transmission unit is divided into data transmitting and data receiving units. In the data transmitting unit, transmission energy consumption is positively correlated with transmission distance, conforming to a first-order radio transmission model. The energy consumption of the transmission circuit can be expressed by Equation 1:

[0093] During data packet transmission, the sensor's radio unit directly consumes energy, and this energy consumption is significantly greater than the monitoring energy consumption. The transmission unit is divided into a data sending unit and a data receiving unit. In the sending unit, the transmission energy consumption is distance-dependent, and its energy consumption expression is shown in Equation 1:

[0094]

[0095] Among them, E elec E represents the energy consumed by the transmitting circuit to process each bit of data. amp Where is the amplification factor of the transmitting amplifier, k is the size of the transmitted data packet, and d is the transmission distance of the data packet. This represents the maximum transmission distance.

[0096] In the receiving unit, the transmission energy consumption is related to the size of the received data packet, and its receiving energy consumption expression is shown in Equation 2:

[0097] E RX (k)=kE elec (2)

[0098] Where E elec The energy consumed by the receiving circuit to process each bit of data.

[0099] 2.tCBWO: Improved Beluga Optimization Algorithm

[0100] The Beluga Optimization Algorithm is a novel heuristic algorithm. It is derived from simulating the behavior of beluga whales. This algorithm combines numerous advantages, reducing parameter control complexity through adaptive parameters, and can be widely applied to both single-modal and multi-modal optimization problems. The algorithm mainly consists of three parts: a global exploration phase, a local exploration phase, and a fall phase.

[0101] 2.1. Original Beluga Optimization Algorithm

[0102] 2.1.1. Initialization of the whale pod

[0103] In the early stages of algorithm execution, randomly generating a beluga whale population ensures global search capability in the solution space, while the development phase controls local search capability within the solution space. By incorporating the whale's crash probability, the whale's current location can be altered.

[0104] The beluga optimization algorithm initially generates an initial whale population X by randomly generating the following:

[0105]

[0106] Where n is the population size of beluga whales, d is the dimension of the variable space, and for all beluga whales, the corresponding fitness value is:

[0107]

[0108] Whether a whale enters a phase of global exploration or localized development depends on the balance factor B. f B f The expression is as follows:

[0109]

[0110] Where t is the current iteration number, T is the maximum iteration number, and B0 is a random number in the interval (0, 1).

[0111] When B f When the value is greater than 0.5, the whale enters the global development stage; otherwise, it enters the local development stage.

[0112] 2.1.2. Global Exploration

[0113] The BWO algorithm incorporates the swimming behavior of beluga whales in different postures during the global exploration phase. Two beluga whales may swim synchronously or in a mirror manner. Based on these characteristics, the position update strategy for global search in BWO is shown in Equation 6.

[0114]

[0115] in, Let p be the new coordinates of the i-th beluga whale in the j-th dimension. j (j = 1, 2, 3, ..., d) is a random number selected in d dimensions. r1 and r2 are random numbers within the interval (0, 1).

[0116] 2.1.3. Local Development

[0117] The development phase of BWO was inspired by the hunting behavior of beluga whales. Beluga whales cooperate in hunting by moving based on the location of nearby beluga whales. Therefore, beluga whales hunt by sharing their location information. In the development phase of BWO, a Levy flight strategy was adopted to improve the algorithm's convergence performance (by assuming that beluga whales can use the Levy flight strategy to capture prey), where the position update formula in the local development phase is shown in Equation 7.

[0118]

[0119] in, Let i represent the next generation individual of the i-th solution. This represents the current optimal solution. The solution is randomly selected. This represents the i-th solution, where r3 and r4 are random numbers within the interval (0,1), and C1 is the adaptive balance factor, where C1 = 2r4(1-T / T) max L F This represents the Levy flight factor.

[0120] 2.1.4. Whale Fall Stage

[0121] During their migrations and foraging, beluga whales are disturbed by other predators, causing them to shift their locations. This predation can cause beluga whales to fall, and these fallen whales can attract other creatures to breed in those areas.

[0122] To simulate whale fall behavior during the iterative process, the BWO algorithm randomly selects a subset of beluga whales from the population with a certain probability to fall, thus simulating subtle changes within the population. The BWO algorithm sets the fall position as shown in Equation 8.

[0123]

[0124] Where r5, r6, and r7 are random numbers within the interval [0, 1]. step The step size for the beluga whale's fall is related to the number of iterations, and the calculation formula is shown in Equation 9.

[0125]

[0126] Where C2 is the step size factor between the probability of whale pod crashes and the population size, bwo sets C2 = 2nW f ub and lb represent the upper and lower bounds of the variable space, respectively. The probability of a whale pod crashing.

[0127] The probability of the whale falling decreased from 0.1 in the initial iteration to 0.05 in the last iteration, indicating that the risk factor of the beluga whale also decreased when it approached a food source during the optimization process.

[0128] 2.2. Improved Beluga Optimization Algorithm

[0129] The standard white whale optimization algorithm determines the development status in the initial stage by establishing linear boundary conditions. However, the original white whale optimization algorithm does not have an even distribution between the global exploration phase and the local development phase, and it spends most of its time in the development phase, which is fatal to the algorithm as it prematurely gets trapped in local optima. To overcome this phenomenon, this invention proposes a dynamic boundary adjustment strategy based on a cosine factor to improve the algorithm's global exploration performance.

[0130] 2.2.1. Boundary Adjustment Strategy Based on Cosine Factor

[0131] To overcome the weakness of the standard white whale optimization algorithm in global exploration, this paper proposes to improve the algorithm by utilizing a cosine factor boundary strategy, and optimizes the algorithm accordingly. The optimized B... f The calculation formula is shown in Equation 10:

[0132]

[0133] Among them, CB f The balancing factor is based on the cosine factor. max and min are the maximum and minimum values ​​of the balancing factor, respectively. By using the maximum and minimum balancing factors, it can be ensured that a portion of the elements are being developed or explored, whether in the early or late stages of the algorithm. In this paper, max = 0.9 and min = 0.1 are set.

[0134] When random number B0 > CB f When the random number B0 ≤ CB, the algorithm enters the global exploration phase; f At this point, the algorithm enters the local development phase. The improved global exploration phase and the local development phase are more evenly distributed, as shown in Figure b, to facilitate finding the global optimum more quickly.

[0135] 2.2.2. Random perturbation factor based on t-distribution

[0136] In the local development of the BWO algorithm, the Levy flight strategy was used to escape local optima. However, the Levy flight strategy resulted in the same escape probability in both the early and late stages of the algorithm, failing to fully consider the impact of iteration updates on the probability. Therefore, we introduced the Student's t-distribution to optimize the algorithm against local optima.

[0137] The t-distribution, also known as the student distribution, has a distribution curve that is closely related to the degree of freedom. As shown in the figure, when the degree of freedom df is small, the distribution curve is flatter. When the degree of freedom df equals 1, the t-distribution curve can approximate the Cauchy distribution curve. The greater the degree of freedom of the t-distribution, the closer its distribution curve is to the standard normal distribution curve. The probability density of the student t-distribution Z ~ t(n) with n degrees of freedom is shown in Equation 11.

[0138]

[0139] Where Γ(x) is the gamma function,

[0140] Based on this principle, and utilizing the influence of degrees of freedom on the t-distribution, a new local exploitation strategy was established:

[0141]

[0142] in, Let i represent the next generation individual of the i-th solution. This represents the current optimal solution. The solution is randomly selected. This represents the i-th solution, where r3 and r4 are random numbers within the interval (0,1), and C1 is the adaptive balance factor, where C1 = 2r4(1-T / T) max Let t(T) follow the student distribution Z~t(T).

[0143] Algorithm pseudocode

[0144]

[0145]

[0146]

[0147] 3.tCBWO-DPR

[0148] In this chapter, combining the network characteristics of WSNs, we will leverage the advantages of metaheuristic tCBWO and classic heuristic prim to plan the network and improve its performance; we call this tCBWO-DPR. Its general process is as follows: Figure 1 As shown.

[0149] In Section 3.1, the strong stability of the tCBWO algorithm is fully utilized to elect the cluster head. A fitness function is established by combining node energy and node position relationships, and the tCBWO algorithm is used to select the node that is more suitable to be elected as the cluster head.

[0150] Section 3.2 improves the Prim algorithm by incorporating the characteristics of WSN networks. The implementation process of the inter-cluster network is described, and the Prim algorithm is improved using a distance factor.

[0151] Section 3.3 describes the process of establishing inter-cluster routes, where ordinary nodes join a cluster by determining their positional relationship with the cluster head.

[0152] Section 3.4 provides a theoretical analysis of the algorithm's complexity.

[0153] 3.1. Election of Cluster Leaders

[0154] Based on the remaining energy information of nodes and the positional relationships between nodes, and combined with an optimization algorithm, the cluster head for the next stage is selected. The optimization function established for cluster head election in this invention is as follows:

[0155] Fitness=αg1(x)+(1-α)g2(x) (13)

[0156] Where α is the variable weight parameter. g1 and g2 represent the energy model and positional relationship, respectively.

[0157] 3.1.1. Node Energy g1

[0158] g1 is the energy model. Since energy directly affects the lifetime of the sensor network, using nodes with more remaining energy as cluster heads can better balance the network's energy consumption. The expression for g1 is as follows:

[0159]

[0160] Among them, E n Let r be the remaining energy of the nth node, and r be the current round number.

[0161] 3.1.2. Node positional relationship g2

[0162] The location of nodes affects data transmission. When the distance between nodes exceeds a certain threshold, the energy required to transmit data packets exhibits a fourth-power relationship with the distance between nodes, meaning it increases dramatically with increasing distance. Therefore, the coverage of network nodes by cluster heads is used to promote a more balanced network. The expression is shown in Equation 15:

[0163]

[0164] Among them, dist(CH) i ,n) is the distance from cluster head j to neighboring node i, and d0 is the effective coverage area of ​​the cluster head node's signal, which is set to in this paper. N is the number of cluster heads, and M is the number of network nodes. This represents the number of nodes that the cluster head can effectively cover.

[0165] 3.2. Inter-cluster transmission

[0166] 3.2.1. Relationship between path hops and distance

[0167] In wireless sensor networks, the data power transmission model can be illustrated in the figure. The figure shows that when the transmission distance is less than 104.4m, direct data transmission can effectively reduce network power consumption. When the node distance is between 104.4 and 192.6 meters, single-hop transmission is suitable; when the physical distance between nodes is greater than 192.6 meters, multi-hop transmission is suitable.

[0168] To further balance network energy consumption, this section will elaborate on inter-cluster transmission methods. This invention is based on an improved Prim algorithm to adapt to the characteristics of Wireless Sensor Networks (WSNs). While the Prim algorithm guarantees the minimum transmission path at each step, it causes data from all network nodes to converge to the node closest to the base station, ignoring the fact that multiple hops waste network energy. Therefore, this invention combines the Prim algorithm with the transmission characteristics of WSNs to establish an inter-cluster path planning algorithm based on the Prim algorithm—the D-Prim algorithm—to overcome the aforementioned problems.

[0169] 3.2.2. Classic Prim Algorithm

[0170] Prim's algorithm is a classic algorithm in graph theory used to find the overall shortest path in a weighted graph. This algorithm employs a greedy strategy to find the optimal path. It provides a simple and fast way to obtain the overall shortest path in a dense network.

[0171] However, since the data of the end node of WSN is forwarded by the upper-level node, and the algorithm tends to treat the node that is closer to the source node as the sink node, the node closest to the source node bears too high energy consumption, which is fatal to the stability of the network and will seriously affect the stability of the network.

[0172] 3.2.3. Improved Prim Algorithm

[0173] To overcome the limitation of the classic Prim algorithm, which treats the distance from the starting node as the new sink node, we propose an improved Prim algorithm based on distance factors. According to the network energy consumption model, when a node is less than 104.6m from the base station, direct communication with the base station can effectively reduce the overall network overhead. Therefore, in the inter-cluster communication phase, cluster head nodes less than 104.4m from the base station communicate directly with the base station. In subsequent phases, we continue to use the Prim algorithm to construct inter-cluster communication. We call this the distance-factor-based Prim algorithm (DPR), and its specific implementation process is as follows:

[0174] Assume the distribution and positional relationship of the cluster heads are as follows: Figure 5 As shown in (a), s is the base station, and A, B, C, E, and D are candidate cluster heads. The execution flow of its Dprim algorithm is as follows:

[0175] h) Construct candidate cluster heads C = {A, B, C, E, D, S}, visited set V = {}, and path R = {}

[0176] i) Starting from base station S, remove base station S from the candidate set C and add it to V. C = {A, B, C, E, D}, V = {S}, R = {}.

[0177] j) Find candidates whose distance s is less than d from the candidate set. max Nodes A and C are selected, and paths (A, S) and (C, S) are constructed with S respectively. These paths are then added to R. A and C are removed from the candidate set C and added to the visited set V. Figure 5 As shown in (b). C = {B, E, D}, V = {S, A, C}, R = {(A, S)},

[0178] (C, S)}

[0179] k) Starting from the visited set V, the paths to the candidate set C are (A, B), (C, D), and (A, D). Among them, the path (C, D) is the shortest and can form a minimum spanning tree. Therefore, (D, C) is added to path R, D is removed from the candidate set C, and D is added to V. Figure 5 As shown in (c). C = {B, E}, V = {S, A, C, D}, R = {(A, S), (C, S), (D, C)}

[0180] l) Starting from the visited set V, the paths to the candidate set C are (A, B), (D, B), and (E, D). Among them, the path (A, B) is the shortest and can form a minimum spanning tree. Therefore, (B, A) is added to path R, B is removed from the candidate set C, and B is added to V. Figure 5 As shown in (d). C = {E}, V = {S, A, B, C, D}, R = {(A, S), (C, S), (D, C)},

[0181] (B, A)}

[0182] m) Starting from the visited set V, there are paths (B, E) and (D, E) to reach the candidate set C. The path (B, E) is the shortest and can form a minimum spanning tree. Therefore, (E, B) is added to path R, E is removed from candidate set C, and E is added to V. Figure 5(e) is shown. C={}, V={S, A, B, C, D, E}, R={(A, S), (C, S), (D, C), (B, A), (E, B)}

[0183] After the above operations, all elements in C have been moved to V, and (A, S), (C, S), (D, C), (B, A), (E, B) form a spanning tree, as shown below. Figure 5 As shown in (f).

[0184] Improved Prim algorithm pseudocode:

[0185]

[0186]

[0187] 3.3. Intra-cluster transmission

[0188] Considering the energy consumption model of WSNs, it is known that the closer the nodes are, the lower the cost of energy transmission. Leveraging this characteristic, we adopted a strategy of directly connecting nodes not yet in the clustering set (CH) to the nearest CH, which effectively reduces node energy consumption. This approach not only reduces the overall energy consumption of the network but also avoids unnecessary transmissions, minimizing the chance of collisions and thus extending the network's lifetime. Furthermore, this technique can be seamlessly integrated with various clustering algorithms to further improve network energy efficiency.

[0189] According to network energy consumption models, the transmission energy consumption between nodes in a wireless sensor network decreases as the distance between nodes decreases. Therefore, we can effectively reduce node energy consumption by directly connecting to the nearest cluster head node that is not yet part of the cluster head set. This method not only maximizes the utilization of the physical distance between nodes but also avoids unnecessary energy waste. Furthermore, this technique can be seamlessly integrated with various clustering algorithms to further improve network energy efficiency.

[0190] 3.4. Algorithm Complexity Analysis

[0191] In the cluster head election process, the tCBWO algorithm is used to evaluate the evaluation function of the cluster head node. The tCBWO algorithm is an improved algorithm based on BWO. Its computational complexity for the cluster head election process is moderate. The time complexity of the cluster head election process is O(pop size * iterations * n), where popsize is the set size of the whale pod, iterations is the number of iterations of the whale pod, and n is the number of cluster head candidates. This algorithm involves several mathematical operations, including the positive selection function, random number generation, and array operations. Multiple nested loops are used. For medium-sized NP problems, this algorithm is efficient and feasible.

[0192] During inter-cluster transmission, an improved DPrim algorithm is used to establish inter-cluster transmission paths. By introducing a distance factor, data at the endpoints are prevented from converging at the same node. The computational complexity of inter-cluster routing is moderate. The computational complexity of inter-cluster routing is O(n²), where n is the size of the cluster head candidate set. In WSN, the number of cluster head nodes in hierarchical routing typically accounts for 10%-20% of all nodes, so its complexity is actually not large. Compared to the tCBWO algorithm, its computational complexity is smaller, making this algorithm feasible.

[0193] 3.4.1.tCBWO Test Analysis

[0194] This invention verifies the performance of the tCBWO algorithm, and the test function is selected from CEC2017[]. This benchmark function is often used for convergence performance analysis of optimization algorithms. In CEC2017, F1-F3 are unimodal functions, F4-F10 are simple multimodal functions, F11-F20 are mixed functions, and F21-F30 are combined functions. The test interval is [-100, 100], and the test dimensions are 10, 30, 50, and 100. The test difficulty increases sharply with the increase of dimension. Its optimal value is min(F i (x))=100i, where i is the function number.

[0195] The proposed algorithm tCBWO was compared with algorithms HHO, SP, PSO, AOA, KHO, and the original algorithm BWO. Each algorithm was evaluated 25,000 times (50*500) on the benchmark function and repeated 50 times. The exploration space for all algorithms was [-100, 100]. Three sets of experiments were designed with problem space dimensions of 10, 30, and 50, respectively. The parameters of each algorithm are shown in Table 1.

[0196] Table 1 Algorithm Parameter Settings

[0197]

[0198] Tables 2-4 reflect the convergence capabilities of various optimization functions under different functions and dimensions. The mean represents the average level across fifty tests, and std represents the stability level during testing. Lower values ​​for both are better. Bold text indicates the optimal solutions of several algorithms under the same function and dimension. Table 2 shows the 10-dimensional results for the CEC2017 test functions. The tCBWO algorithm outperforms other algorithms in both stability and convergence. Table 3 shows the 30-dimensional results for the CEC2017 test functions. The tCBWO algorithm outperforms other algorithms in both stability and convergence. Table 4 shows the 50-dimensional results for the CEC2017 test functions. The SPO algorithm outperforms other algorithms in convergence, but also in convergence stability, with its convergence capability second only to the SPO algorithm.

[0199] Table 2: CEC2017 dim=10

[0200]

[0201]

[0202]

[0203] Table 3: CEC2017 test dim=30

[0204]

[0205]

[0206] Table 4: CEC2017 test dim=50

[0207]

[0208]

[0209] 3.5.tCBWO-DPR Test

[0210] 3.5.1. Evaluation Indicators

[0211] To evaluate the performance of the SAOA algorithm, this paper conducts experimental analysis on the KSAOA clustering routing algorithm, analyzing the impact of each contribution of the paper on the WSN network, as well as the impact of network parameters on the WSN. The meanings of the evaluation metrics are as follows:

[0212] 1) FND: First Node Dead. This parameter is an important parameter for evaluating network stability. The death of a node will cause structural changes in the monitoring system. Theoretically, the larger the FND, the better.

[0213] 2) HND: Half of Nodes Dead. This parameter is an important parameter for evaluating network lifetime and network stability. When half of the nodes die, the monitoring network still has a certain network monitoring capability. Theoretically, the higher the value, the better. The smaller the difference between HND and FND, the better, indicating that the network is more stable and reliable.

[0214] 3) LND: LastNode Dead. This parameter is an important indicator for evaluating network lifetime. When the last node dies, the WSN network's lifecycle ends, reflecting the complete loss of monitoring capabilities. The larger this value, the better, and the smaller the difference between it and FND, the better.

[0215] 4) Node energy variance: This parameter directly reflects the load balance of the network. Its magnitude directly reflects the energy comparison relationship between nodes. The larger the value, the more unbalanced the network load, and the smaller the value, the more balanced the network load.

[0216] 5) Base station received data volume: This parameter reflects the total amount of data received by the WSN network from sensor nodes during its lifecycle. The more data received, the richer the data that can be received. Therefore, the larger the amount of data received, the better.

[0217] To verify the performance of the tCBWO-DPR algorithm, this invention was compared with other algorithms, including the LEACH algorithm, HPR-LEACH, and HFAPSO algorithm.

[0218] 3.5.2. Parameter Settings

[0219] Table 5 Simulation Parameter Settings

[0220]

[0221]

[0222] To verify the algorithm's performance, ablation experiments and comparative experiments were designed. In the ablation experiments, the proposed tCBWO-DPR was compared and analyzed with BWO-DPR and tCBWO-PR. BWO-DPR consists of the original BWO and the improved Prim algorithm DPR, while tCBWO-PR is a clustering routing algorithm composed of the improved tCBWO and the original Prim algorithm. In the comparative experiments, the invention was combined with LEACH, HFAPSO, and HPR-LEACH algorithms for simulation verification. In this experiment, 200 nodes were randomly deployed within a 300*300 area, with the base station located at the network vertex (0,0). The initial node distribution is as follows. Figure 6 As shown.

[0223] 3.5.3. Node Survival Status

[0224] Figure 7 Based on node survival data in the ablation experiments, the tCBWO algorithm achieved FND, HND, and LND distributions of 94, 188, and 459 rounds, respectively. Compared to other algorithms, tCBWO demonstrated a significant improvement in stability. FND improved by 34 and 31 rounds compared to BWO-DPR and tCBWO-PR, respectively. HND improved by 16 and 23 rounds compared to BWO-DPR and tCBWO-PR, respectively. LND improved by 120 and 145 rounds compared to BWO-DPR and tCBWO-PR, respectively. Therefore, this algorithm significantly improves network performance.

[0225] Figure 7 (b) Comparing node survival in the experiments, the tCBWO algorithm maintains a stable network duration of 94 rounds, demonstrating better stability compared to the other four algorithms. FND improves network survival by 90 rounds, 44 rounds, 48 ​​rounds, and 36 rounds compared to the LEACH, HPR-LEACH, HFAPSO, and SCA-Lévy algorithms, respectively. Therefore, this algorithm significantly improves the lifespan of wireless sensor networks compared to existing algorithms.

[0226] 3.5.4. Changes in Node Remaining Energy

[0227] The average remaining energy curve of each node allows us to observe the overall energy changes in the network and directly observe the trend of energy changes. Its characteristics can be used for analysis; for example, changes in average remaining energy... Figure 8 As shown in the figure, in the ablation experiment, the tCBWO-DPR algorithm exhibited a more gradual decrease in average energy compared to the other two algorithms. With the same number of rounds, tCBWO-DPR had the highest remaining energy.

[0228] In the comparative experiments, the remaining energy slope of the tCBWO algorithm was significantly lower than that of the other three algorithms in the initial stage. Within 200 rounds, the average remaining energy of tCBWO was higher than the other three algorithms. Furthermore, the energy decrease was relatively gradual and showed a linear decreasing trend, indicating that the network's energy consumption was relatively more balanced. Figure 8 (b) LEACH shows a non-linear downward trend in the medium term, reflecting that the network load is very unstable.

[0229] 3.5.5. Node Energy Variance

[0230] Depend on Figure 9(a) Ablation experiments show that although the maximum variance of the tCBWO algorithm is improved compared to the other two algorithms, it is similar to the first two algorithms in the initial stage, and the maximum energy variance of the nodes shifts to the right, which to a limited extent delays the network's death time.

[0231] Depend on Figure 9 (b) Comparison shows that among the five algorithms, tCBWO-DPR's node energy variance is closer to the right. Compared to algorithms like LEACH, the maximum node energy variance of this algorithm is 0.0169, while LEACH's maximum node energy variance is 0.0333. The decrease in node energy variance compared to LEACH indicates that this algorithm significantly balances network energy consumption, delays the premature death of some nodes, and improves network stability. This verifies the effectiveness of this algorithm in balancing node load.

[0232] 3.5.6. Data Transmission Status

[0233] Regarding data transmission, this invention uses the data received at the receiving station as a reference. Figure 10 (a) In the ablation experiment, the total amount of data received by the tCBWO-DPR algorithm was increased by 10.55 MB and 13.14 MB compared to the BWO-DPR and tCBWO-PR algorithms, respectively. Both improvements to the algorithm are effective.

[0234] Combination Figure 10 (b) The comparative experiment shows that, throughout the entire network lifecycle, tCBWO, with a data fusion rate of 0.6, received more data than the other three types, with a total data transmission volume of 89.34MB. This is an improvement of 40.49MB, 21.94MB, 18.81MB and 18.41MB compared to LEACH, HPR-LEACH, HFAPSO and SCA-Lévy, respectively, effectively improving network efficiency.

[0235] 4. Summary

[0236] In this invention, an improved WSN clustering routing algorithm based on the beluga optimization algorithm is proposed to improve the energy utilization efficiency of sensor networks.

[0237] First, based on the White Whale Optimization (BWO) algorithm, a t-distributed cosine optimization algorithm (tCBWO) is proposed. tCBWO enhances the global exploration capability of BWO by introducing a cosine dynamic boundary strategy, enabling a broader exploration of the search space. Furthermore, SAOA enhances the local exploitation capability of BWO through a t-distributed dynamic factor, which helps the algorithm converge to the optimal solution faster and more accurately. The improved algorithm is tested using CEC2017 under different dimensions. The test results show that SAOA improves convergence and stability compared to other algorithms across different functions and dimensions.

[0238] Secondly, this invention proposes a novel WSN clustering routing algorithm, tCBWO-DPR. During cluster head election, a fitness function based on node capacity and location relationships is introduced, and the tCBWO algorithm is used to select the cluster head. Furthermore, considering the energy consumption characteristics of WSNs, a distance threshold is introduced to improve the performance of the Prim algorithm. Ablation and comparative experiments verify the algorithm's performance, showing that the tCBWO-DPR algorithm outperforms other algorithms in terms of stability and convergence during the cluster head election process. This algorithm has certain practical application value and can provide new ideas and methods for WSN research and application.

[0239] The improved algorithm comprehensively considers multiple factors such as the positional relationships between clusters and node energy to construct a clustering model; the data transmission stage comprehensively considers computational complexity and the positional relationships of nodes. However, relying solely on traditional heuristic algorithms results in long running times and excessive computational resource consumption. To address this issue, future research will explore deep learning techniques, such as GNN and CNN, to reduce the overall computational load and thus improve network reliability.

[0240] The technical features of the above embodiments can be combined in any way. For the sake of brevity, not all possible combinations of the technical features in the above embodiments are described. However, as long as there is no contradiction in the combination of these technical features, they should be considered to be within the scope of this specification.

[0241] The embodiments described above are merely illustrative of several implementation methods of this application, and while the descriptions are relatively specific and detailed, they should not be construed as limiting the scope of the invention patent. It should be noted that those skilled in the art can make various modifications and improvements without departing from the concept of this application, and these all fall within the protection scope of this application. Therefore, the protection scope of this patent application should be determined by the appended claims.

Claims

1. A wireless sensor network clustering routing based on an improved white whale optimization algorithm, characterized in that, The network model includes: hierarchical routing divides the network into multiple clusters and uses cluster head rotation to ensure balanced energy utilization and improve WSN efficiency; nodes are divided into multiple units, and the nodes in each unit merge the data within the unit through the cluster head node and then send it to the base station; First-order radio transmission model: During the operation of the wireless sensor, the data transmission energy consumption only considers the data transmission energy consumption; Energy consumption expression for the transmitting unit: The energy consumed by the transmitting circuit to process each bit of data. This is the amplification factor of the transmitting amplifier. It is the amplified energy of free space. For the size of the transmitted data packets, The transmission distance of the data packet. Maximum transmission distance; Energy consumption expression for receiving unit: in The energy consumed by the receiving circuit to process each bit of data; Beluga optimization algorithm: Initialization of the whale pod: Initially, an initial whale population is generated randomly. : in, For the population size of beluga whales, Let be the dimension of the variable space, and for all beluga whales, the corresponding fitness value is: Whether a whale enters a phase of global exploration or partial development depends on a balance factor. , The expression is as follows: in, This represents the current iteration number. This represents the maximum number of iterations. A random number in the interval (0, 1); when When the whale is in a certain state, it enters the overall development phase; otherwise, it enters the partial development phase. Global exploration: The position update strategy for global search defined in this algorithm is as follows: in, Let the i-th beluga whale have the new coordinates in the j-th dimension; It is a random number selected in d dimensions; and It is an interval Random numbers within; Partial development: To improve the convergence performance of the algorithm, a Levy flight strategy is employed, where the position update formula during the local development phase is as follows: in, This represents the next generation individual of the i-th solution. This represents the current optimal solution. The solution is randomly selected. This represents the i-th solution. and It is an interval Random numbers within, For adaptive balance factor, where ; Indicates the Levy flight factor; Whale fall phase: The position of the whale after it falls is as follows: in, and For interval Random numbers within; This represents the step size during the beluga whale's fall, and its value depends on the number of iterations. in, bwo sets the step size factor between the probability of a whale pod crashing and the pod size. ; ub and lb represent the upper and lower bounds of the variable space, respectively; the probability of a whale pod falling. .

2. The wireless sensor network clustering routing based on the improved white whale optimization algorithm according to claim 1, characterized in that: The algorithm was improved and optimized by utilizing a cosine factor boundary strategy; the optimized algorithm... The calculation formula is as follows: in, This is a balance factor based on the cosine factor; and These are the maximum and minimum values ​​of the balance factor, respectively, set in the text. , ; When random number When the random number is reached, the algorithm enters the global exploration phase; when the random number is reached... At this point, the algorithm enters the partial development stage; Random perturbation factor based on t-distribution During the local development of this algorithm, the student t-distribution was introduced to optimize the algorithm from getting trapped in local optima; When the degrees of freedom df are small, the distribution curve is flatter. When the degrees of freedom df equals 1, the t-distribution curve can approximate the Cauchy distribution curve. The greater the degrees of freedom of the t-distribution, the closer its distribution curve is to the standard normal distribution curve. The probability density of the student t-distribution Z~t(n) with n degrees of freedom is as follows: in, For gamma function, , ; By utilizing the influence of degrees of freedom on the t-distribution, a new local exploitation strategy was established: in, This represents the next generation individual of the i-th solution. This represents the current optimal solution. The solution is randomly selected. Show the i-th solution, and It is an interval Random numbers within, For adaptive balance factor, where ; The distribution follows the student distribution Z~t(T).

3. The wireless sensor network clustering routing based on the improved white whale optimization algorithm according to claim 1, characterized in that: A fitness function was established by combining node energy and node position relationship, and the tCBWO algorithm was used to select the node more suitable to be elected as the cluster head; the prim algorithm was improved by using the distance factor; ordinary nodes were added to the cluster by judging their position relationship with the cluster head; Based on the remaining energy information of the nodes and the positional relationships between the nodes, and combined with the optimization algorithm, the cluster head for the next stage is selected. The optimization function established for cluster head election is as follows: in, For the weight parameters of the variables, and These represent the energy model and the positional relationship, respectively; energy model The expression is as follows: in, For the first The remaining energy of each node. This is the current round number; Combining cluster head coverage of network nodes to promote a more balanced network, and considering node position relationships. The expression is as follows: in, Let be the distance from cluster head j to neighbor node i. The effective coverage area of ​​the cluster head node signal is set in this paper as N, where N is the number of cluster heads and M is the number of network nodes. This represents the number of nodes that the cluster head can effectively cover.

4. The wireless sensor network clustering routing based on the improved white whale optimization algorithm according to claim 1, characterized in that: Inter-cluster transfer: The relationship between path hop count and distance: When the transmission distance is less than 104.4m, direct data transmission can effectively reduce network energy consumption; when the node distance is between 104.4 and 192.6m, single-hop transmission is suitable; when the physical distance between nodes is greater than 192.6m, multi-hop transmission is suitable.

5. The wireless sensor network clustering routing based on the improved white whale optimization algorithm according to claim 1, characterized in that: During the inter-cluster communication phase, cluster head nodes less than 104.4 km from the base station communicate directly with the base station. In subsequent phases, the Dprim algorithm is used to continue constructing inter-cluster communication, and the specific implementation process is as follows: Let s be the base station, and A, B, C, E, and D be the candidate cluster heads; the execution flow of its Dprim algorithm is as follows: Construct candidate cluster heads C={A, B, C, E, D, S}, visited set V={}, and path R={}; Starting from base station S, remove base station S from candidate set C and add it to V; C={A, B, C, E, D}, V={S}, R={}; Find candidates whose distance s is less than s from the candidate set. Nodes A and C are selected, and paths (A, S) and (C, S) are constructed with S respectively, and added to R. A and C are removed from the candidate set C and added to the visited set V; C = {B, E, D}, V = {S, A, C}, R = {(A, S), (C, S)}; Starting from the visited set V, the paths to the candidate set C are (A, B), (C, D) and (A, D). Among them, the path (C, D) is the shortest and can form a minimum spanning tree. Therefore, (D, C) is added to the path R, D is removed from the candidate set C, and D is added to V; C = {B, E}, V = {S, A, C, D}, R = {(A, S), (C, S), (D, C)}; Starting from the visited set V, the paths to the candidate set C are (A, B), (D, B), and (E, D). Among them, the path (A, B) is the shortest and can form a minimum spanning tree. Therefore, (B, A) is added to the path R, B is removed from the candidate set C, and B is added to V; C = {E}, V = {S, A, B, C, D}, R = {(A, S), (C, S), (D, C), (B, A)}; Starting from the visited set V, there are two paths to the candidate set C: (B, E) and (D, E). The path (B, E) is the shortest and can form a minimum spanning tree. Therefore, (E, B) is added to the path R, and E is removed from the candidate set C and added to V. C = {}, V = {S, A, B, C, D, E}, R = {(A, S), (C, S), (D, C), (B, A), (E, B)}. After the above operations, all elements in C have been moved to V, and (A, S), (C, S), (D, C), (B, A), (E, B) form a spanning tree.

6. The wireless sensor network clustering routing based on the improved white whale optimization algorithm according to claim 1, characterized in that: Intra-cluster transfer: The strategy of directly connecting nodes that have not joined the CH set to the nearest CH; the method of directly connecting nodes that have not yet joined the cluster head set to the nearest cluster head node.

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