Power Transmission Network Optimization Strategy Based on Random Fractal Beetle Antenna Algorithm

In order to optimize the performance of the transmission network (TN), this paper introduces the random fractal search al-gorithm based on the beetle antenna search algorithm, thus proposing the random fractal beetle antenna algorithm (SFBA). Te main work of this research is as follows: (1) in the beetle antenna search algorithm, this study used a population of beetles and introduced elite members of the population in order to make the algorithm more stable and to some extent improve the accuracy of its answers. (2) Utilizing the elite reverse learning method and the leader’s multilearning strategy for elites helps to strike a balance between the global exploration and local development of the algorithm. Tis strategy also further improves the ability of the algorithm to fnd the optimal solution. (3) Experiments on real experimental data show that the SFBA algorithm proposed in this paper is efective in improving TN performance. In summary, the research content of this paper provides a good reference value for the performance optimization of TN in actual production.


Introduction
Grid betweenness centrality is a crucial global geometric topology parameter that measures the signifcance and infuence of key nodes and edges in the power network (PN) in the entire network (EN). For understanding the propagation mechanism of cascading faults, defending and mitigating the impact of major faults in the PN, topology optimization, PN elastic behavior and elastic optimal control, and other aspects related to the safe and stable operation (SO) and SDH technology is therefore proposed. Tis technology can be combined with devices such as IP edge routers and SDH multiplexers to establish a network of independent individuals [14]. In the transmission process of business data fow, the characteristics of SDH technology with low delay and the application of various recovery and protection capabilities are used to optimize the network business support layer in order to facilitate the development of multibusiness applications and to thoroughly analyze the second and third layer multitype services. Te present development trend of CNs will be the intelligence of optical transmission technology ASON, viewed at a large scale. MSTP, which can allocate the bandwidth of nodes based on requirements, is one of the signifcant development directions. Currently, the intelligent optical node of ASON has been implemented in the base layer of a long-distance fundamental network or metropolitan area network [15]. According to the currently available technologies, SDH-based MSTP is still undergoing accelerated development, and numerous new technologies have been developed. Notable among the current research hotspots [16] is the data layer processing technology, specifcally how to use the elastic packet ring and multiprotocol label switching (MPLS) in MSTP to realize the application of Ethernet services and the enhancement of networking capabilities. In addition, some scholars have introduced intelligent algorithms to optimize the operation of transmission networks. One of the more classic methods is the transmission network optimization method proposed by Tang et al. based on the random fractal search algorithm [17]. Tis paper focuses on optimizing the operation of transmission power networks through the application of an enhanced stochastic fractal search algorithm. Te proposed algorithm aims to improve the accuracy and efciency of fnding optimal solutions for power network operation, considering factors such as power generation, transmission, and load demand. By utilizing the improved stochastic fractal search algorithm, the study aims to enhance the stability, reliability, and cost-efectiveness of power network operations. Te algorithm's efectiveness is evaluated through simulations and compared with other existing optimization techniques. Te results demonstrate that the improved stochastic fractal search algorithm outperforms the alternatives, leading to more efective operation strategies for transmission power networks. Overall, the paper presents a promising approach for optimizing the operation of power networks, ofering potential benefts for the energy industry.
Enhance the Stability and Security of the TN. Te transport network is the foundation of the EN, and its security and stability are directly related to the operation of the CN and other devices. Te signifcance of security and stability for the PG is self-evident; therefore, enhancing the security and stability of the CN is one of the primary objectives of network optimization [18]. Improve the TN's Dependability. Te connectivity rate of the network is used to determine the network's reliability, so the reliability also refects the network's connectivity. In order to assure the safety and SO of the PG system as a whole, the PCN's dependability is directly related to whether the power system can respond correctly and quickly to potential safety hazards the frst time [19]. Optimize Information TN Channel Utilization. How to rationally allocate resources, reduce network constraints as much as possible, balance network loads, reduce routine maintenance costs, and increase response speed as the TN scale continue to grow. With the continuous development of the PG system, the PCN's communication capacity should increase proportionally. Improving the PCN's load capacity and optimizing the network's resource utilization are crucial for the safe and secure development of the PG system and PG CN [20]. In the process of dismantling and repurposing obsolete communication equipment, various constructions must comply with applicable safety regulations and work requiring fre and power disruptions must complete work tickets in accordance with applicable regulations. Te equipment room, transmission rack, power supply, optical fber, and other conditions should be thoroughly considered, and a detailed and comprehensive circuit cutover plan should be developed to ensure the safety of the circuit cutover during the cutover process. In addition, a complete circuit cutover record should be maintained to ensure operation. Open Circuit Protection. During the implementation of the network optimization plan, adjustments should be made in the order of core, aggregation, and edge layers, from top to bottom. In addition to subnets and regions, structure and equipment adjustments should be divided into subnets. It has formed a ring network; after gaining experience with network optimization and adjustment [21], it can be fully extended to the entire CN after being tested out in specifc areas.
Tis paper combines the improved stochastic fractal search algorithm to optimize the power TN model, constructs the power TN optimization model, and promotes the improvement of power transmission efciency. Te random fractal algorithm and beetle antenna algorithm can be used together to optimize the transmission and transformation network (TN) in the following ways: Random Fractal Algorithm. Te random fractal algorithm can be used to generate a fractal structure that mimics the complexity and randomness found in nature. Tis can be applied to the TN to improve its robustness and resilience. Te fractal structure can be used to design the network's topology and optimize its connections, resulting in a more efcient and stable TN. Beetle Antenna Algorithm. Te beetle antenna algorithm is inspired by the behavior of beetles and their ability to locate resources efciently. Tis algorithm can be used to optimize the parameters of the TN, such as the transmission power, frequency, and direction. By modeling the TN as a network of sensors, the beetle antenna algorithm can optimize the transmission and reception of signals, leading to improved network performance. By combining these two algorithms, we can design a more optimized TN that is both robust and efcient. Te random fractal algorithm can provide a strong backbone for the TN, while the beetle antenna algorithm can optimize its parameters. Tis approach can lead to improved transmission and transformation of data, reduced energy consumption, and increased network lifetime. In addition, this approach can be applied to various types of TNs, including wireless sensor networks, ad hoc networks, and Internet of Tings (IoT) networks. Te main contribution of this paper is to use random fractal search algorithm [22,23] and beetle antennae search algorithm to improve the performance of power transmission and transformation network. Experimental results show that the method used in this paper can improve the performance of the network.

Optimization of the Power Transmission Network
Problem. Te optimization of power transmission networks is necessary because it can enhance the efciency, reliability, and sustainability of the electrical systems. With the increasing energy demand and the expansion of power systems, transmission networks face numerous challenges, including load growth, voltage stability, losses, and energy wastage. By optimizing the transmission networks, we can maximize the utilization of existing resources, reduce energy losses and environmental impacts, and improve the reliability and stability of the grid. Optimization measures include rational planning of transmission lines, optimizing power transmission and distribution methods, and enhancing grid control strategies. Trough these measures, we can better adapt to the demands of future energy transition, achieve efcient delivery of clean energy, and promote sustainable development. In conclusion, the optimization of transmission networks is crucial for enhancing the overall performance and sustainability of power systems.
Te optimization of transmission networks is closely related to optimization algorithms, as these algorithms provide efective tools and methods for achieving optimal solutions in transmission network optimization. Te objective of transmission network optimization is to maximize the efciency and reliability of power systems by adjusting factors such as transmission line confgurations, power allocation, and grid control strategies. On the other hand, optimization algorithms are mathematical and computational tools designed to solve complex optimization problems, capable of fnding optimal or near-optimal solutions under given constraints. Optimization algorithms can be applied to the planning, operation, and scheduling of transmission networks. By establishing mathematical models, considering various constraints and objective functions, and utilizing algorithms for calculations and searches, optimal confgurations and operating strategies for transmission networks can be obtained. Common optimization algorithms include linear programming, integer programming, genetic algorithms, and particle swarm optimization, among others. By integrating optimization algorithms with the optimization objectives of transmission networks, comprehensive optimization of power systems can be achieved, leading to improved transmission efciency, reduced energy losses and costs, and addressing the challenges of sustainable development in power systems. Terefore, optimization algorithms play a crucial role in transmission network optimization, providing vital support in achieving optimal performance of power systems.

Metaheuristic Search Algorithm Design.
Metaheuristic search (MHS) algorithms are optimization algorithms designed to solve complex problems that are difcult to solve using traditional mathematical methods. Tese algorithms are inspired by natural or social phenomena and use heuristic search techniques to explore the solution space and fnd near-optimal or satisfactory solutions. Te general steps of the search process in the MHS algorithm [24] are as follows (Algorithm 1): Te Bat search algorithm (BSA) is a metaheuristic search algorithm inspired by the echolocation behavior of bats. In BSA, the generation of the population involves the following steps: Random initialization: Similar to other metaheuristic algorithms, BSA starts by randomly initializing the population with a set of candidate solutions. Frequency and velocity update: Each bat in the population updates its frequency and velocity based on the previous iteration's information. Tis update allows bats to explore the solution space dynamically. Local search: Bats perform a local search around their current positions to improve their solutions. Tis local search helps to refne the solutions and enhance their quality. Solution update: Bats update their positions and solutions based on their updated frequencies, velocities, and the results of the local search. Tis step allows bats to move towards promising regions of the solution space.
By iteratively performing these steps, the population of bats in BSA explores the solution space, adjusts their positions, and refnes their solutions in search of the optimal or near-optimal solutions for the given problem.

SFBA Algorithm
Te frst version of the BAS algorithm just requires one long beetle, and it is also able to produce appropriate answers to several straightforward optimization issues. However, optimization issues can be found in many other sectors, and they are becoming increasingly difcult to solve as a result of factors such as the increasing complexity of optimization variables. Te BAS algorithm is frequently unable to produce a solution that satisfes the requirements when it is used to problems of this nature. In order to accomplish this goal, this paper creates a cluster of these beetles and applies the mothfame optimization (MFO) algorithm on the population structure as a point of reference. Tese sorts of enhancements have the potential to render the algorithm more stable and, to some extent, boost its capacity for optimization.
Te elite individual matrix E and its ftness value F E are respectively shown in the formula. In addition, the following provisions are made in terms of population structure: (1) In the elite individual matrix E, each beetle is sorted according to the increasing ftness value, and F E is also sorted in this order. For minimization optimization problems, the smaller the ftness value, the better. Terefore, the frst one is the best individual so far. (2) Each individual beetle can only update its place based on the elite people in E who have the same order as it does. Te positions of the remaining beetles are updated using the fnal individual in E as a reference point.
According to the regulations presented above, the beetle is permitted to hunt in the vicinity of the elite solution. Additionally, the beetle does not only search around a predetermined answer, which to some degree enhances the algorithm's ability to explore the search space. Te link that exists between insects and elite persons after they have been updated is depicted in Figure 1.
If n beetles are updated each time relative to a set number of elite solutions and the elite individuals are always changing, then the capacity of the algorithm to produce potentially optimum solutions will be lowered when each iteration is updated relative to various elite solutions. Tis is because the ability of the algorithm to develop possible optimal solutions depends on the elite individuals. It is for this reason that, throughout the iterative process, the number of retained elite individuals undergoes a constant reduction: where t is the current number of iterations, T is the maximum number of iterations, round() is the function that symbolizes rounding, n is the number of long beetles, n′ is the number of retained elite individuals, t is the current number of iterations, and T is the maximum number of iterations. Tis paper adopts cat chaotic map with relatively good ergodicity and uniformity. Te classical cat chaotic map is a two-dimensional reversible chaotic map, and its dynamic equation can be described as follows: Among them, sx m is the value of the sx sequence at the mth iteration. Te structure of this chaotic map is simple, so the computation is fast. In addition, the chaotic sequence generated by it is also more uniformly distributed in the interval [0, 1]. If it is assumed that the size of the beetle population is n and the dimension of the variable is d, the resulting chaotic sequences are sx � sx j , j � 1, 2, · · · , d and sy � sy j , j � 1, 2, · · · , d , where sx j � sx i,j , i � 1, 2, · · · , n} and sy j � sy i,j , i � 1, 2, · · · , n . It should be noted that the chaotic sequence needs to be given an initial value on the interval [0, 1]. Ten, for each dimension in the population, the cat chaos map can be expressed as follows: It should be noted that since the cat chaotic map has two sequences sx and sy, only sy is selected in this paper. After that, it is necessary to map the chaotic sequence into the search space to obtain the represented population X. We take x i,j as an example and calculate it by the following formula: where x i,j is the jth dimension of the ith beetle and ub j and lb j are the upper and lower bounds of the jth dimension of the variable, respectively. Te fundamental BAS algorithm is quite sensitive to the settings of its parameters, and the use of alternative parameters can frequently provide substantially diferent optimization outcomes. Alternately, a certain combination of parameters may be appropriate for one problem, but it may not be possible to solve another problem in an efcient manner. Te following formula is used to compute the distance along each dimension: (1) Begin (initialization) (2) P: Create the P-population (3) for i � 1: n (the number of solution candidates) (4) F: calculate the ftness values of members in P (5) end (6) while (search process lifecycle) Step 1: guide selection mechanism (create a mating pool) selection of reference positions from the P by using guide selection methods ("ftness distance balance, FDB," greedy, randomly, and roulette wheel) (8) Step 2: search operators: (9) Exploitation (neighborhood search around reference positions) (10) Exploration (diversifcation operations in P) (11) Step 3: update mechanism: update the P-population depending on the ftness values of solution candidates or the NSM (natural survivor method)-scores [25] of them (12) next generation until termination criterion (13) End Wireless Power Transfer where x t i,j represents the jth dimension of the ith beetle at time t, e t i,j is the jth dimension of the ith current optimal individual at time t, D t i,j represents the distance between the ith beetle and the corresponding elite individuals in the jth dimension at time t, and n ′ represents the number of elite individuals currently reserved.
After considering the random time delay, the step size is expressed as the following formula: M is the delay factor, which is used to decide whether to add the delay term, and c is the acceleration coefcient. Both of these factors are discussed further. Te range of possible values for k, which denotes the delay time, is [0, t − 1]. Te acceleration coefcient c found in the BAS-RDEO algorithm is conceptually comparable to the cognitive and social factors found in the PSO algorithm. An acceleration coefcient that varies over time is utilized in this piece of work. To be more explicit, it is diminishing in a linear fashion, which can be stated as follows: Among them, c i and c f represent the initial value and termination value of the acceleration coefcient, respectively.
In this paper, the evolutionary factor is used to judge the evolutionary state of the population, which has been introduced. According to the size of the evolution factor and the characteristics of the search process, four evolution states can be defned: the convergence state, the development state, the exploration state, and the jumping state. Before calculating the evolution factor, the average distance I i between each long beetle and other long beetles needs to be calculated by the following formula: Among these variables, n and d stand for the size of the population and the variable dimension, respectively. When all is said and done, the evolutionary factor known as EF can be defned as follows: Among them, ξ(t) � 1, 2, 3, 4 represents the convergence state, the development state, the exploration state, and the hop state, respectively. Transform the abovementioned formula into the following form: Te concept of inverse learning has been explained. Elite reverse learning is a novel technology in the feld of intelligent computing that is analogous to traditional reverse learning but is more efective. Following this, you will fnd a defnition of the concept of elite reverse learning. Defnition Among them, ω is a generalized coefcient uniformly distributed in [0, 1]; da t j and db t j are dynamically changing boundaries and can be defned as follows: However, for a given problem, a certain dimension of individual ox e ′ after using elite reverse learning may jump out of the boundary [lb j , ub j ], which will make the algorithm inefective. To avoid this situation, the following equation resets individuals outside the variable bounds: ox t e,j � lb j , ox t e,j < lb j , ub j , ox t e,j > ub j .
In addition, the number n ′ of elite individuals decreases with the increase of the number of iterations. In view of this, this paper only selects the frst individual in the elite individual matrix E for L times of elite reverse learning and sets L equal to the population size n in this paper. After the elite reverse learning, it is necessary to merge the L elite reverse solutions with the individuals in the matrix, and then select n ′ better individuals to replace the elite solutions in the matrix. So far, elite reverse learning has been executed. After that, it is also necessary to introduce the leader's multilearning strategy.
Te leader learns to randomly select one dimension of the globally optimal individual. For example, if the jth dimension is chosen, it can be expressed as e t 1,j . Te reason for choosing only one dimension is because the local optimum is most likely to have a better solution in a certain dimension. After selecting a dimension, leader multilearning is carried out through the following 3 formulas: 6 Wireless Power Transfer e t 1,j � e t 1,j + λ 1,j − λ 2,j · rand 2 − λ 1,j · R 2 , Among them, rand1, rand2, and rand3 are random numbers in [0, 1]; η 1 and η 2 are the maximum and minimum values of all dimensions of the globally optimal individual e t 1 in each generation. R 1 , R 2 , and R 3 are the search radius of the multilearning method. Obviously, formula (14) is used to improve the global exploration ability, while formulas (15)  and (16) are used to improve the local development ability. It should be noted that the search radii R 1 , R 2 , and R 3 are determined by the Markov chain c t (t > 0): Among them, α t ij ≥ 0(i, j ∈ S) is the transition probability from i to j. Te number of states set in this paper is N � 2. At the same time, this paper assumes that the values of R 1 , R 2 , and R 3 are the same, namely, R 1 � R 2 � R 3 . Terefore, when choosing the value of the search radius, we only take R 1 as an example. When the state is c t � 1, R 1 is taken as ρ 1 � 1. When the state is c t � 2, the value of R 1 is ρ 2 � 0.1. It should be pointed out that the adopted probability transition matrix Γ t is time-varying and can be expressed as follows: Among them, α t is a time-varying probability variable whose value decreases linearly in the iterative process and can be expressed as the following formula: Among them, α i and α f are the initial and fnal values of α t , respectively. In this paper, they are set to α i � 1 and α f � 0. Terefore, ρ 1 occurs more frequently than ρ 2 in the early stages. However, in the late period, ρ 1 rarely occurs and ρ 2 occurs frequently. It should be noted that in leader multilearning, if the new position is better than the previous global optimal individual, the new position is accepted. Otherwise, the previous global optimal individual remains unchanged.

Power TN Optimization Experiment
In order to provide high-reliability and uninterrupted communication services for power systems, power communication must meet and adapt to the features that power cannot be stored, and that production, supply, and sales are all fnished at the same time. A basic architecture of a smart grid is depicted in a schematic form in Figure 2, which may be seen here.   Figure 3 illustrates the design of the PCN's two fundamental networks, which are the integrated service data network and the dispatching data network. Figure 3 also illustrates the PCN's overall structure.
To validate the performance of the proposed method in power TN optimization, the experimental setup in this paper is mainly conducted from two perspectives. Firstly, it verifes the optimization performance of the proposed method, and secondly, it applies the method to optimize the power transmission network.
Firstly, to validate the performance of the proposed algorithm, this paper will conduct a comparative analysis of solution accuracy and convergence using several typical test functions. Specifcally, a classic single-peak spherical function and two multipeak functions, Rosenbrock and Rastrigin, will be employed for testing. Te functional forms of these test functions are as follows: Te parameter settings of each algorithm are shown in Table 1.
Based on the parameter settings provided in Table 1, the experimental results obtained by each algorithm are shown in Table 2.
According to the experimental data shown in Table 2, it can be observed that the proposed BAS-RDEO algorithm outperforms other algorithms in both the average optimal value and standard deviation indicators. Tis indicates that the proposed algorithm has shown signifcant improvements in both computational accuracy and stability. Moreover, the BAS-RDEO algorithm is more adept at locating the global optimum in the solution space.
In order to further compare and analyze the performance of the model in this paper and similar algorithms, this paper selects [26][27][28][29] as comparison algorithms. Te parameter settings of each model are the same as in references. Te efect of each algorithm in the optimization of the power TN is shown in Table 3.
From the experimental results shown in Table 2, it can be seen that in most cases, our method obtains the optimal efect, and the average optimization efect is 86.067. Tere are two sets of data in [26] that exceed our method, and the average obtained was 85.368. Te experimental results obtained by [28,29] are relatively close, and their mean values are 84.567 and 85.375, respectively, which are lower than the experimental data obtained by the algorithm in this paper. Our method utilizes random perturbations and selfsimilarity to explore the solution space efectively. It can escape local optima by introducing randomness and adapt its search strategy to diferent scales within the problem domain. Te algorithm requires minimal problem-specifc information, making it versatile for various optimization problems. In comparison, the gaining-sharing knowledgebased algorithm emphasizes knowledge exchange among individuals in a population, promoting collective intelligence and exploration. However, when focusing on the advantages of the stochastic fractal search algorithm, it stands out in its ability to efciently explore the solution space, especially in high-dimensional problems and noisy environments. Its simplicity of implementation, robustness, and adaptability to diverse problem domains contribute to its practicality. In addition, the algorithm's stochastic nature and self-similarity enable it to overcome local optima and discover global optima. In general, our method provides an efcient and fexible solution for optimization tasks that demand efcient exploration, adaptability, and ease of implementation. Tis makes our method suitable for a wide range of optimization problems. In comparison to the strategy described in [27], our approach demonstrates clear and convincing advantages. Tis demonstrates that nonparametric statistical methods function satisfactorily in general when it comes to the optimization efect of transmission networks.

Conclusion and Future Directions
Te graphical connection relationship between each electrical component in the PN is referred to as the "PN topology," and it is described here. Te topological structure and system function of the PN are its two fundamental qualities, and the two are interrelated and afect each other in the following way: the structure places restrictions on and determines the size, type, and boundary of the power system function; the structure also sets the size of the PN. Te function of the power system is the exterior manifestation of its structure, and the change in function is typically accompanied by a change in the system's structure. Both the structure of the PN and the stability of the power system are directly impacted by the essential nodes and edges that make up the PN. In this study, an enhanced stochastic fractal search technique is used with the power TN model in order to achieve optimal results. Te empirical research demonstrates that the improved stochastic fractal search method that was suggested in this paper is able to successfully increase the optimization efect of the power TN, and that it also has a benefcial efect on enhancing the efciency of power transmission. Tis paper has some shortcomings that need to be addressed. To give just one illustration, the identifcation of the model's ideal parameters necessitates several iterations, each of which takes a considerable amount of time and contributes to an increase in the algorithm's level of complexity about the passage of time. Te main work of this paper in the future will be carried out to address the abovementioned limitations.

Data Availability
Te labeled dataset used to support the fndings of this study is available from the corresponding author upon request.

Conflicts of Interest
Te authors declare that there are no conficts of interest.