Digital twin network resource optimization method based on multi-objective genetic algorithm

Abstract

The invention discloses a digital twin network resource optimization method based on a multi-target genetic algorithm, which adopts a fast genetic algorithm to solve a multi-target problem so as to cope with the fast changing resource allocation requirement of a mobile ad hoc network, adopts a matrix coding mode and uses the two-dimensional data structure. According to the method, modeling is carried out on frequency domain, space domain and energy domain problems, time domain information is taken into consideration, the conflict problem of nodes of the whole network is converted into a problem model with a subnet as a unit, the decision space of an algorithm is greatly reduced, and the single operation time of iteration is shortened. The power control and frequency point allocation problem is modeled as a network transmission capacity maximization problem, so that power optimization allocation and frequency point interference minimization are unified into a multi-objective optimization problem with relevance, and the probability of power consumption and frequency point conflict can be minimized while maximization of system communication performance and frequency point utilization efficiency can be realized.

Description

Technical Field

[0001] The present invention relates to a digital twin network resource optimization method based on a multi-objective genetic algorithm, and belongs to the technical field of computer communications. Background Art

[0002] The basic idea of ​​traditional fixed frequency allocation is to allocate spectrum resources through deterministic rules or algorithms. The advantages are simple implementation and easy management, but often lack flexibility and adaptability. For the frequent topology changes and time-varying channel environment of mobile ad hoc networks, fixed frequency allocation is obviously unable to adapt to the rapidly changing ad hoc network situation, so dynamic spectrum allocation is needed.

[0003] However, the current intelligent optimization algorithms focus on solving the frequency allocation problem in cellular network communications, and there are relatively few studies on spectrum allocation for self-organizing networks. Therefore, when modeling problems, such optimization algorithms often only set variable constraints in the frequency domain, lacking comprehensive consideration of the time domain, space domain, and energy domain. In addition, when performing multi-objective optimization of frequency allocation, different optimization objectives may restrict each other or even be completely opposite. The current algorithms often use a simple linear weighting and conversion single-objective method. Since different optimization objectives may have different dimensions, this may cause the algorithm to converge slowly or fall into a local optimal solution. At the same time, some optimization algorithms focus on reducing the number of iterations for algorithm convergence, and tend to ignore the complexity of a single iteration operation, resulting in a long algorithm operation time. Therefore, when dealing with scenarios where the self-organizing network topology changes rapidly, energy consumption is limited, and real-time requirements are high, the current intelligent optimization algorithms often cannot meet the needs. Summary of the invention

[0004] The purpose of the present invention is to address the defects and shortcomings of the above-mentioned prior art and propose a digital twin network resource optimization method based on a multi-objective genetic algorithm. This method models the frequency domain, spatial domain, and energy domain problems, and takes time domain information into consideration, converting the conflict problem of the entire network nodes into a problem model based on subnets, greatly reducing the decision space of the algorithm and reducing the single operation time of the iteration. The power control and frequency allocation problems are modeled as the problem of maximizing the network transmission capacity, so that the power optimization allocation and minimization of frequency interference are unified into a related multi-objective optimization problem, which can maximize the system communication performance and frequency utilization efficiency while minimizing power consumption and the probability of frequency conflict.

[0005] The technical solution adopted by the present invention to solve its technical problems is: a digital twin network resource optimization method based on a multi-objective genetic algorithm. In order to meet the rapidly changing frequency optimization requirements of the self-organizing network, the method adopts an improved genetic algorithm to optimize the frequency allocation problem. The adaptive crossover operator based on environmental perception adjusts the crossover probability in real time according to the population fitness and network topology to balance the algorithm convergence and global search capabilities, thereby achieving efficient network optimization. Specifically including:

[0006] A digital twin network resource optimization method based on a multi-objective genetic algorithm, which adopts a fast genetic algorithm to solve multi-objective problems to cope with the rapidly changing resource allocation needs of mobile ad hoc networks. The algorithm takes reducing frequency conflicts as the core optimization goal, and power allocation optimization as a secondary optimization goal to solve the optimal solution. The present invention adopts a matrix coding method, using this two-dimensional data structure, which has a larger representation space than a one-dimensional data structure, and the way to generate new individuals is more flexible. The coding strategy is shown in Table 1, where "1" indicates that the frequency and power corresponding to the column where the element is located are allocated to the subnet corresponding to the row (gene), and each subnet power has only one choice. This coding strategy is achieved by randomly generating a two-dimensional array (chromosome) with elements of "0" and "1".

[0007] Table 1 Genetic algorithm coding table

[0008]

[0009] 1.1.1 Good point set initialization and selection operator

[0010] (1) Initialization of good point set

[0011] The traditional random population generation method has uncertainty. The population is usually unevenly distributed in space and may only be distributed in a specific solution space, causing the algorithm to fall into a local optimal solution in the early stage, affecting the convergence of the algorithm. In order to overcome these problems, we introduced the best point set population generation method. This method generates a set of point sets through a series of calculations, so that the generated point sets can cover as much of the solution space as possible with high fitness values, which helps the algorithm find high-quality solutions more quickly in the early stages. The number of populations in the algorithm is Q, and the number of gene values ​​of each individual is c = n·(z+q). Therefore, the number of good points in the good point set that needs to be generated is Q, and each good point is represented by P Q (i)=(r1·i,r2·i,…,r c ·i), i∈[1,Q], which is the initialized single individual.

[0012] Therefore, in the best point set population generation method, for each individual in the population, a set of specific values, called r value vectors, must first be calculated. The number of vectors is the number of genes c of each individual, that is, r = (r1, r2, ..., rc ), use formula (4.25) to calculate the r value.

[0013] r j =mod(2cos(2πj / k)·i,1)(4.1)

[0014] In the formula, i represents the i-th individual in the population, j represents the j-th element in the r-value vector, and k is the smallest prime number that satisfies (k-3) / 2≧c. Then, these r-value vectors can be used to construct the good point set P Q .

[0015] Next, we need to map the good point set to the feasible region of the population, using equation (4.26) for mapping, y ij represents the best point after mapping, a j and b j are the upper and lower limits of the feasible region respectively.

[0016] y ij =a j +P Q (i)·(b j -a j )(4.2)

[0017] Finally, each good point in the good point set is converted into a specific individual code to complete the population initialization. Since the algorithm has frequency constraints and power constraints for single subnets, adjustments need to be made when converting good points into individual gene values ​​to meet the constraints. Finally, a group of populations with good spatial distribution and structure are initialized, which can eliminate the uncertainty in the population initialization process, which helps to improve the convergence speed and search efficiency of the genetic algorithm, thereby better solving the optimization problem.

[0018] (2) Individual evaluation and selection operators

[0019] In genetic algorithms, the roulette operator is a commonly used selection method. Its disadvantage is that it is easy to cause premature maturity. Therefore, a selection method combining the best individual retention and roulette is adopted. First, the best individual retention operator is adopted so that the individuals with excellent genes and the top 5% of fitness values ​​are retained and allowed to evolve directly to the next generation; secondly, the roulette operator is used to select the remaining individuals with relatively high fitness through roulette, and then they are copied and randomly operated with the two parent chromosomes. The present invention can directly reduce the probability of inferior individuals with excellent genes being eliminated, so that the population can better adapt to the living environment. The probability of individual i being selected is:

[0020]

[0021] In the formula, E i is the fitness value of individual i, and Q is the population size.

[0022] Beneficial effects:

[0023] 1. The present invention adopts matrix coding, combines the good point set population initialization method, and introduces an adaptive crossover operator based on environmental perception, so that the algorithm can perceive environmental changes and adapt quickly during the iteration process, thereby ensuring the quality of the solution.

[0024] 2. The present invention uses a binary parent-induced mutation operator based on adjacency relationship to induce the algorithm to explore in the direction of high fitness, thereby improving the convergence and operation efficiency of the algorithm.

[0025] 3. The simulation results show that the present invention can respond quickly to sudden changes in network topology in the dynamic and changeable scenarios of mobile ad hoc networks, and can adjust the resource allocation strategy in time to maximize the communication efficiency of the link, ensuring the stability of the link and the continuity of data transmission under frequently changing network conditions, thereby demonstrating excellent solution performance. BRIEF DESCRIPTION OF THE DRAWINGS

[0026] Figure 1 Schematic diagram of the system model of the present invention.

[0027] Figure 2 This is a schematic diagram of the division of impact assessment areas between subnets of the present invention.

[0028] Figure 3 This is a simplified schematic diagram of the division of impact assessment areas between subnets of the present invention.

[0029] Figure 4 Schematic diagram of multi-link interference with different signal strengths of the present invention.

[0030] Figure 5 This is a schematic diagram of the selection of variant parent chromosomes of the present invention.

[0031] Figure 6 This is a schematic diagram of the primary variation induced by binary parents of the present invention.

[0032] Figure 7 This is a schematic diagram of the binary parent-induced secondary variation of the present invention.

[0033] Figure 8 It is a schematic diagram of the real-time packet loss rate of the single frequency point and the same power allocation scheme of the present invention.

[0034] Fig. 9 It is a schematic diagram of the real-time packet loss rate of the NSGA-II resource allocation scheme of the present invention.

[0035] Fig.10 Schematic diagram of real-time packet loss rate of the resource allocation scheme of the present invention.

[0036] Fig.11It is a schematic diagram of the convergence comparison of the present invention. DETAILED DESCRIPTION

[0037] The invention will be further described in detail below in conjunction with the accompanying drawings.

[0038] The system model and problem construction specifically include:

[0039] like Figure 1 As shown, the scenario of the system of the present invention includes multiple different communication subnets, the nodes in the subnet adopt frequency hopping communication mode, and there are multiple communication links in each subnet. In this task scenario, nodes may move frequently, the network topology changes rapidly, and the adjacent relationship between different subnets also changes accordingly, causing the communication links to change constantly. There is mutual communication interference and enemy frequency interference between nodes. When allocating frequency and power resources, consideration should be given to minimizing communication conflicts and optimizing power allocation on this basis.

[0040] 1.1.2 Establishing the electromagnetic compatibility constraint model

[0041] In order to minimize electromagnetic interference, the frequency allocation process requires electromagnetic compatibility analysis (EMC). This problem is mainly caused by the interference of useless signals to the receiving system through coupling when the receiver and the transmitter are working in the same position or near each other, resulting in misjudgment or loss of effective signals, resulting in reduced communication quality or even blocking. Therefore, such problems need to be considered during design to reduce their impact. The present invention converts interference from different generation mechanisms into a series of inequalities or equations, establishes a constrained mathematical model, and searches for the optimal frequency allocation scheme under this condition. The specific constraints include the following:

[0042] (1) Co-Channel Interference

[0043] Co-channel interference refers to the mutual interference caused by multiple communication devices communicating on the same frequency due to the close distance between the devices, resulting in a decrease in communication quality or even interruption. i and f j Represent the frequencies of device i and device j respectively, d ij Indicates the physical distance between device i and device j, D CCI Indicates the minimum distance between two devices without causing co-channel interference. The co-channel constraint can be expressed as:

[0044]

[0045] (2) Adjacent Channel Interference

[0046] Adjacent frequency interference refers to when multiple communication devices communicate on adjacent frequencies, the distance between the devices is close, and the interval between the transmission signal frequency of one device and the reception signal frequency of another device is small, resulting in the aliasing of the useful signal received by the device and the adjacent frequency signal. Due to the poor filtering performance of the receiver, the useful signal cannot be correctly demodulated and identified. i and f j represents the adjacent frequencies used by device i and device j, m represents the number of channel spacing, Δf represents the frequency value of the channel spacing, and the adjacent frequency interference constraint can be expressed as:

[0047]

[0048] (3) Harmonic Interference

[0049] Harmonic interference refers to the mixing in device i that will produce frequency components that are integer multiples of the input frequency. These frequency components are harmonics. When the harmonics formed happen to be the operating frequency of device j, they will interfere with the device, among which the amplitude of the second harmonic is the strongest. i 、f j denote the operating frequencies of device i and device j respectively. The harmonic interference constraint can be expressed as:

[0050]

[0051] (4) Intermodulation Interference

[0052] Intermodulation interference refers to when multiple signals are transmitted simultaneously through nonlinear devices, the different frequencies of device i interact with each other to produce sum or difference frequencies. These new frequency components happen to interfere with the operating frequency of device j, affecting the reception and demodulation of the original signal by the receiving device. Intermodulation interference is multi-order, with third-order intermodulation interference being the most serious, expressed as f i 、f j 、f k represents the frequency component, f x represents the new frequency components generated in the nonlinear device, and the intermodulation interference constraint can be expressed as:

[0053]

[0054] (5) Enemy Interference

[0055] The enemy's interference with frequencies mainly includes three types: targeted interference, tracking interference and blocking interference. Targeted interference refers to the enemy's conscious interference with concentrated power on a specific frequency band to weaken or interrupt communications. It uses precise frequency, time and power control to interfere with certain frequency bands, resulting in communication link interruption and information leakage, which has a greater impact on fixed-frequency communications; tracking interference refers to the enemy's continuous monitoring of our communication system to track our communication mode and frequency changes, and then implements interference strategies in a targeted manner. Its characteristic is that it can perform synchronous hopping interference on different frequency bands according to our frequency changes; blocking interference refers to the enemy's interference on a wide range of frequency bands by greatly increasing the power of the interference signal, so that our communication signals are submerged. Affecting multiple communication links, causing our communication to be interrupted, thereby affecting combat effectiveness. When allocating frequencies, try to avoid the enemy's interference frequencies and use f i 、f e represents our communication frequency and the enemy interference frequency, and its constraints can be expressed as:

[0056]

[0057] (6) Unavailable Frequency

[0058] In the frequency allocation process, it is necessary to avoid civil frequencies such as aviation communications and satellite navigation to avoid interference. In addition, it is also necessary to pay attention to the prohibited frequencies set by the international or national authorities, which are usually used for specific international or domestic communication services, such as emergency rescue and safety communications. At the same time, it is necessary to pay attention to the protection frequencies for performing specific tasks such as air raid alarms to ensure that their normal operation is not interfered with. i 、f u represents the working frequency and the unavailable frequency, and its constraints can be expressed as:

[0059]

[0060] 1.1.3 Establishing a network relationship model based on spatial distribution

[0061] Time division multiplexing technology reduces communication conflicts by allocating different time periods to nodes in the network, but this method does not consider the communication resource conflicts caused by other adjacent subnets in the spatial domain, which is particularly prominent in the dynamic topology scenario of mobile ad hoc networks. In some network designs, an adjacency relationship matrix is ​​used to describe the topological relationship, but it simply regards the connection relationship between subnets as adjacent or non-adjacent, lacking a quantitative description of the degree of influence on adjacent subnets. Therefore, the present invention uses a weighted adjacency relationship matrix to express spatial domain information, and by considering the spatial distribution of nodes between adjacent subnets, the adjacent relationship of the subnets is characterized using different connection weight values ​​to accurately describe its degree of connection and evaluate the impact of communication resource conflicts.

[0062] Assume that there are n subnets in a multi-subnet scenario, denoted by S = {S1, S2, ...S n}, each subnet S i The number of nodes in is u i = {u1, u2, ... u n}, each node is denoted by N i,j , indicating subnet S i The jth node in , where i∈[1,n], j∈[1,u i ], the latitude and longitude coordinates of each node are expressed as (x i,j ,y i,j ), calculate each subnet S according to the latitude and longitude information of the nodes in the subnet i The center node coordinates

[0063]

[0064]

[0065] Use the Haversine formula to calculate the distance between the central nodes of any two subnets:

[0066]

[0067] where d ij is the distance between node i and node j, R is the radius of the earth, x i and x j are the latitudes of the two nodes, Δx and Δy represent the latitude difference and longitude difference of the two nodes, respectively. Therefore, the adjacency relationship of the cluster can be obtained as follows:

[0068]

[0069] Where w ij represents the adjacency relationship of nodes, D adj The distance threshold for determining node adjacency is D. If the distance between the central nodes of two subnets is less than the threshold Dadj , then the two subnets are considered to be adjacent, and the node adjacency matrix A represented by 0-1 is obtained:

[0070]

[0071] In order to more accurately describe the adjacency relationship between subnets, the weight coefficient W is introduced. ij The adjacency matrix is ​​further modified to characterize the influence strength of adjacent subnets, so as to distinguish the influence of different neighboring subnets on the subnet. The weight coefficient is calculated based on the center distance of adjacent subnets and the distribution relationship of adjacent nodes. First, the impact assessment area between subnets is divided, such as Figure 2 The nodes of the three different subnets are distinguished by different colors. The coordinates of the central node of each subnet can be obtained. The central nodes of adjacent subnets are connected, and then the midpoint of the connection is taken as the center of the circle, and the distance d between the central nodes is taken as the center. ij Draw a circle with the diameter as the center and calculate the node density in the area, where the density is defined as the number of nodes in two adjacent subnets that fall into the evaluation area.

[0072] Calculate the weight value based on the density of the impact assessment area between subnets:

[0073]

[0074] Where w ij is the weight coefficient of adjacent subnet i and subnet j, d ij is the distance between two subnets, e ij is the number of nodes falling into the evaluation area, u i and u j are the total number of nodes in subnet i and subnet j respectively.

[0075] In actual application scenarios, to determine whether a node falls into the evaluation area, it is necessary to traverse all nodes in the two subnets and calculate their distances from the center of the evaluation area. When the node scale is large, it may lead to a large amount of computing resource consumption. Therefore, the model can be simplified, such as Figure 3 As shown, an inscribed square is drawn based on the original circular inter-subnet impact assessment area.

[0076] The simplified evaluation area means that when determining whether a node falls into the evaluation area, it is only necessary to determine the relationship between the node's longitude and latitude and the longitude and latitude of the four vertices of the evaluation area, without the need for complex distance calculations. This allows the algorithm to maintain good operating efficiency, and the simplified area can still be used for evaluation while maintaining the degree of influence on different adjacent subnets. The judgment model is as follows:

[0077]

[0078] Finally, the 0-1 adjacency matrix A is updated to a real number matrix, and the adjacency values ​​in the matrix are:

[0079]

[0080] The updated weighted adjacency matrix is:

[0081]

[0082] 1.1.4 Establishing the power allocation target model

[0083] In a mobile ad hoc network, nodes use a distributed communication mode, and each node is a transmitting and receiving node. It is necessary to consider the mutual influence between multiple adjacent communication links according to the network topology. This not only involves the frequency conflict of different links, but also includes the different interference levels caused by the link signal strength, such as Figure 4 Therefore, the algorithm needs to combine the power allocation problem and consider reducing link conflict interference.

[0084] When establishing the power model, further analysis will be performed based on the aforementioned adjacency relationship model. When calculating the adjacency value weight of the adjacency relationship matrix, each group of adjacent subnets is divided into an inter-subnet impact assessment area, which is mainly used to characterize the degree of mutual influence between nodes in adjacent subnets and is also the main area where frequency point conflicts occur. Therefore, when considering the power model, the link conflicts and node power in this area are mainly used as the objects of problem modeling.

[0085] Since the network management can obtain the protocol-level status information of all nodes in the network, it can obtain the available time slot allocation for each node. Assume that there are L communication links in the evaluation area, the length of a superframe is T, and link l represents the receiving node r l and sending node s l The communication link between them is l∈[1,L], and the receiving node r l At time slot t, it receives a signal from the sending node s. l The effective signal power P l,l,t for:

[0086] P l,l,t =h l,l,t p l,t (4.19)

[0087] In the formula, h l,l,t For the receiving node r l With the sending node s l The channel gain at time slot t, p l,t For the sending node s l The transmission power at time slot t. The receiving node r l At time slot t, the signal from the interfering node s is received. o The interference power Pl,o,t for:

[0088] P l,o,t =c l,o h l,o,t p o,t (4.20)

[0089] In the formula, c l,o represents the link interference factor, h l,o,t For the receiving node r l Received node s o The channel gain at time slot t. Therefore, the received signal-to-interference-to-noise ratio of node communication link l at time slot t is:

[0090]

[0091] In the formula, N0 represents the power spectrum density of Gaussian white noise, and B represents the channel bandwidth. According to Shannon's formula, the transmission capacity of link l in the entire frame can reach:

[0092]

[0093] In the formula, the received signal-to-noise ratio of the node needs to meet the threshold constraint γ min , that is, γ l ≥γ min , and the transmission power of each node is p l The maximum power constraint needs to be met, that is, p l ≤p max .

[0094] Therefore, the frequency conflict and power allocation problem in the evaluation area is modeled as the total link transmission capacity problem of the entire network. Assuming that there are L communication links in the entire network and the length of a superframe is T, the transmission capacity of the entire network is C l (p):

[0095]

[0096] The transmission capacity of the entire network C l (p) is a function of power allocation, where h l,l,t For the receiving node r l With the sending node s l The channel gain at time slot t, h l,o,t For the receiving node r l With the sending node s o The channel gain at time slot t, p l,t For the sending node s l The transmission power at time slot t, p o,t For the sending node s o The transmission power in time slot t, c l,o,tis the influence factor of link l on link o in time slot t.

[0097] 1.1.5 Problem Construction

[0098] Now assume that the available frequency band of the network is [f L , f H ], the minimum frequency interval is b, so the number of available frequency points z = (f H -f L ) / b, an available frequency point set F = (f1, f2, ... f z ), the frequency demand of each subnet is m, and the frequency set F of each subnet can be established i =(f i,1 , f i,2 , …f i,m ), F i ∈F. The available power includes q gears, and the available power set is P = (p1, p2, ... p q ).

[0099] When performing frequency allocation, the main consideration is the conflict interference problem after the frequency allocation. Based on the analysis in the previous section, a frequency conflict function I(f) can be established, in which some frequencies are disabled or unavailable for the network, and they are converted into frequency constraints. The frequency allocation goal is to minimize the probability of frequency conflict, so the frequency allocation objective function can be obtained as:

[0100]

[0101] In the formula, I CCI ,I ACI ,I HI ,I IMI are the co-channel interference, adjacent-channel interference, harmonic interference and intermodulation interference models respectively, α, β, η, μ are their corresponding weight coefficients respectively, and f e is the enemy interference frequency, f u is the unavailable frequency, w ij is the adjacency weight value corresponding to two subnets i and j in the subnet adjacency matrix.

[0102] When performing power allocation, in Section 4.2.3, the power allocation problem is transformed into a transmission capacity problem, and the goal considered is to maximize the transmission capacity of the entire network. Therefore, the power allocation objective function can be obtained as:

[0103]

[0104] Since the links that can form mutual interference are related to the frequency allocation scheme and the subnet adjacency relationship, the power allocation objective function can be associated with the frequency allocation objective function, and the influence factor c of link l on link k in time slot t can be calculated. l,o,tUsing I(f) for characterization, the power allocation objective function based on the frequency allocation scheme is obtained as follows:

[0105]

[0106] Furthermore, since the frequency allocation solution of the algorithm is to minimize the frequency interference I(f) by solving the frequency combination that violates the least interference constraint, the power allocation solution is to maximize the link transmission capacity C by solving the best power combination. l (p,I(f)), although the resource allocation objectives are related, they are negatively correlated. Therefore, the problem functions of frequency allocation and power allocation are combined in a similar mathematical form to obtain the resource allocation multi-objective function E(f,p):

[0107]

[0108] Where ξ is a constant, and ξ=1 is taken here. C1 and C2 are available frequency constraints, so that the frequency allocated to each subnet is within the specified frequency band; C3 is an unavailable frequency constraint, ensuring that the interference frequency and the specified unavailable frequency are not used; C4 is the adjacency weight value corresponding to subnet i and subnet j in the weighted adjacency matrix A, and C5 is the weight coefficient of different electromagnetic interference types; C6 is the available power constraint, ensuring that the power used by each link is within the specified power range; at the same time, the power allocation must also meet the minimum receive signal-to-interference-to-noise ratio threshold of C7. Through the modeling analysis of the problem, the resource allocation is a multi-objective mixed integer nonlinear programming problem, which is an NP-Hard problem. Therefore, for the dynamic topology scenario of mobile ad hoc networks, it is necessary to use an algorithm that can be solved quickly to obtain the optimal solution that meets the requirements.

[0109] 1.2 Digital twin network resource optimization based on multi-objective genetic algorithm

[0110] 1.2.1 Fitness function construction and chromosome encoding

[0111] The present invention adopts a fast genetic algorithm to solve multi-objective problems to cope with the rapidly changing resource allocation needs of mobile ad hoc networks. The algorithm takes reducing frequency conflicts as the core optimization goal, and power allocation optimization as a secondary optimization goal to solve the optimal solution. The present invention adopts a matrix coding method, using this two-dimensional data structure, which has a larger representation space than a one-dimensional data structure, and the way to generate new individuals is more flexible. The coding strategy is shown in Table 1, where "1" indicates that the frequency and power corresponding to the column where the element is located are allocated to the subnet corresponding to the row (gene), and each subnet power has only one choice. This coding strategy is achieved by randomly generating a two-dimensional array (chromosome) with elements of "0" and "1".

[0112] Table 2 Genetic algorithm coding table

[0113]

[0114] 1.2.2 Good Point Set Initialization and Selection Operator

[0115] (2) Initialization of good point set

[0116] The traditional random population generation method has uncertainty. The population is usually unevenly distributed in space and may only be distributed in a specific solution space, causing the algorithm to fall into a local optimal solution in the early stage, affecting the convergence of the algorithm. In order to overcome these problems, we introduced the best point set population generation method. This method generates a set of point sets through a series of calculations, so that the generated point sets can cover as much of the solution space as possible with high fitness values, which helps the algorithm find high-quality solutions more quickly in the early stages. The number of populations in the algorithm is Q, and the number of gene values ​​of each individual is c = n·(z+q). Therefore, the number of good points in the good point set that needs to be generated is Q, and each good point is represented by P Q (i)=(r1·i,r2·i,…,r c ·i), i∈[1,Q], which is the initialized single individual.

[0117] Therefore, in the best point set population generation method, for each individual in the population, a set of specific values, called r value vectors, must first be calculated. The number of vectors is the number of genes c of each individual, that is, r = (r1, r2, ..., r c ), use formula (4.25) to calculate the r value.

[0118] r j =mod(2cos(2πj / k)·i,1)(4.28)

[0119] In the formula, i represents the i-th individual in the population, j represents the j-th element in the r-value vector, and k is the smallest prime number that satisfies (k-3) / 2≧c. Then, these r-value vectors can be used to construct the good point set P Q .

[0120] Next, we need to map the good point set to the feasible region of the population, using equation (4.26) for mapping, y ij represents the best point after mapping, a j and b j are the upper and lower limits of the feasible region respectively.

[0121] y ij =a j +P Q (i)·(b j -a j )(4.29)

[0122] Finally, each good point in the good point set is converted into a specific individual code to complete the population initialization. Since the algorithm has frequency constraints and power constraints for single subnets, adjustments need to be made when converting good points into individual gene values ​​to meet the constraints. Finally, a group of populations with good spatial distribution and structure are initialized, which can eliminate the uncertainty in the population initialization process, which helps to improve the convergence speed and search efficiency of the genetic algorithm, thereby better solving the optimization problem.

[0123] (2) Individual evaluation and selection operators

[0124] In genetic algorithms, the roulette operator is a commonly used selection method. Its disadvantage is that it is easy to cause premature maturity. Therefore, a selection method combining the best individual retention and roulette is adopted. First, the best individual retention operator is adopted so that the individuals with excellent genes and the top 5% of fitness values ​​are retained and allowed to evolve directly to the next generation; secondly, the roulette operator is used to select the remaining individuals with relatively high fitness through roulette, and then they are copied and randomly operated with the two parent chromosomes. The present invention can directly reduce the probability of inferior individuals with excellent genes being eliminated, so that the population can better adapt to the living environment. The probability of individual i being selected is:

[0125]

[0126] In the formula, E i is the fitness value of individual i, and Q is the population size.

[0127] 1.2.3 Adaptive crossover operator based on environment perception

[0128] Crossover is a method of forming a new individual by replacing and recombining parts of the structures of two parents. c Selection is a key factor affecting the behavior and performance of genetic algorithms, and it directly affects the convergence of the algorithm. c It can accelerate the generation of new individuals, increase population diversity, help the algorithm quickly explore a wider solution space, avoid falling into the local optimal solution, and thus improve the global search ability. However, a too high crossover probability P c It may destroy the genetic structure of excellent individuals and affect the stability and convergence of the algorithm. On the contrary, low crossover probability P c It helps to retain the excellent individual structure and improve the stability of the algorithm, but it may slow down the generation of new individuals, resulting in insufficient population diversity, slowing down the search process or even stagnating, and increasing the risk of falling into a local optimal solution. At the same time, in the algorithm optimization calculation process for digital twin networks, the algorithm faces a dynamically changing network environment, which causes the solution performance after the algorithm runs to decline and cannot adapt to the changed network environment. Therefore, the present invention proposes an adaptive crossover probability based on environmental perception.

[0129] First, in order to balance the convergence and stability of the algorithm and avoid falling into the local optimal solution, the present invention adaptively adjusts the crossover probability according to the change of population fitness. The calculation method is shown in formula (4.28):

[0130]

[0131] In the formula, E max is the maximum fitness in the group; E avg is the average fitness value of each generation; E h is the higher fitness value of the two crossover individuals; P c1 Set to 0.9, P c2 Set to 0.6. By incorporating the fitness value into the calculation of the crossover probability, when there are more individuals with high fitness, we tend to retain these excellent individuals and reduce their chances of being crossed over, thereby avoiding the premature loss of valuable genes. In the case of low fitness, we tend to increase the possibility of crossover to help the search space explore more widely and help escape from the local optimal solution.

[0132] Secondly, in order to adapt to the impact of dynamic environment and improve the performance of algorithm solution, the present invention further introduces an environmental perception mechanism based on the adaptive crossover probability, so as to dynamically adjust the crossover probability according to environmental changes during the algorithm iteration process. When the environment changes during the operation of the algorithm, by increasing the crossover probability, it can quickly adapt to the new environment to find a better solution. The weighted adjacency relationship matrix A defined in formula (4.15) is used to characterize the strength of the adjacency relationship between subnets. When the network topology changes, the matrix A also changes accordingly. Therefore, the algorithm uses the changes in the elements in the matrix A to measure the dynamic changes of the network topology, defines the adjacency matrix change index (Matrix Change Index, MCI), and uses M g It means that since matrix A is a symmetric matrix, the calculation formula of MCI is:

[0133]

[0134] In the formula, n represents the number of subnets, that is, the dimension of matrix A, and w ij,g and w ij,g-1 Respectively represent the weight values ​​of the i-th row and j-th column in the adjacency matrix in the g-th generation and the g-1-th generation. In addition to network topology changes, network environment changes also include changes in minimum power constraints caused by channel environment changes and changes in frequency usage constraints caused by external interference. Therefore, the constraint violation index (CVI) is introduced, using G gTo further evaluate the environmental changes, for the equality constraint s(x) = 0, the violation index is calculated by |s(x)|; for the inequality constraint h(x) ≦ 0, the violation index is calculated by max(0, h(x)). Therefore, the constraint violation index G(x) of the individual can be calculated. i ):

[0135]

[0136] In the formula, C s and C h are the number of equality constraints and inequality constraints, respectively, and x i is the i-th individual in the population, then the total constraint violation index is:

[0137]

[0138] The adjacency matrix change index and constraint violation index are unified into the environment change rate (ECR), and R g express:

[0139] R g =δ·M g +ε·G g (4.35)

[0140] Where δ and ε are the weights of MCI and CVI respectively. Based on the environmental change rate, the crossover probability P c Further adjusted to:

[0141] P c =P c +φ·R g (4.36)

[0142] Here, φ is a global adjustment coefficient that controls the increase in the crossover probability in order to quickly respond to environmental changes.

[0143] The adaptive crossover probability obtained through the above design can ensure that the algorithm can effectively balance the convergence speed and stability at different stages according to the population fitness and environmental changes, and can also guarantee good solution quality in a dynamic and complex network environment, so that the algorithm can more effectively find the optimal solution and improve the overall optimization performance.

[0144] 1.2.4 Binary Parent-Induced Mutation Operator

[0145] Mutation refers to the modification or replacement of certain gene values ​​in individual chromosomes to form new individuals. m The setting has a significant impact on the genetic algorithm: high mutation probability P mIt can significantly increase the diversity of the population, help the algorithm escape from the local optimal solution, and enhance the global search capability, especially in the environment where the problem space is complex or dynamically changing. m This will lead to excessive randomness of the individual structure, and the genetic algorithm may become a purely random search. On the contrary, a low mutation probability P m It helps to preserve the genetic structure of individuals with high fitness, maintain the stability and convergence of the algorithm, and is especially helpful for fine search when approaching the optimal solution, but the mutation probability P is too low. m It will lead to insufficient population diversity, causing the algorithm to fall into a local optimal solution in the early stage and fail to fully explore the entire solution space. At the same time, the traditional genetic algorithm has the problem of premature convergence, which is mainly due to the inability to produce effective new individuals, attributed to the lack of effective alleles in individuals, that is, the lack of gene value diversity on the chromosomes at the same gene position. In the selection stage, the algorithm tends to speed up the convergence process, which may lead to a decrease in the proportion of specific gene values ​​at a certain gene position. Therefore, in order to prevent premature convergence, it is necessary to increase the diversity of alleles through mutation operators to expand the space of algorithm exploration solutions as much as possible, but at the same time, it is also necessary to maintain the algorithm's better target convergence and effectiveness. Therefore, the present invention proposes a binary parent induced mutation operator.

[0146] First, the algorithm uses adaptive mutation probability to maximize the exploration of the solution space and optimize samples in the direction of high fitness. m The selection of is determined by formula (4.34):

[0147]

[0148] Where P mmax , P mmin are the maximum and minimum values ​​of the mutation probability, E h is the larger fitness value of the two individuals in the cross selection; E avg is the average fitness value of the population in each generation.

[0149] Secondly, when performing mutation operations, in order to solve the problem of effective allele loss caused by random selection and assignment of traditional mutation operators and keep the algorithm converging towards the expected goal, a binary parent-induced mutation operator based on the adjacency relationship matrix is ​​introduced. Avoid chromosomes using the same gene value at the same gene position as much as possible, and make the gene position with a gene value of 1 in different chromosomes selected by the subnet adjacency relationship matrix value. In this problem model, it is expressed as two subnets avoiding selecting the same frequency and power as much as possible, and the adjacency value of the two subnets with the same frequency is as small as possible. The binary parent-induced mutation operator of the algorithm needs to select two effective parent chromosomes first. The subnet adjacency weights corresponding to the two chromosomes should be as high as possible, so that the two subnets with a high degree of adjacency avoid selecting the same frequency as much as possible. Since each chromosome only selects one power value, in order to avoid affecting the power allocation, the mutation operator only operates on the chromosomes of the frequency part, and the chromosomes of the power part still use random selection mutation. The specific mutation operation is as follows:

[0150] Randomly select a parent chromosome i, and query the adjacency matrix A according to the subnet number corresponding to the chromosome, and obtain the one-dimensional adjacency weight array w of the subnet i , select the maximum weight value w ij Get the subnet number, that is, the parent chromosome j. Figure 5 As shown, a parent chromosome is randomly selected, that is, the chromosome of subnet S2, and the subnet with the highest adjacency weight value is subnet S1, so its corresponding chromosome 1 and chromosome 2 are selected. If the parent chromosome 1 and chromosome 2 are all 0 after the "logical AND" operation, it means that the two parents are all opposite, and the above process is repeated to reselect new parents.

[0151] There are multiple effective allele deletions in the two parents selected in the figure, that is, the gene values ​​of the two chromosomes at multiple gene positions are 0. The "XOR" and "XOR" operations are performed on the two chromosomes to ensure the full transposition of the two chromosomes. Figure 6 shown.

[0152] After the mutation, there are two completely opposite chromosomes in the offspring chromosomes, and at least one chromosome with the same gene value is 1. In the problem model, this means that completely different frequency points are selected for the two subnets, but the number of frequency points required for a subnet is fixed. Therefore, further secondary mutation processing is required for the offspring chromosomes after the operation.

[0153] Assume that after the first-level mutation, the chromosome with the most frequency points in the offspring chromosome is V1, and the required frequency is m. v1 , the number of allocated frequency points is n v1 ; The offspring chromosome with fewer frequency points is V2, and the required frequency is mv2 , the number of allocated frequency points is n v2 .

[0154] 1) First, if n v2 <m v2 , then randomly select Δm in V1 v2 -n v2 Set the gene positions that are 0 to 1 to make up the required number of frequencies, and determine whether there are any extra frequency points in V1. If so, set the same gene positions to 0 and update n v1 ; if n v2 >m v2 , and Δn v2 -m v2 <m v2 , then randomly select Δn v2 -m v2 The gene position is 0; if Δn v2 -m v2 >m v2 , then proceed to the next step for processing;

[0155] 2) After processing in 1), if there are still extra gene bits in the chromosome, determine whether the number of extra gene bits in a single chromosome is greater than the subnet frequency requirement, that is, Δn vi -m vi Is it greater than m? vi , if Δn vi -m vi <m vi , then randomly select Δn vi -m vi The gene position 0 is 0 to satisfy the frequency constraint; if Δn vi -m vi >m vi , then obtain the adjacent subnet with the second highest weight value in the adjacency matrix of its corresponding subnet, and select its corresponding chromosome as the secondary parent chromosome;

[0156] 3) "Invert" each bit of the secondary parent chromosome and perform "logical AND" with the offspring chromosome bit by bit, and move the redundant gene positions of the offspring chromosome to 0 to meet the frequency constraint; if the number of redundant gene bits is still greater than the subnet frequency requirement, that is, Δn vi -m vi >m v2 , then repeat the operation with the adjacent subnet with the next higher weight;

[0157] 4) When the number of redundant gene bits is less than the subnet frequency demand, that is, Δn vi -m vi <m vi , then the redundant gene position 0 is randomly selected to satisfy the frequency constraint.

[0158] According to the above description, Figure 7 The secondary mutation process of the two daughter chromosomes obtained in Figure 7 As shown, here we take the frequency demand number in both children as 3 as an example:

[0159] After secondary mutation, we finally get offspring chromosomes 1 and 2 that meet the constraints. While dealing with the loss of effective alleles, they also have the tendency to reduce conflicts between frequency points of adjacent subnets, allowing the algorithm to evolve in the expected direction, expanding the exploration solution space while improving the convergence speed.

[0160] The algorithm performs selection, crossover and mutation in a loop, and the algorithm convergence criteria are as follows: The termination evolution generation of the genetic algorithm is 200 generations in the present invention; after 30 generations, there is no obvious increase in fitness. The chromosome individual with the highest fitness value in the termination generation is selected, and the gene value of its part is the frequency point allocation that minimizes the interference probability.

[0161] 1.2.5 Overall algorithm process

[0162]

[0163] 1.3 The simulation and analysis of the present invention specifically include:

[0164] The present invention simulates a resource optimization algorithm based on an improved genetic algorithm. In terms of algorithm performance analysis, a traditional genetic algorithm, a non-dominated sorting genetic algorithm II (NSGA-II) and the improved genetic algorithm of the present invention are compared. By comparing the solution performance, convergence curves and running time of the three algorithms, the optimization performance of the present invention in a mobile ad hoc network communication scenario is analyzed from multiple dimensions. The parameter index mainly considers the real-time packet loss rate caused by link conflicts during runtime.

[0165] 1.3.1 Simulation scenario

[0166] The constant fading model is used in the network scenario setting; the application layer service flow uses a fixed bit rate based on EXata, and the size of a single service packet is 1024Bytes; the number of scene nodes is 200, and the number of subnets is divided into 20. The nodes move crosswise in the area in units of subnets, and the speed is 2-5m / s; the nodes use frequency hopping, and each frequency hopping table contains 3 frequency hopping points, so the number of frequency points that need to be allocated is 60. The frequency band uses 1.2GHz to 1.8GHz, and the bandwidth is 20MHz. Therefore, the number of frequency points available for allocation is 30, and there is frequency reuse. Initially, the entire network uses the same frequency hopping table and the same transmission power of 10dBm. The simulation running time is 105 seconds. In order to reduce the impact of the route establishment time on the simulation results, the service data transmission and parameter statistics are all started from the 5th second of the simulation run, and the node movement starts from the 30th second. The network parameter configuration is shown in Table 2:

[0167] Table 3 Network parameter configuration

[0168] Network parameters value Business flow model CBR Business flow size 1024Bytes Number of network nodes 200 Number of subnets 20 Network frequency 60 Network available frequencies 30 Node moving speed 2~5m / s Node bandwidth 20MHz Node power 10dBm

[0169] The common parameter settings of the traditional genetic algorithm, NSGA-II and the present invention are shown in Table 3:

[0170] Table 4 Algorithm common parameter configuration

[0171] Network parameters value Population size 50 Initial crossover probability 0.9 Initial mutation probability 0.001 Maximum number of iterations 250

[0172] The NSGA-II mating pool size is 80, the number of bidding candidates is 4, the crossover distribution index is 20, and the mutation distribution index is 20.

[0173] 1.3.2 Algorithm solution performance evaluation

[0174] (1) The entire network uses the same single frequency and the same power allocation. The simulation results are as follows: Figure 8As shown in the figure, the real-time packet loss rate of 20 links in 20 subnets during the simulation process is shown. The simulation results show that the overall packet loss rate under this strategy is very high, especially the communication of some links (link 1 and link 8) is even completely interrupted. From the 5th to the 15th second, there are 8 links with complete packet loss. This is because the probability of routing signaling packets in the node network is high, which leads to slow communication connection establishment and the inability of service data to find the correct path, resulting in packet loss. This phenomenon is mainly attributed to the dense nodes in the large-scale self-organizing network sharing the same frequency, causing co-frequency interference, resulting in a large number of data packets lost. After 30 seconds, the simulation shows that the packet loss rate of large-scale links gradually increases to 60%. This increase is due to the random cross-movement of all nodes in subnets from the 30th second, which causes changes in the network topology and the effective distance between nodes, thereby increasing the probability of link conflict and instability, and then causing the link packet loss rate to gradually increase. This result shows that in a network environment with dense nodes and continuously changing network topology, a single resource allocation strategy for the entire network will seriously affect network performance.

[0175] (2) The simulation results of frequency and power allocation using NSGA-II are as follows Fig. 9 As shown in the figure, since the resource allocation algorithms studied in the past cannot meet the real-time processing requirements of high mobility of self-organizing networks in terms of operating efficiency, only a one-time resource allocation scheme can be run within the limited simulation time. Based on the objective function designed by the present invention, the resource allocation scheme solved by the NSGA-II algorithm through the initial network topology has good applicability in the early stage of simulation. The initial packet loss rate of the whole network link is significantly reduced compared with the single resource allocation scheme, the nodes of the whole network can quickly establish routes, and all links can communicate normally. However, since the number of network frequencies is greater than the number of available frequency points, the reuse of frequencies will still cause link conflicts within a certain range. As the network nodes move, the network topology changes. After the 30th second, the performance of the frequency allocation scheme solved based on the initial topology is significantly reduced, and the packet loss rate of 8 links rises rapidly, and the packet loss rate of 6 links (link 5, link 20, etc.) rises for a long time, indicating that these links are in a dense network area and are greatly affected by topology changes, and the initial resource allocation scheme fails.

[0176] (3) The real-time distribution simulation results of the present invention are as follows Fig.10 As shown:

[0177] Under the real-time resource allocation strategy of the present invention, the packet loss rate of the entire network link is significantly reduced compared with the above two algorithms. There are 12 links that still maintain a packet loss rate of 0 for the entire simulation time under the network topology change scenario, indicating that the algorithm can dynamically reallocate resources according to the real-time network topology changes and the connection strength of adjacent subnets. The peaks and troughs in the figure also show that the algorithm can respond quickly to sudden changes in network topology, adjust the resource allocation strategy in time, and maximize the communication efficiency of the link. The analysis results show that the algorithm can ensure the stability of the link and the continuity of data transmission under frequently changing network conditions through fast real-time resource management, showing the algorithm's better solution performance.

[0178] 1.3.3 Algorithm Performance Evaluation

[0179] (1) The number of available frequencies in the network is 30, and the number of frequencies required in the network is 60. The available frequencies cannot meet the demand, and the fitness value curve when frequency reuse is required is as follows: Fig.11 As shown in the figure, the fitness value is inversely proportional to the conflict probability. The larger the fitness value, the smaller the frequency point conflict probability. Figure 4-9 It can be seen that the traditional genetic algorithm converges slowly, and after 250 generations of iterations, it cannot converge to the optimal solution. Although the frequency point allocation scheme obtained by the algorithm can reduce the probability of frequency point conflict to a certain extent, there is still a possibility of large local frequency point conflict. The NSGA-II algorithm also shows good performance in algorithm convergence. After 150 iterations, it also converges to the optimal solution. This depends on the algorithm using fast non-dominated sorting and crowded comparison operators, which can significantly improve the algorithm convergence speed while ensuring the quality of the solution. The algorithm of the present invention has a good fitness value when initialized, and can converge quickly when performing solution exploration, and tends to be stable after 55 generations. This is because when initializing, the initialization method of the good point set is adopted, so that the initial population can cover more possible solutions, and at the same time, an adaptive crossover probability and mutation probability are adopted, and a double chromosome mutation scheme is used to reduce the effective allele loss, so that better individuals can be obtained faster in the early stage of evolution to achieve rapid convergence.

[0180] (2) The number of available frequency points in the network is 30, and the frequency demand of a single subnet is 3. Therefore, the frequency demand of the entire network will increase exponentially with the increase in the number of subnets. The computational complexity faced by the algorithm will also increase significantly. The solution running time of the three algorithms as the decision space becomes larger is as follows:

[0181] As the number of subnets increases, the decision space of the algorithm becomes larger. It can be seen that the running time of the traditional genetic algorithm increases rapidly. When the number of subnets reaches 100, the running time of the algorithm exceeds 220 seconds. The algorithm can only meet the real-time allocation requirements when the number of subnets is less than 20. However, since the NSGA-II algorithm needs to perform non-dominated sorting and solve the congestion, the algorithm has good convergence, but the running time of each generation is long. The running time required by the algorithm also cannot meet the requirements. After the number of subnets exceeds 35, the algorithm running time has exceeded 20s. This is because the NSGA-II algorithm uses a non-dominated sorting method, which needs to first calculate the domination count and the dominated solution set of each solution, which requires a square-level time complexity; the congestion comparison operator is used to further compare the advantages and disadvantages of the solutions in the solution set after non-dominated sorting, and the time complexity of this operator is logarithmic. The present invention can always maintain good operating efficiency as the decision space becomes larger. When the number of subnets is within 80, the algorithm running time is maintained below 10s. Even if the number of subnets increases to 100, the algorithm running time is still maintained within 18s, which can meet the real-time changing resource requirements of large-scale self-organizing networks.

[0182] The present invention first establishes an electromagnetic compatibility model including co-channel interference, adjacent channel interference and harmonic interference, aiming at minimizing the frequency allocation target model of interference. Subsequently, the problem is simplified to resource allocation optimization based on subnets, by considering the nodes of time-division multiplexing in the same subnet as conflict-free, and using a weighted adjacency matrix to describe the connection strength between subnets. In addition, the power allocation problem is transformed into the problem of maximizing the transmission capacity of the entire network, and it is effectively associated with the frequency allocation problem to ensure the consistent solution direction of the multi-objective optimization problem. Considering that the constructed problem belongs to the NP-hard class and needs to be solved quickly, this study proposes an improved genetic algorithm to obtain an approximate optimal solution. The algorithm adopts a matrix encoding method, combined with a good point set population initialization method, and introduces an adaptive crossover operator based on environmental perception, so that the algorithm can perceive environmental changes and adapt quickly during the iteration process, thereby ensuring the quality of the solution. At the same time, a binary parent-induced mutation operator based on adjacency is used to induce the algorithm to explore in the direction of high fitness, thereby improving the convergence and operation efficiency of the algorithm. The simulation results show that the algorithm can respond quickly to sudden changes in network topology and adjust resource allocation strategies in a timely manner to maximize the communication efficiency of the link in the dynamic and changeable scenario of mobile ad hoc networks. By comparing the running time of the three algorithms, the present invention can quickly converge and output the optimal solution, ensuring the stability of the link and the continuity of data transmission under frequently changing network conditions, thus showing excellent solution performance.

Claims

1. A digital twin network resource optimization method based on a multi-objective genetic algorithm, characterized by: The method adopts a fast genetic algorithm to solve the multi-objective problem to cope with the rapidly changing resource allocation requirements of mobile ad hoc networks. The matrix encoding method is used. Compared with the one-dimensional data structure, this two-dimensional data structure has a larger representation space and a more flexible way to generate new individuals. The encoding strategy is shown in Table 1, where "1" indicates that the frequency and power corresponding to the column where the element is located are allocated to the subnet corresponding to the row (gene). Each subnet power has only one choice. This encoding strategy is achieved by randomly generating a two-dimensional array (chromosome) with elements of "0" and "1". Table 1 Genetic algorithm coding table The method of generating a population with a good point set is introduced. Through a series of calculations, a set of point sets is generated so that the generated point set can cover as many solution spaces with high fitness values ​​as possible. The number of populations is Q, the number of gene values ​​of each individual is c = n (z + q), the number of good points in the generated good point set is Q, and each good point is represented by P Q (i)=(r1·i,r2·i,…,r c i), i∈[1,Q], i.e., the initialized individual; In the best point set population generation method, for each individual in the population, a set of specific values, called r value vectors, must first be calculated. The number of vectors is the number of genes c of each individual, that is, r = (r1, r2, ..., r c ), use formula (4.25) to calculate the r value; r j =mod(2cos(2πj / k)·i,1)(4.1) In the formula, i represents the i-th individual in the population, j represents the j-th element in the r-value vector, and k is the smallest prime number that satisfies (k-3) / 2≧c. Then, these r-value vectors can be used to construct the good point set P Q ; Map the good point set to the feasible region of the population, using formula (4.26) for mapping, y ij represents the best point after mapping, a j and b j are the upper and lower limits of the feasible region respectively; y ij =a j +P Q (i)·(b j -a j )(4.2) Each good point in the good point set is converted into a specific individual code to complete the population initialization. When converting the good points into individual gene values, adjustments need to be made to meet the constraints. Finally, a group of populations with good spatial distribution and structure are initialized, which can eliminate the uncertainty in the population initialization process. The selection method is a combination of best individual retention and roulette wheel; First, the best individual operator is used to retain the individuals with good genes and the top 5% of fitness values, allowing them to evolve directly to the next generation. Second, the roulette operator is used to select the remaining individuals with relatively high fitness through roulette, and then they are copied and randomly operated with the two parent chromosomes, directly reducing the probability of inferior individuals with good genes being eliminated, so that the population can better adapt to the living environment. The probability of individual i being selected is: In the formula, E i is the fitness value of individual i, and Q is the population size.

2. According to claim 1, a digital twin network resource optimization method based on a multi-objective genetic algorithm is characterized in that: The method includes adaptive crossover probability based on environment perception: First, in order to balance the convergence and stability of the algorithm and avoid falling into the local optimal solution, the crossover probability is adaptively adjusted according to the change of population fitness. The calculation method is shown in formula (4.28): In the formula, E max is the maximum fitness in the group; E avg is the average fitness value of each generation; E h is the higher fitness value of the two crossover individuals; P c1 Set to 0.9, P c2 Set to 0.

6. By incorporating the fitness value into the calculation of the crossover probability, when there are many individuals with high fitness, we tend to retain these excellent individuals and reduce their chances of being crossed over, thereby avoiding the premature loss of valuable genes. When the fitness is low, we tend to increase the possibility of crossover to help the search space explore more widely and help escape from the local optimal solution. Secondly, an environment perception mechanism is introduced to dynamically adjust the crossover probability according to environmental changes during the algorithm iteration process. When the environment changes during the algorithm operation, by increasing the crossover probability, it can quickly adapt to the new environment to find a better solution, which is defined in The weighted adjacency matrix A in formula (4.15) is used to characterize the strength of the adjacency relationship between subnets. When the network topology changes, the matrix A also changes accordingly. Therefore, the change of elements in the matrix A is used to measure the dynamic change of the network topology. The adjacency matrix change index (MCI) is defined and M is used. g It means that since matrix A is a symmetric matrix, the calculation formula of MCI is: In the formula, n represents the number of subnets, that is, the dimension of matrix A, and w ij,g and w ij,g-1 Represent the weight values ​​of the i-th row and j-th column in the adjacency matrix in the g-th generation and the g-1-th generation respectively. In addition to the network topology change, the network environment change also includes the minimum power constraint change caused by the channel environment change and the frequency usage constraint change caused by external interference. The constraint violation index (CVI) is introduced and G is used g To further evaluate the environmental changes, for the equality constraint s(x) = 0, the violation index is calculated by |s(x)|; for the inequality constraint h(x) ≦ 0, the violation index is calculated by max(0, h(x)). Therefore, the constraint violation index G(x) of the individual can be calculated. i ): In the formula, C s and C h are the number of equality constraints and inequality constraints, respectively, and x i is the i-th individual in the population, then the total constraint violation index is: The adjacency matrix change index and constraint violation index are unified into the environment change rate (ECR), and R g express: R g =δ·M g +ε·G g (4.8) In the formula, δ and ε are the weights of MCI and CVI respectively. Based on the environmental change rate, the crossover probability P c Further adjusted to: P c =P c +φ·R g (4.9) Here, φ is a global adjustment coefficient that controls the increase in the crossover probability in order to quickly respond to environmental changes.

3. According to claim 1, a digital twin network resource optimization method based on a multi-objective genetic algorithm is characterized in that: The method includes a binary parent-induced mutation operator, and the specific method includes: First, the algorithm adopts adaptive mutation probability to maximize the exploration of solution space and optimize samples in the direction of high fitness. m The selection of is determined by formula (4.34): Where P mmax , P mmin are the maximum and minimum values ​​of the mutation probability, E h is the larger fitness value of the two individuals in the cross selection; E avg is the average fitness value of each generation; Secondly, when performing mutation operations, in order to solve the problem of effective allele loss caused by random selection and assignment of traditional mutation operators and keep the algorithm converging towards the expected goal, a binary parent-induced mutation operator based on the adjacency relationship matrix is ​​introduced to avoid chromosomes using the same gene value at the same gene position as much as possible, and make the gene position with a gene value of 1 in different chromosomes selected by the subnet adjacency relationship matrix value. In this problem model, it is expressed as two subnets avoiding selecting the same frequency and power as much as possible, and the adjacency relationship value of two subnets with the same frequency is as small as possible. The binary parent-induced mutation operator of the algorithm needs to first select two effective parent chromosomes. The subnet adjacency weights corresponding to the two chromosomes should be as high as possible, so that two subnets with a high degree of adjacency avoid selecting the same frequency as much as possible. Since each chromosome only selects one power value, in order to avoid affecting the power allocation, the mutation operator only operates on the chromosomes of the frequency part, and the chromosomes of the power part still use random selection mutation.

4. According to claim 3, a digital twin network resource optimization method based on a multi-objective genetic algorithm is characterized in that: The mutation operation of the method includes: randomly selecting a parent chromosome i, and querying the adjacency matrix A according to the subnet number corresponding to the chromosome, to obtain the one-dimensional adjacency weight array w of the subnet i , select the maximum weight value w ij Get the subnet number, that is, the parent chromosome j, and randomly select a parent chromosome, that is, the chromosome representing subnet S2. The subnet with the highest adjacent weight value is subnet S1, so select its corresponding chromosomes 1 and 2. If the "logical AND" operation of parent chromosomes 1 and 2 is all 0, it means that the two parents are all opposite, then repeat the above process to reselect new parents.

Images