Wireless sensor network coverage multi-task optimization method for knowledge migration among similar individuals

Abstract

The invention discloses a wireless sensor network coverage multi-task optimization method for knowledge migration among similar individuals, and the method comprises the steps: modeling a wireless sensor network coverage problem into a multi-task optimization problem, and obtaining a target function of each optimization task; and then an evolutionary multi-task optimization method based on knowledge migration among similar individuals is designed to solve the multi-task optimization problem, so that the optimal placement position and the optimal coverage radius of a group of sensors are obtained, and the aims of higher coverage rate and lower cost are fulfilled. According to the strategy, knowledge migration occurs between similar individuals of similar tasks, the quality of knowledge migration is improved, and positive migration of knowledge is promoted. The knowledge migration effect is evaluated according to the survival rate of the migration individuals in the population, the probability of knowledge migration is adaptively adjusted, and negative migration is effectively reduced.

Description

Technical Field

[0001] The present invention relates to a multi-task optimization method for wireless sensor network coverage based on knowledge transfer between similar individuals, and belongs to the technical field of the Internet of Things. Background Art

[0002] In the field of the Internet of Things, a wireless sensor network is an important part, which can help people break the information barrier between the physical world and the information world and realize the monitoring of any environment. Coverage is an important issue in wireless sensor networks, and the coverage quality is an important indicator for people to evaluate the performance of wireless sensor networks. Therefore, the solution of the coverage problem is of great significance for people to collect, summarize, query, analyze, etc. data through wireless sensor networks.

[0003] The wireless sensor network coverage problem can be represented as an optimization problem, and its optimization goal is to obtain the optimal placement positions and optimal coverage radii of a group of sensors, so as to maximize the coverage of a given domain at a lower cost. An important feature of such optimization problems is that the length of the variables is variable, and the length of the optimal variables is not known in advance. By solving each variable-length case as an optimization task, the wireless sensor network coverage problem can be transformed into a multi-task optimization problem to solve.

[0004] Evolutionary algorithms are considered to be methods suitable for solving optimization problems. However, traditional evolutionary algorithms can only solve one task in one run. Evolutionary multi-task optimization algorithms can fully exploit the potential parallel processing ability under the population search method and improve the solution performance through knowledge transfer between tasks, and can well solve multi-task optimization problems, and have gradually become a research hotspot in recent years.

[0005] Existing evolutionary multi-task optimization methods usually rely only on the similarity of population distributions to select knowledge sources. However, it is worth noting that even among populations with similar distributions, there are individuals with obvious distribution differences. If knowledge transfer occurs between these individuals, it will affect the evolutionary process of the population corresponding to the target task, resulting in negative transfer. Therefore, how to promote positive knowledge transfer and avoid negative knowledge transfer through knowledge transfer between similar individuals of similar tasks is still a very challenging topic. Summary of the Invention

[0006] The present invention proposes a multi-task optimization method for wireless sensor network coverage based on knowledge transfer between similar individuals. This method models the wireless sensor network coverage problem as a multi-task optimization problem, obtains the objective function of each optimization task, and then designs an evolutionary multi-task optimization method based on knowledge transfer between similar individuals to solve this multi-task optimization problem, so as to obtain a set of optimal placement positions and optimal coverage radii of sensors to meet the goal of higher coverage rate and lower cost.

[0007] The main idea of implementing the present invention is as follows: If the knowledge transfer condition is met, the maximum mean discrepancy metric is used to calculate the distribution difference between the current task and other tasks, and the task most similar to the current task is selected as the source task. Then, K-means clustering is used to cluster and divide the current task population, and the excellent individuals from the source task are added to the cluster most similar to them in the current task to achieve fine-grained knowledge transfer between similar individuals, thereby effectively reducing knowledge negative transfer. Finally, the knowledge transfer probability of each optimization task is adjusted in real time according to the survival rate of the transferred individuals, so as to further reduce knowledge negative transfer. If the knowledge transfer condition is not met, a Gaussian distribution model is constructed for the current task population, and offspring are generated by sampling the model.

[0008] A multi-task optimization method for wireless sensor network coverage based on knowledge transfer between similar individuals proposed by the present invention includes the following steps:

[0009] Step 1, model the wireless sensor network coverage problem as a multi-task optimization problem. In this multi-task optimization problem, each optimization task uses a given number of sensors to cover a specific square area. Each sensor can completely cover a circular area around it, and the larger the coverage radius of the sensor, the higher the cost. The optimization goal of each optimization task is to determine the placement positions and coverage radii of the given number of sensors to meet higher coverage rate and lower cost.

[0010] Step 2, in the initialization stage, for a multi-task optimization problem of wireless sensor network coverage with K optimization tasks, K populations are randomly initialized. Each population corresponds to an optimization task respectively, and the individuals in the population are evaluated for fitness according to the objective function of the task corresponding to the population. At the same time, the knowledge transfer probabilities of K tasks are initialized.

[0011] Step 3, for the current task, make a conditional judgment on whether to perform knowledge transfer. If the knowledge transfer condition is met, perform Steps 4-6 to generate offspring through knowledge transfer. If the knowledge transfer condition is not met, perform Step 7 to generate offspring through task self-evolution.

[0012] Step 4, select a most similar task as the source task for the current task according to the Maximum Mean Discrepancy (MMD) metric. Calculate the maximum mean discrepancy values between the current task and other tasks respectively, and then select the task with the smallest discrepancy value as the source task of the current task.

[0013] Step 5, select similar individuals from the source task to perform knowledge transfer with the current task. First, use the K-means clustering method to divide the population corresponding to the current task to form multiple clusters. Second, select the most excellent part of the individuals from the population corresponding to the source task as the transfer individuals. Then, for each transfer individual, calculate its distance from different cluster centers, and add the transfer individual to the cluster with the closest distance to it, that is, the most similar cluster. Finally, repeat the above process for all transfer individuals until all transfer individuals are transferred to the clusters of the current task, so as to achieve a more refined knowledge transfer between similar individuals of different tasks.

[0014] Step 6, construct local Gaussian distribution models on multiple clusters of the current task respectively, and sample from the models corresponding to the clusters where the parent individuals are located to generate offspring.

[0015] Step 7, generate offspring through the self-evolution process of the current task. Generate offspring by constructing a Gaussian probability model on some excellent individuals in the population corresponding to the current task and sampling from it.

[0016] Step 8, perform environmental selection on the combined population composed of the parent population and the offspring population, and retain the most excellent individuals to form the new generation population of the current task.

[0017] Step 9, adjust the knowledge transfer probability of the current task according to the survival rate of transfer individuals. Define the proportion of transfer individuals that successfully replace parent individuals after environmental selection in each generation of the evolution process as the survival rate of transfer individuals. According to this definition, first calculate the survival rate of transfer individuals of the current task. Then update the knowledge transfer probability according to the survival rate of transfer individuals of the current task. The lower the survival rate of transfer individuals, the more limited the auxiliary effect of knowledge transfer on population evolution. At this time, the transfer probability should be appropriately reduced to avoid the potential negative knowledge transfer affecting the convergence of the target task. On the contrary, the higher the survival rate of transfer individuals, the greater the help of knowledge transfer to population evolution. At this time, the transfer probability should be appropriately increased to promote positive knowledge transfer.

[0018] Step 10, repeat Steps 3 - 9 for each task until the termination condition is met, and then output the optimal result, that is, the sensor parameters that meet the optimal objective value.

[0019] Compared with the prior art, the present invention has the following obvious advantages and beneficial effects:

[0020] 1) To avoid negative transfer caused by knowledge sharing among randomly selected individuals, the present invention proposes a knowledge transfer strategy based on similar individuals. This strategy enables knowledge transfer to occur between similar individuals in similar tasks, improves the quality of knowledge transfer, and promotes positive knowledge transfer.

[0021] 2) The present invention designs an adaptive transfer probability adjustment strategy based on individual survival rate to evaluate the knowledge transfer effect of each task. This strategy evaluates the knowledge transfer effect according to the survival rate of transferred individuals in the population and adaptively adjusts the knowledge transfer probability, effectively reducing negative transfer. BRIEF DESCRIPTION OF THE DRAWINGS

[0022] Figure 1 is a flowchart of the method proposed by the present invention.

[0023] Figure 2 is a graph of the optimal results obtained by the method proposed by the present invention and other algorithms in solving the multi-task optimization problem of wireless sensor network coverage. DETAILED DESCRIPTION OF THE INVENTION

[0024] To further explain the technical solution of the present invention, the following will elaborate on the present invention through specific implementation cases.

[0025] Figure 1 is a schematic diagram of the process of the present invention. As Figure 1 shown, first in the initialization stage, the populations of each task and parameter settings are randomly initialized. Then, the judgment of knowledge transfer conditions is carried out. If the knowledge transfer conditions are met, the task most similar to the current task will be selected as the source task, and then knowledge transfer between similar individuals will be carried out with the source task to generate offspring. If the knowledge transfer conditions are not met, the self-evolution process of the population of the current task will be carried out, a Gaussian distribution model will be constructed for the population, and then offspring will be generated through model sampling. In the environmental selection stage, the most excellent individuals in the joint population composed of the parent population and the offspring population will be selected as the new generation population. Finally, the above process is repeated until the termination condition is met, and the result is output.

[0026] The performance of the method IS-EMTO proposed by the present invention is tested on the multi-task optimization problem of wireless sensor coverage, and is compared with 5 most representative algorithms, including ASCMFDE, BLKT-DE, MFEA-DGD, MFMP and MTES. Each test function is independently run 20 times, and the obtained average optimal objective function values are recorded.

[0027] The multi-task optimization method IS-EMTO for wireless sensor network coverage based on knowledge transfer between similar individuals proposed by the present invention is described in detail below.

[0028] (Step 1) Model the wireless sensor network coverage problem as a multi-task optimization problem. In this multi-task optimization problem, each optimization task uses a given number of sensors to cover a specific square area. Each sensor can fully cover a circular area around it, and the larger the coverage radius of the sensor, the higher the cost. The optimization goal of each optimization task is to determine the placement positions and coverage radii of the given number of sensors to achieve higher coverage rate and lower cost. Thus, the multi-task optimization problem of wireless sensor network coverage can be expressed in the following form:

[0029] {x 1 ,x 2 ,…,x K}=argmin{f 1 (x 1 ),f 2 (x 2 ),…,f K (x K )} (1)

[0030] where f k (·), k ∈ {1, 2, …, K} represents the objective function of the k-th optimization task; x k , k ∈ {1, 2, …, K} represents the optimal solution obtained by solving the k-th optimization task; K is the number of optimization tasks that need to be solved simultaneously, and each optimization task has a different number of sensors. In particular, for an optimization task T with N sensors, its objective function f(x) can be expressed in the following form:

[0031]

[0032] where A represents the target rectangular area to be covered by N wireless sensors, i.e., A = [-1, 1] × [-1, 1]; (x i , y i ) represents the placement position of the i-th wireless sensor; r i represents the coverage radius of the i-th wireless sensor; represents the area jointly covered by these N wireless sensors. In particular, the solution x includes the placement positions and coverage radii of these N wireless sensors, i.e., x = {(x 1 , y 1 , r 1 ), (x 2 , y 2 , r 2 ),...,(x N , y N , r N )}.

[0033] (Step 2) In the initialization stage, for a wireless sensor network coverage multi-task optimization problem with K optimization tasks, the method proposed by the present invention randomly initializes K populations, and each population has 100 individuals. The K populations respectively correspond to the K optimization tasks, and the individuals in the population will evaluate the fitness according to the tasks corresponding to the population. At the same time, initialize the knowledge transfer probability atp of the K tasks 1 , atp 2 , …, atp K .

[0034] (Step 3) For the current task T k , make a conditional judgment on whether to perform knowledge transfer. By generating a random number r in the range of [0, 1] and comparing it with the knowledge transfer probability atp k corresponding to the task T K to make a conditional judgment. If the knowledge transfer condition is met, that is, r ≤ atp k , then go to Steps 4-6. If the knowledge transfer condition is not met, that is, r > atp k , then go to Step 7.

[0035] (Step 4) According to the Maximum Mean Discrepancy (MMD) metric, select a most similar task as the source task T k for the current task T s . Calculate the MMD values between the current task and other tasks respectively, and then select the task with the smallest difference value as the source task of the current task. Suppose the populations of two tasks are X = {x 1 , x 2 , …, x m} and Y = {y 1 , y 2 , …, y n}, then the formula for calculating the MMD value between two tasks is as follows:

[0036]

[0037] where P and Q respectively represent the probability distributions corresponding to the current task and another task; m and n respectively represent the number of individuals in the current task population and another task population; represents the Reproducing Kernel Hilbert Space (RKHS); f(·) is a mapping function that can map the solutions in the original decision space to the RKHS . For the convenience of calculation, square and simplify Formula (3) and represent it using the kernel function to obtain the following formula:

[0038]

[0039] Among them, x i and x j ' are two individuals belonging to the current task; y i and y i ' are two individuals belonging to another task; k(·,·) represents the kernel function, and its form is as follows:

[0040]

[0041] (Step 5) Select similar individuals from the source task T s to perform knowledge transfer with the current task T k . First, use the K-means clustering method to partition the population P k corresponding to the current task T k into Cn clusters. Second, select the top p% of the individuals with the best performance from the population P s corresponding to the source task T s as the transfer individuals. Then, for each transfer individual Tr i , calculate its distances from different cluster centers, and add the transfer individual Tr i to the cluster with the closest distance, that is, the most similar cluster. Finally, repeat the above process for all transfer individuals until all transfer individuals are transferred to the Cn clusters of the current task T k , thus achieving more refined knowledge transfer between similar individuals of different tasks.

[0042] (Step 6) Build local Gaussian distribution models on the Cn clusters of the current task T k , and sample from the model corresponding to the cluster where the parent individual is located to generate offspring. The calculation formulas for the model mean μ and variance Σ are as follows:

[0043]

[0044] Among them, S represents the set composed of all individuals in the cluster where the parent individual x i is located.

[0045] (Step 7) Generate offspring through the self-evolution process of the current task T k . Generate offspring by building a Gaussian probability model on the top N / 2 excellent individuals in P k and sampling from it. The calculation formulas for the mean and standard deviation of the model are shown in Formulas (6) and (7). At this time, S represents the set composed of the top N / 2 excellent individuals in P k .

[0046] (Step 8) Perform environmental selection on the combined population composed of the parental population and the offspring population, and retain the top N individuals with the best performance to form the current task T k The new generation of population.

[0047] (Step 9) Adjust the knowledge transfer probability atp of the current task T k according to the survival rate of migrating individuals. k In the present invention, the proportion of migrating individuals that successfully replace parental individuals after environmental selection in each generation of the evolutionary process is defined as the survival rate of migrating individuals. According to this definition, the survival rate sr of migrating individuals in task T k in the g-th generation can be calculated by the following formula: g

[0048]

[0049] where ∈ is a very small positive number to avoid the denominator being zero; represents the number of migrating individuals in the evolutionary process of the g-th generation;

[0050]

[0051]

[0052] where P k,g and P k,g+1 represent the populations corresponding to task T k in the g-th generation and the (g + 1)-th generation respectively; |·| represents the cardinality of the set. Next, according to the survival rate sr of migrating individuals in task T k in the g-th generation obtained above, update the knowledge transfer probability, and the update formula is as follows: g

[0053]

[0054] where represents the probability of knowledge transfer in task T k in the (g + 1)-th generation; atp lb and atp ub are the lower limit and the upper limit of the knowledge transfer probability respectively.

[0054] (Step 10) Repeat Steps 3 - 9 for each task until the termination condition is met, and then output the optimal result, that is, the sensor parameters that meet the optimal objective value.

[0055] The method proposed in the present invention is compared with other algorithms in a wireless sensor network coverage multi-task optimization problem that requires simultaneous optimization of 11 optimization tasks, and each optimization task has a different number of sensors. The comparison results are shown in Table 1. From the results in Table 1, it can be obtained that the method IS-EMTO proposed in the present invention has achieved the best results in all optimization tasks, indicating that IS-EMTO has better performance.

[0056] Table 1 Performance comparison between the method proposed in the present invention and other methods on the CEC2017-MTSO benchmark test set

[0057]

[0058] In addition, the best results found by each algorithm are as Figure 2 shown. It can be seen from the figure that compared with other methods, the method IS-EMTO proposed in the present invention can obtain the optimal objective function value with a smaller number of sensors, that is, it meets a higher coverage rate and lower cost, indicating the powerful performance of the method IS-EMTO proposed in the present invention.

Claims

1. A multi-task optimization method for wireless sensor network coverage based on knowledge transfer between similar individuals, characterized in that: The following steps are involved: Step 1, model the wireless sensor network coverage problem as a multi-task optimization problem; in the multi-task optimization problem, each optimization task uses a given number of sensors to cover a specific square area; each sensor completely covers a circular area around it, and the larger the coverage radius of the sensor, the higher the cost; the optimization goal of each optimization task is to determine the placement and coverage radius of a given number of sensors to meet higher coverage and lower cost; Step 2: In the initialization phase, for a wireless sensor network coverage multi-task optimization problem with K optimization tasks, K populations will be randomly initialized; each population corresponds to an optimization task, and the individuals in the population will be evaluated for fitness according to the objective function of the task corresponding to the population; the knowledge transfer probability of the K tasks will be initialized; Step 3: for the current task, make a conditional judgment on whether to perform knowledge transfer; if the knowledge transfer condition is met, proceed to steps 4-6 to generate offspring through knowledge transfer; if the knowledge transfer condition is not met, proceed to step 7 to generate offspring through task self-evolution; Step 4: Select the most similar task as the source task for the current task based on the maximum mean difference (MMD) metric; Calculate the maximum mean difference between the current task and other tasks respectively, and then select the task with the smallest difference as the source task for the current task; Step 5: Select similar individuals from the source task to transfer knowledge with the current task. First, use the K-means clustering method to divide the population corresponding to the current task to form multiple clusters. Second, select the best performing individuals from the population corresponding to the source task as transfer individuals. Then, for each migrated individual, calculate its distance from the center of different clusters, and add the migrated individual to the cluster with the closest distance to it, that is, the most similar cluster; finally, repeat the above process for all migrated individuals until all migrated individuals are migrated to the cluster of the current task, thereby achieving more refined knowledge transfer between similar individuals of different tasks; Step 6: construct local Gaussian distribution models on multiple clusters of the current task, and sample from the model corresponding to the cluster where the parent individual is located to generate offspring; Step 7, generating offspring through the self-evolution process of the current task; generating offspring by constructing a Gaussian probability model on some excellent individuals of the population corresponding to the current task and sampling from them; Step 8: Perform environmental selection on the joint population composed of the parent population and the offspring population, and retain the individuals with the best performance to form the new generation population for the current task; Step 9, adjust the knowledge transfer probability of the current task according to the survival rate of the migrated individuals; the proportion of the migrated individuals that successfully replace the parent individuals after environmental selection in each generation of evolution is called the migration individual survival rate; According to this definition, firstly, the survival rate of the migration individuals of the current task is calculated; Then, the knowledge transfer probability is updated according to the survival rate of the migrated individuals of the current task; The lower the survival rate of migrated individuals, the more limited the auxiliary effect of knowledge transfer on population evolution. At this time, the migration probability should be appropriately reduced to avoid the potential negative transfer of knowledge affecting the convergence of the target task. On the contrary, the higher the survival rate of migrated individuals, the greater the help of knowledge transfer to population evolution. At this time, the migration probability should be appropriately increased to promote positive knowledge transfer. Step 10, repeat steps 3-9 for each task until the termination condition is met, and output the optimal result, that is, the sensor parameters that meet the optimal target value.

2. The multi-task optimization method for wireless sensor network coverage by knowledge transfer between similar individuals according to claim 1 is characterized in that: In step 1, the multi-task optimization problem of wireless sensor network coverage is expressed as follows: {x1,x2,…,x K }=arg min{f1(x1),f2(x2),…,f K ( x K )} (1) Among them, f k (·), k∈{1,2,…,K} represents the objective function of the kth optimization task; x k , k∈{1,2,…,K} represents the optimal solution obtained by solving the kth optimization task; K is the number of optimization tasks that need to be solved simultaneously, where each optimization task has a different number of sensors; for an optimization task T with N sensors, its objective function f(x) can be expressed as follows: Where A represents the target rectangular area that needs to be covered by N wireless sensors, that is, A = [-1, 1] × [-1, 1]; (x i ,y i ) represents the placement position of the i-th wireless sensor; r i represents the coverage radius of the i-th wireless sensor; represents the area covered by these N wireless sensors. In particular, the solution x includes the placement and coverage radius of these N wireless sensors, that is, x = {(x1, y1, r1), (x2, y2, r2), ..., (x N ,y N ,r N )}.

3. The multi-task optimization method for wireless sensor network coverage by knowledge transfer between similar individuals according to claim 2 is characterized in that: In step 2, K populations are randomly initialized, each with 100 individuals. The K populations correspond to K optimization tasks, and the individuals in the populations will be evaluated for fitness according to the tasks corresponding to the populations. At the same time, the knowledge transfer probabilities of the K tasks are initialized as atp1, atp2, …, atp K .

4. The multi-task optimization method for wireless sensor network coverage by knowledge transfer between similar individuals according to claim 3 is characterized in that: In step 3, for the current task T k , make a conditional judgment on whether to transfer knowledge; generate a random number t in the range [0,1] and task T k The corresponding knowledge transfer probability atp K Compare and make conditional judgment; if the knowledge transfer condition is met, that is, r≤atp k , then proceed to step 4-6; if the knowledge transfer condition is not met, that is, r>atp k , then proceed to step 7.

5. The multi-task optimization method for wireless sensor network coverage by knowledge transfer between similar individuals according to claim 4 is characterized in that: In step 4, the maximum mean difference (MMD) is used to measure the current task T k Select the most similar task as the source task T s ; Calculate the maximum mean difference (MMD) value between the current task and other tasks respectively, and then select the task with the smallest difference value as the source task of the current task; Suppose the populations of the two tasks are X = {x1, x2, …, x m } and Y={y1,y2,…,y n }, then the MMD value calculation formula between two tasks is as follows: Among them, P and Q represent the probability distribution corresponding to the current task and another task respectively; m and n represent the number of individuals in the current task population and another task population respectively; represents the reproducing kernel Hilbert space (RKHS); f(·) is the mapping function that can map the solution in the original decision space to In order to facilitate calculation, formula (3) is squared and simplified, and expressed using a kernel function to obtain the following formula: Among them, x i and x′ j are two individuals belonging to the current task; y i and y′ j are two individuals belonging to the same task; k(·,·) represents the kernel function, which is as follows:

6. The multi-task optimization method for wireless sensor network coverage by knowledge transfer between similar individuals according to claim 5 is characterized in that: In step 5, from the source task T s Select similar individuals to the current task T k To transfer knowledge, firstly, use K-means clustering method to cluster the current task T k The corresponding population P k Divide into Cn clusters; secondly, from the source task T s Corresponding population P s Select the top p% individuals with the best performance as migration individuals; Then, for each migration individual Tr i , calculate its distance from the center of different clusters, and migrate individual Tr i Add it to the cluster closest to it, that is, the most similar cluster; finally, repeat the above process for all migrated individuals until all migrated individuals are migrated to the current task T k Thus, more refined knowledge transfer between similar individuals in different tasks can be achieved.

7. The multi-task optimization method for wireless sensor network coverage by knowledge transfer between similar individuals according to claim 6 is characterized in that: In step 6, in the current task T k A local Gaussian distribution model is constructed on each of the Cn clusters, and samples are taken from the model corresponding to the cluster where the parent individual is located to generate the offspring; the calculation formulas for the model mean μ and variance Σ are as follows: Among them, S represents the parent individual x i The set of all individuals in the cluster.

8. The multi-task optimization method for wireless sensor network coverage by knowledge transfer between similar individuals according to claim 7 is characterized in that: In step 7, through the current task T k The self-evolution process generates offspring, in P k A Gaussian probability model is constructed on the first N / 2 excellent individuals and samples are generated from them to generate offspring; the calculation formulas for the mean and standard deviation of the model are shown in formulas (6) and (7), where S represents P k The set consisting of the first N / 2 excellent individuals.

9. The multi-task optimization method for wireless sensor network coverage by knowledge transfer between similar individuals according to claim 8 is characterized in that: In step 8, environmental selection is performed on the joint population composed of the parent population and the offspring population, and the top N individuals with the best performance are retained to form the current task T k A new generation of species.

10. The multi-task optimization method for wireless sensor network coverage by knowledge transfer between similar individuals according to claim 9, characterized in that: In step 9, the current task T is adjusted according to the survival rate of the migrated individuals. k The probability of knowledge transfer atp k ; The proportion of migrating individuals that successfully replace their parents after environmental selection in each generation of evolution is called the survival rate of migrating individuals; According to this definition, task T k The survival rate of migrant individuals in the gth generation is sr g Calculate using the following formula: Among them, ∈ is a small positive number to avoid the denominator being 0; represents the number of migrated individuals in the evolutionary process of the gth generation; It represents the number of individuals that successfully replace their parents after environmental selection. The calculation formula is as follows: Among them, P k,g and P k,g+1 Represents the tasks T in the gth generation and g+1th generation respectively k The corresponding population; |·| represents the cardinality of the set; Next, according to the above-obtained task T k The survival rate sr of the migrated individuals in the gth generation g To update the knowledge transfer probability, the update formula is as follows: in, Represents task T k The probability of knowledge transfer in the g+1th generation; atp lb and ATP ub are the lower and upper bounds of the probability of knowledge transfer, respectively.

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