Transferable element learning algorithm framework

Abstract

The invention relates to the technical field of high-entropy alloy, and discloses a transferable element learning algorithm framework, which integrates element learning based on an adaptive migration sea image optimizer, a balanced relative density peak value clustering (DPC) algorithm and a migration strategy, and constructs a transferable element learning model. Wherein the self-adaptive migration sea elephant optimizer dynamically adjusts a migration strategy according to the change of a population average fitness value, and the convergence speed is improved; according to the balanced relative DPC algorithm, the clustering effect is optimized by considering the local density and the mutual nearest neighbor relation, and the density difference problem between different clusters is solved. According to the migration strategy, a most matched historical problem is searched from a source domain by using the maximum mean difference (MMD), optimal solution information is migrated to a target domain, and the model performance is enhanced; according to the method, by combining meta-learning and transfer learning strategies, the calculation burden is relieved, the prediction accuracy is improved, efficient and accurate algorithm recommendation is provided for material designers, and the material development period is remarkably shortened.

Description

Technical Field

[0001] The present invention relates to the technical field of high entropy alloys, and in particular to a transferable meta-learning algorithm framework. Background Art

[0002] As a new type of material composed of five or more main elements, high entropy alloys (HEAs) have shown broad application prospects in aerospace, electronics, medical and other fields due to their high strength, high hardness, excellent corrosion resistance and high thermal stability. However, the phase composition of HEAs (including solid solution, intermetallic compound, amorphous and mixed phase) has a significant impact on its material properties, and accurately predicting the phase of HEAs has become a key task for material designers.

[0003] Traditionally, methods for predicting the phase of high entropy alloys include trial and error, phase diagram (CALPHAD) method, density functional theory (DFT) and first-principles calculation, and parameterization method. However, each of these methods has significant limitations. The trial and error method is costly, has a long cycle, and is inefficient; the CALPHAD method is difficult to apply to multi-principal alloys; DFT and first-principles calculations are large and inefficient; and parameterization methods rely heavily on empirical knowledge, which limits their scope of application.

[0004] In recent years, machine learning has been widely used in the field of materials due to its high efficiency and powerful learning ability, and has achieved certain results. However, the accuracy of different machine learning algorithms based on the same data set may vary significantly, which poses a challenge for material designers to choose the right algorithm. Meta-learning, as a method of recommending suitable algorithms, can reduce the workload of designers to a certain extent, but the existing meta-learning optimization algorithms do not fully utilize the optimal solution set information of similar historical problems, which limits the further improvement of their performance.

[0005] In terms of optimization algorithms, although group intelligence optimization algorithms such as particle swarm optimization (PSO), whale optimization algorithm (WOA) and walrus optimizer (WO) have their own advantages, they also have problems such as slow convergence or failure to consider changes in the average fitness value of the population. In particular, in the migration phase of the walrus optimizer, only the number of iterations is considered, ignoring the phenomenon that the average fitness value of the population hardly changes in multiple iterations, which affects the efficiency of algorithm evolution and optimization effect.

[0006] In addition, clustering algorithms play a vital role in the process of transfer learning. However, the classic K-means method cannot identify non-spherical clusters and requires the number of cluster centers to be given in advance. Although the clustering algorithm that quickly searches and finds density peaks (DPC) can identify non-spherical clusters and is efficient and robust, it often ignores cluster centers with relatively low density and cannot eliminate the density differences between different clusters. These problems limit the application effect of clustering algorithms in transfer learning. Summary of the invention

[0007] The purpose of the present invention is to provide a transferable meta-learning algorithm framework to solve the problems raised in the above background technology.

[0008] To achieve the above-mentioned object, the present invention provides the following technical solutions: a transferable meta-learning algorithm framework: including meta-learning based on an adaptive migrating walrus optimizer, a balanced relative DPC algorithm and a migration strategy;

[0009] The meta-learning based on the adaptive migrating walrus optimizer is used to recommend the optimal integrated model to predict the phase of HEAs, the balanced relative DPC algorithm is used to cluster the samples in the source domain and the target domain into several clusters with similar distributions, and the migration strategy is used to improve the search speed and efficiency of the population during the search process by migrating the optimal solution information of similar historical problems to the target domain.

[0010] Preferably, the implementation steps of the adaptive migrating walrus optimizer algorithm include:

[0011] Step 1: Initialize the population;

[0012] Step 2: Obtain the fitness value Fit_value of the population by calculation, then the average fitness value of the population is

[0013] Step 3: calculate and D_signal; if Then Tn=Tn+1; if Then Tn=0; when Tn>ε, the walruses migrate; otherwise, when |D_signal|≥1, the walruses migrate; where Tn represents the number of times the average fitness value of the population hardly changes;

[0014] Step 4: When |D_signal|≥1, the walrus will migrate;

[0015] Step 5: If |D_signal|<1, enter the breeding stage; calculate the value of S_signal, if S_signal>0.5, the walrus chooses the roosting behavior; otherwise, the walrus chooses the foraging behavior;

[0016] Step 6: If t=T, output the optimal solution, otherwise, return to step 2.

[0017] Preferably, the calculation formula of S_signal value is: Where A = 2 × α and is a risk factor, α=1-t / T decreases from 1 to 0 as the number of iterations t decreases, T is the maximum number of iterations, and is a random number in the range (0,1).

[0018] Preferably, when |D_signal|≥1, the walrus group will migrate to an area more suitable for population survival, and the walrus position update formula is: in, is the step length of the walrus, is a random number in the range (0,1); is the new position of the i-th walrus in the j-th dimension, and is the position of a vigilante randomly selected from the population, is the migration step length control factor.

[0019] Preferably, the steps for implementing the balanced relative DPC algorithm include:

[0020] Step 1: For any point x in the data set X i , calculate the point x i Mutual neighborhood MH i ;

[0021] Step 2: Calculate point x i The local density ρ;

[0022] Step 3: Pass through point x i The equilibrium relative density brd;

[0023] Step 4: Set the candidate cluster center to ct = {ct1, ct2, ..., ct g};

[0024] Step 5: Calculate point x i The relative distance δ;

[0025] Step 6: For any ct i , its credibility as a cluster center is obtained by calculation;

[0026] Step 7: Assign sample points that are not cluster centers;

[0027] Step 8: Output the final clustering results.

[0028] Preferably, any point x i The calculation formula of the local density is: Among them, d max is the maximum distance between points in the set X.

[0029] Preferably, the source domain sample cluster Sc is obtained by the balanced relative DPC algorithm. k′} and the target domain sample cluster Tc={Tc1,Tc2,L,Tc k′};

[0030] The maximum mean difference (MMD) method is used to find the most matching cluster in the source domain for each cluster in the target domain. The most matching cluster with the smallest MMD value in Sc is found by calculation, and the average MMD of all sample clusters in the target domain is calculated. Finally, the inverse of the MMD average value is used as the overall similarity Sid between the source domain and target domain samples. The larger the Sid value, the greater the similarity between the source domain and the target domain. The MMD is expressed as:

[0031]

[0032] Preferably, MMD is used to find the historical problem that best matches the target problem in the source domain, and the optimal solution set of the historical problem is migrated to generate new walruses to replace part of the walruses in the target domain population; in order to increase population diversity and avoid negative migration, the replacement ratio of the initial population is automatically set according to the Sid value between the historical problem and the target problem, and the calculation formula is: rat = γ min +(γ max -γ min )×Sid, where γ max = 0.5 and γ min =0.1 are the upper and lower limits of the proportion of walruses initialized by the migration strategy to control the value of rat.

[0033] Compared with the prior art, the present invention has the following beneficial effects:

[0034] Improve prediction accuracy: The present invention can more accurately predict the phases of high entropy alloys (HEAs) by combining meta-learning based on the adaptive migrating walrus optimizer, the balanced relative DPC algorithm and the migration strategy. The adaptive migrating walrus optimizer model can adaptively adjust the migration strategy according to the changes in the average fitness value of the population, improve the convergence speed and optimization effect of the algorithm, and thus enhance the accuracy of phase prediction.

[0035] Enhanced model robustness: The balanced relative DPC algorithm can identify non-spherical clusters and consider the density differences between different clusters, making the clustering results more robust. This feature helps the model maintain stable prediction performance when dealing with complex and variable high-entropy alloy data.

[0036] Shorten the material development cycle: The migration strategy allows the model to use the optimal solution set information of similar historical problems, thereby accelerating the solution process of new problems. This feature can significantly shorten the development cycle of new high-entropy alloy materials and reduce R&D costs.

[0037] Improved computational efficiency: The combination of the adaptive migrating walrus optimizer model and the migration strategy optimizes the algorithm’s computational process and reduces unnecessary computational burden. This enables the model to provide prediction results faster while maintaining high-precision predictions, improving the efficiency of material design. BRIEF DESCRIPTION OF THE DRAWINGS

[0038] Figure 1 Schematic diagram of the transferable meta-learning algorithm framework of the present invention;

[0039] Figure 2 Schematic diagram of AMWO algorithm;

[0040] Figure 3 Schematic diagram of the BRDPC algorithm. DETAILED DESCRIPTION

[0041] The following will be combined with the drawings in the embodiments of the present invention to clearly and completely describe the technical solutions in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0042] See also Figure 1-3 The present invention provides a technical solution: a transferable meta-learning algorithm framework, which consists of meta-learning based on the adaptive migrating walrus optimizer algorithm (AMWO), balanced relative DPC algorithm (BRDPC) and migration strategy. The schematic diagram of the transferable meta-learning algorithm framework is shown in the attached figure. Figure 1 shown.

[0043] High entropy alloys are composed of five or more main elements. Due to their excellent material properties, high entropy alloys have attracted more and more attention from scholars. Their phase structure has a great influence on the performance. In the field of materials, some scholars use parameter methods to determine the phase formation of high entropy alloys. At present, the main parameters for predicting the phase of high entropy alloys include mixing enthalpy (ΔH mix ), mixing entropy (ΔS mix ), atomic size difference (δ), electronegativity difference (Δχ), dimensionless parameter (Ω). The calculation formulas of these five parameters are shown in formula (1) to formula (5).

[0044]

[0045] where c i and cj are the atomic percentages of the i-th and j-th elements, respectively. ij is the mixing enthalpy of the ith and jth binary liquid alloys.

[0046]

[0047] Where R = 8.314JK -1 mol -1 is the gas constant.

[0048]

[0049] in, is the average atomic radius, r i is the atomic radius of the ith element.

[0050]

[0051] in is the average Pauling electronegativity, χ i is the Pauling electronegativity of the ith element.

[0052]

[0053] in is the average melting point of the constituent elements.

[0054] Attached Figure 1 On the left side of the figure, AMWO-based meta-learning can recommend the optimal integrated model to predict the phase of HEAs, thereby improving the prediction accuracy of the framework. AMWO adopts an adaptive migration strategy to adaptively migrate walruses according to the changes in the average fitness value of the population during multiple iterations. On the right side of the framework diagram, the BRDPC algorithm can cluster samples in the source domain and the target domain into several clusters with similar distributions. The migration strategy can improve the search speed and efficiency of the population during the search process by migrating the optimal solution information of similar historical problems to the target domain. Therefore, the transferable meta-learning algorithm framework consists of AMWO-based meta-learning, the BRDPC algorithm, and the migration strategy.

[0055] Calculate the parameter ΔH of each sample by formula (1)-formula (5) mix , ΔS mix ,δ,Δχ and Ω. The statistical characteristics of the data set are in, They are ΔH mix ,ΔS mix ,δ,Δχ,Ω, They are ΔH mix ,ΔS mix ,δ,Δχ,Ω. The statistical characteristics of the training data set are SF=[SF1 ,SF 2 ,L,SF K ],

[0056] SF k =[SF1,SF2,L,SF R ] 1×R (k=1,2,L,K),

[0057] The statistical characteristics of the test data set are SF′=[SF′ 1 ,SF′ 2 ,L,SF′ W ],SF′ w =[SF′1,SF′2,L,SF′ R ],

[0058] The parameter of the Cart tree is P = [P 1 ,P 2 ,L,P k ,L,P K ] T , P k =[p1,L,p R ] 1×R , p1=[C1,C2,L,C c ].

[0059] The detailed steps of the proposed framework are as follows:

[0060] Input: D train ={(x1,y1),(x2,y2),L,(x n ,y n )} is an unbalanced training data set. Through UnderBagging, D train Transformed into n balanced data sets The statistical features and meta-features are SF k =[SF1,SF2,L,SF R ] 1×R (k=1,2,L,K) and MF k =[SF k ,P k ](k=1,2,L,K),

[0061] P k =[p1,L,p R ] 1×R .

[0062] D test ={(x1,y1),(x2,y2),L,(xn ,y n )} is an unbalanced test data set. Through UnderBagging, D test Transformed into n balanced test data sets The statistical features and meta-features are

[0063] SF′ w =[SF′1,SF′2,L,SF′ R ] 1×R (w=1,2,L,W) and MF′ w =[SF′ w ,P′ w ](w=1,2,L,W),P′ w =[p′1,p′2,L,p′ R ] 1×R .

[0064] SEM k The accuracy is acc=[acc1,acc2,L,acc k ,L,acc K ] T The history library (HL) stores information about similar historical problems solved by the optimization algorithm. HL = {(SF1, sol′1), (SF2, sol′2), L, (SF o ,sol′ o ),L,(SF pn ,sol′ pn )}, SF o and sol′ o are the statistical characteristics and optimal solution set information of the oth historical problem respectively.

[0065] Output: Phases of high entropy alloys.

[0066] Select historical problems with the same alloy component number, learner type, number of learners, and number of parameters corresponding to the learners, and store the statistical characteristics of these historical problems and the optimal solution set of the learners in HL.

[0067] Step 1: k = 1, t = 0, o = 1

[0068] Step 2: Cart with different parameters i (i=1,2,L,n) trees are respectively in the corresponding On training, randomly select R trained Cart i Selective Ensemble Model (SEM) k (k=1,2,L,K).

[0069] Step 3: On the validation dataset Dvalidation obtain SEM k with precision acc k (k = 1, 2, …, K).

[0070] Step 4: k = k + 1. If k > K, proceed to Step 5. Otherwise, return to Step 2.

[0071] Step 5: Based on the meta - feature MF k and the precision acc of the selective integration model k construct a meta - knowledge database. The values of the meta - feature and the precision of the selective integration model are the input variable MF and the output variable acc of the meta - learner respectively.

[0072] Step 6: Train the meta - learner according to the input variable MF and the output variable acc in Step 5, thereby obtaining a trained meta - learner, also known as a meta - model.

[0073] Step 7: t = t + 1. Encode the meta - features of to form an initial population. The AMWO algorithm iterates a small number of times. Each iteration inputs the values of the meta - features into the meta - model, and then obtains the precision of SEM.

[0074] Step 8: If t = ft, the solution set is Sol t = {sol t,1 , sol t,2 , …, sol t,N}, where sol t,n is a solution to the target problem, representing the parameters of the Cart tree. In addition, the solution set and its corresponding statistical features constitute the target - domain sample set Tar S = {(SF′ t,1 , sol t,1 ), (SF′ t,2 , sol t,2 ), …, (SF′ t,N , sol t,N )}. Otherwise, when t < ft, return to Step 7, and when t > ft, proceed to Step 9.

[0075] Step 9: The solution set Sol′ o = {sol′ o,1 , sol′ o,2 , …, sol′ o,M} of the o - th similar historical problem in HL and its statistical features constitute the source - domain sample set Sou S = {(SF o,1 , sol′ o,1 ), (SF o,2 , sol′ o,2 ), …, (SFo,M ,sol′ o,M )}.

[0076] Step 10: Use the BRDPC algorithm to convert Sou S and Tar S The samples in the source domain are clustered into several clusters with similar distributions. The source domain and target domain sample cluster sets are Sc = {Sc1, Sc2, L, Sc k′} and Tc={Tc1,Tc2,L,Tc k′}.

[0077] Step 11: Use MMD to find the cluster in the source domain that best matches each cluster in the target domain, and take the inverse of the MMD average of all sample clusters in the target domain as the overall similarity Sid between the source domain and the target domain.

[0078] Step 12: o=o+1, if o>pn, continue to step 13. Otherwise, return to step 9.

[0079] Step 13: The solution set of the historical problem with the largest Sid value is regarded as the optimal solution set.

[0080] Step 14: Adopt a migration strategy to S The optimal solution set in is transferred to the target domain Tar S middle.

[0081] Step 15: t=t+1, iteratively run the AMWO algorithm to continuously update the position of each walrus.

[0082] Step 16: Update the representative set L = {l1,l2,L,l k′} and HL, each individual in L is the walrus with the highest fitness in each cluster.

[0083] Step 17: If t=T, output the optimal solution. Otherwise, return to step 15.

[0084] Step 18: Store L and its corresponding SF into HL.

[0085] Step 19: Use the recommended optimal selective ensemble algorithm to predict D test Phases of the high-entropy alloy samples.

[0086] Walrus Optimizer (WO) is a novel swarm intelligence algorithm. It includes migration and reproduction stages. The details of WO are as follows:

[0087] The fitness values ​​of all walruses are shown in formula (6):

[0088]

[0089] Walruses are very vigilant when foraging and resting. Arrange one or two walruses to patrol around. Once an abnormal situation is found, they will send out a danger signal. The calculation formula of the danger signal is shown in formula (7):

[0090] D_signal=A * Z (7)

[0091] The safety signal formula is shown in formula (8):

[0092]

[0093] Where A = 2 × α and It is a risk factor, α=1-t / T decreases from 1 to 0 as the number of iterations t, and T is the maximum number of iterations. and is a random number in the range (0,1).

[0094] When |D_signal|≥1, the walrus group will migrate to an area more suitable for population survival, and the walrus position update is shown in formula (9):

[0095]

[0096] in, is the step length of the walrus, is a random number in the range (0,1). is the new position of the i-th walrus in the j-th dimension, and is the position of a vigilante randomly selected from the population. is the migration step length control factor.

[0097] In the migration phase of WO, the number of iterations is taken into account, but the phenomenon that the average fitness value of the population is almost unchanged during multiple iterations due to the stagnation problem is ignored. According to the changes in the average fitness value of the population during multiple iterations, the walrus is adaptively migrated to a more suitable living area, thereby reducing the possibility of the algorithm falling into a local optimum. Therefore, this paper proposes a walrus optimizer algorithm (AMWO) based on an adaptive migration strategy. The specific steps are as follows:

[0098] Input: population size Num, maximum number of iterations T, Tn represents the number of times the average fitness value of the population hardly changes, Tn=0.

[0099] Output: optimal solution.

[0100] Step 1: Initialize the population.

[0101] Step 2: Calculate the fitness value Fit_value of the population using formula (6), then the average fitness value of the population is

[0102] Step 3: calculate and D_signal. If Then Tn=Tn+1. If Then Tn=0. When Tn>ε, the walrus is migrated according to formula (9). Otherwise, when |D_signal|≥1, the walrus is migrated according to formula (9).

[0103] Step 4: When |D_signal|≥1, the walrus is migrated according to formula (9).

[0104] Step 5: If |D_signal| < 1, enter the breeding stage. Calculate the value of S_signal according to formula (8). If S_signal > 0.5, the walrus chooses the roosting behavior. Otherwise, the walrus chooses the foraging behavior.

[0105] Step 6: If t=T, output the optimal solution, otherwise, return to step 2.

[0106] The schematic diagram of AMWO algorithm is as follows Figure 2 shown.

[0107] As attached Figure 2 As shown, in In addition to the number of iterations, the phenomenon that the average fitness value of the population hardly changes during multiple iterations due to the stagnation problem is also considered. Tn=Tn+1. Otherwise, Tn=0. When Tn>ε, the walrus will migrate to an area more suitable for survival. Otherwise, if |D_signal|≥1, the walrus will migrate to an area more suitable for survival. If |D_signal|<1, the walrus enters the breeding stage. The AMWO algorithm adopts an adaptive migration strategy, which can reduce the possibility of the algorithm falling into a local optimum.

[0108] Walruses tend to breed in less dangerous currents than when migrating. Led by Walrus and male walrus With the iterative process, the influence of the leader walrus on the female walrus gradually increases, while the influence of the spouse gradually decreases. The position update formula is shown in formula (10):

[0109]

[0110] in, and are the positions of the i-th female and male walrus in the j-th dimension respectively. is the new position of the i-th female walrus in the j-th dimension.

[0111] Killer whales and polar bears often prey on young walruses at the edge of the population, so young walruses It is necessary to update its own position to avoid being preyed on. The position update is shown in formula (11):

[0112]

[0113] in, is the new position of the i-th walrus in the j-dimension, For reference safety position, is the panic coefficient of the baby walrus and is a random number in the range of (0,1).

[0114] Assume a data set X = {x1, x2, ..., x i ,…,x n} and any point x i =[x i1 ,x i2 ,…,x im ], where n and m are the number and dimension of X respectively.

[0115] Point x i The mutual nearest neighbor set of points is called point x i Mutual Neighborhood (MH i ). MH i As shown in formula (12):

[0116]

[0117] Among them, for any point x i , if its KNN contains x j , and x j The KNN also contains x i , then f(i,j)=1. Otherwise f(i,j)=0.

[0118] Any point x i The local density of is shown in formula (13):

[0119]

[0120] Among them, d max is the maximum distance between points in the set X.

[0121] Point x i The relative density is shown in formula (14):

[0122]

[0123] Among them, μ1(i) is KNNi The set of all points in which the local density is greater than 0.

[0124] The candidate cluster centers based on mutual neighborhood are shown in formula (15):

[0125]

[0126] Where fm(i)=1 means x i is a candidate cluster center, otherwise, x i It is not a candidate cluster center. Suppose there are g candidate cluster centers, then ct = {ct1, ct2, …, ct g} is the set of candidate cluster centers.

[0127] The credibility of any candidate cluster center is shown in formula (16):

[0128] crd(ct i )=rnd(ct i )δ(ct i ) (16)

[0129]

[0130] When the density difference between different clusters is large, DPC cannot eliminate the density difference between different clusters, and it is easy to ignore the cluster center with relatively low local density in the data set. Although NADPC takes into account the problem of cluster centers with low local density, it cannot obtain ideal results for the density difference between different clusters. The mutual nearest neighbor relationship depends on the distribution of data points and is insensitive to changes in distance, which can eliminate the influence of density differences between different clusters. Therefore, the present invention proposes a new balanced relative DPC (BRDPC) algorithm. The schematic diagram of the BRDPC algorithm is shown in the attached figure. Figure 3 shown.

[0131] As attached Figure 3 As shown, ρ is any point x i The local density of MH is calculated as shown in formula (13). i Any point x i The mutual nearest neighbor set of i The mutual neighborhood of is calculated as shown in formula (12). i The equilibrium relative density is shown in formula (18):

[0132]

[0133] where |·| is the cardinality of the set.

[0134] Balancing the relative density can increase the possibility of selecting the correct cluster center, while considering the point x iThe local density and the number of nearest neighbors can eliminate the influence of density differences between different clusters.

[0135] Step 1: For any point x in X i , calculate point x by formula (12) i MH i .

[0136] Step 2: Calculate x using formula (13) i The local density of .

[0137] Step 3: Calculate x using formula (18) i The equilibrium relative density.

[0138] Step 4: According to formula (15), the candidate cluster centers are set as ct = {ct1, ct2, ..., ct g}

[0139] Step 5: Calculate x using formula (17) i relative distance.

[0140] Step 6: For any ct i , and its credibility as a cluster center is calculated by formula (16).

[0141] Step 7: Assign references to sample points that are not cluster centers.

[0142] The source domain sample cluster Sc={Sc1,Sc2,…,Sc k′} and the target domain sample cluster Tc={Tc1,Tc2,…,Tc k′}. This section uses the maximum mean difference (MMD) method to find the best matching cluster in the source domain for each cluster in the target domain. For example, for a cluster in Tc, the best matching cluster with the smallest MMD value in Sc is found by formula (19). The average MMD of all sample clusters in the target domain is calculated. Finally, the inverse of the MMD average value is used as the overall similarity (Sid) between the source domain and target domain samples. The larger the Sid value, the greater the similarity between the source domain and the target domain. The MMD is expressed as follows:

[0143]

[0144] Through MMD, we search for the historical problem that best matches the target problem in the source domain, and migrate the optimal solution set of the historical problem to generate new walruses to replace some walruses in the target domain population. In order to increase population diversity and avoid negative migration, the replacement ratio of the initial population is automatically set according to the Sid value between the historical problem and the target problem. The calculation formula is shown in formula (20):

[0145] rat=γ min +(γmax -γ min )×Sid (20)

[0146] where γ max = 0.5 and γ min =0.1 are the upper and lower limits of the proportion of walruses initialized by the migration strategy to control the value of rat.

[0147] Assume that the optimal solution set obtained from the source domain is Sol s ={sol s,1 ,sol s,2 ,…,sol s,M}, the target domain solution set is Sol t ={sol t,1 ,sol t,2 ,…,sol t,N}, first from Sol t Randomly select Q = rat × N walruses except the optimal walrus to generate the solution set Sol′ to be initialized t ={sol′ t,1 ,sol′ t,2 ,…,sol′ t,Q}; Secondly, select Sol′ from Sols t The individuals closest to each walrus form the solution set Sol′ s ={sol′ s,1 ,sol′ s,2 ,…,sol′ s,Q}; Finally, based on Sol′ s , update Sol′ through formula (21) t All walruses in , generate Q new walruses, and replace Sol with these Q new walruses t The corresponding walrus in .

[0148]

[0149] in, is a newly generated walrus, ΔV=[N(0,1),N(0,1),…,N(0,1)] T is a random vector that follows a standard normal distribution.

[0150] The method to update the history library is: loop iterate the AMWO algorithm, update Sol t The position of each walrus in. Let the current walrus group be Sol = {sol1, sol2, ..., sol N}, calculate the Fit_value of each walrus. Store the walrus with the highest Fit_value in each cluster in the representative set L = {l1,l2,…,l k′}, calculate the distance between any two walruses in L, and take the minimum distance value as the initial cluster radius R1. During the iteration process, each iteration (μ is a random number in the range of (0,1)) updates L and R1 once until the algorithm terminates.

[0151] The update strategy is: starting from the first walrus in Sol, evaluate its position and fitness relationship with each walrus in L in turn until all walruses in Sol are evaluated.

[0152] For example, calculate the walrus and sol in L n Find the distance between l in L min The nearest walrus sol n , let their distance be d. If d(sol n ,l min )<R1 and Fit_value(sol n )>Fit_value(l min ), then use sol n Replace l min If d(sol n ,l min )<R1 and Fit_value(sol n ) <Fit_value(l min ), then keep l min In L. If d(sol n ,l min )>R1 and Fit_value(sol n )>Fit_value(l min ), then use sol n Replace the walrus with the worst fitness value in L. If d(sol n ,l min )>R1 and Fit_value(sol n ) <Fit_value(l min ), then delete sol n , the walrus in L remains unchanged.

[0153] Calculate the distance between any two walruses in L and take the minimum distance as the new cluster radius. The statistical features of the target problem and L are stored in HL.

[0154] It should be noted that, in this article, relational terms such as first and second, etc. are only used to distinguish one entity or operation from another entity or operation, and do not necessarily require or imply any such actual relationship or order between these entities or operations. Moreover, the terms "include", "comprise" or any other variants thereof are intended to cover non-exclusive inclusion, so that a process, method, article or device including a series of elements includes not only those elements, but also other elements not explicitly listed, or also includes elements inherent to such process, method, article or device.

[0155] Although embodiments of the present invention have been shown and described, it will be appreciated by those skilled in the art that various changes, modifications, substitutions and variations may be made to the embodiments without departing from the principles and spirit of the present invention, and that the scope of the present invention is defined by the appended claims and their equivalents.

Claims

1. A transferable meta-learning algorithm framework, characterized by: Including meta-learning based on the adaptive migration strategy walrus optimizer, balanced relative DPC algorithm and migration strategy; The meta-learning based on the adaptive migration strategy walrus optimizer is used to recommend the optimal integrated model to predict the phase of HEAs, the balanced relative DPC algorithm is used to cluster the samples in the source domain and the target domain into several clusters with similar distributions, and the migration strategy is used to improve the search speed and efficiency of the population during the search process by migrating the optimal solution information of similar historical problems to the target domain.

2. A transferable meta-learning algorithm framework according to claim 1, characterized in that: The implementation steps of the adaptive migrating walrus optimizer include: Step 1: Initialize the population; Step 2: Obtain the fitness value Fit_value of the population by calculation, then the average fitness value of the population is Step 3: calculate and D_signal; if Then Tn=Tn+1; if Then Tn=0; when Tn>ε, the walruses migrate; otherwise, when |D_signal|≥1, the walruses migrate; where Tn represents the number of times the average fitness value of the population hardly changes; Step 4: When |D_signal|≥1, the walrus will migrate; Step 5: If |D_signal|<1, enter the breeding stage; calculate the value of S_signal, if S_signal>0.5, the walrus chooses the roosting behavior; otherwise, the walrus chooses the foraging behavior; Step 6: If t=T, output the optimal solution, otherwise, return to step 2.

3. A transferable meta-learning algorithm framework according to claim 2, characterized in that: The calculation formula of S_signal value is: Where A = 2 × α and is a risk factor, α=1-t / T decreases from 1 to 0 as the number of iterations t decreases, T is the maximum number of iterations, and is a random number in the range (0,1).

4. The transferable meta-learning algorithm framework according to claim 3, characterized in that: When |D_signal|≥1, the walrus group will migrate to an area more suitable for the survival of the population, and the walrus position update formula is: in, is the step length of the walrus, is a random number in the range (0,1); is the new position of the i-th walrus in the j-th dimension, and is the position of a vigilante randomly selected from the population, is the migration step length control factor.

5. A transferable meta-learning algorithm framework according to claim 1, characterized in that: The steps for implementing the balanced relative DPC algorithm include: Step 1: For any point x in the data set X i , calculate the point x i Mutual neighborhood MH i ; Step 2: Calculate point x i The local density ρ; Step 3: Calculate point x i The equilibrium relative density brd; Step 4: Set the candidate cluster center to ct = {ct1, ct2, ..., ct g }; Step 5: Calculate point x i The relative distance δ; Step 6: For any ct i , its credibility as a cluster center is obtained by calculation; Step 7: Assign sample points that are not cluster centers; Step 8: Output the final clustering results.

6. The transferable meta-learning algorithm framework according to claim 5, characterized in that: Any point x i The calculation formula of the local density is: Among them, d max is the maximum distance between points in the set X.

7. The transferable meta-learning algorithm framework according to claim 6, characterized in that: The source domain sample cluster Sc={Sc1,Sc2,L,Sc k′ } and the target domain sample cluster Tc={Tc1,Tc2,L,Tc k′ }; The maximum mean difference (MMD) method is used to find the most matching cluster in the source domain for each cluster in the target domain. The most matching cluster with the smallest MMD value in Sc is found by calculation, and the average MMD of all sample clusters in the target domain is calculated. Finally, the inverse of the MMD average value is used as the overall similarity Sid between the source domain and target domain samples. The larger the Sid value, the greater the similarity between the source domain and the target domain. The MMD is expressed as:

8. The transferable meta-learning algorithm framework according to claim 7, characterized in that: Through MMD, we search for the historical problem that best matches the target problem in the source domain, migrate the optimal solution set of the historical problem to generate new walruses to replace some walruses in the target domain population; in order to increase population diversity and avoid negative migration, the replacement ratio of the initial population is automatically set according to the Sid value between the historical problem and the target problem, and the calculation formula is: rat = γ min +(γ max -γ min )×Sid, where γ max = 0.5 and γ min =0.1 are the upper and lower limits of the proportion of walruses initialized by the migration strategy to control the value of rat.

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