A multi-objective recommendation method based on multi-task evolutionary optimization

Abstract

This invention discloses a multi-objective recommendation method based on multi-task evolutionary optimization, comprising the following steps: auxiliary task generation, which simplifies the original task at two different levels of users and items to obtain auxiliary tasks; population initialization of the original and auxiliary tasks; population evolution and interaction, wherein a novel knowledge transfer mechanism is proposed for the auxiliary and original tasks to effectively realize knowledge transfer between tasks; and environment selection. This invention not only overcomes the limitation of traditional recommendation algorithms that only focus on accuracy, achieving a balance between accuracy and inaccuracy metrics and providing higher-quality recommendation list combinations for users to choose from, but also accelerates the convergence speed of the original task through simple auxiliary tasks, thus optimizing the time aspect.

Description

Technical Field

[0001] This invention relates to the field of multi-objective recommendation, and more specifically to a multi-objective recommendation method based on multi-task evolutionary optimization. Background Technology

[0002] Recommender systems are considered one of the most promising tools for alleviating information overload. They can select information resources that users are interested in based on their historical experience, thereby saving people time and costs. To address the shortcomings of traditional recommendation techniques that only focus on accuracy, multi-objective evolutionary algorithms have been successfully applied. In these algorithms, recommendation is modeled as a multi-objective optimization problem by simultaneously considering both accuracy and non-accuracy metrics. However, in most existing multi-objective evolutionary recommendation algorithms, individual representations are typically represented in the form of matrix encoding, leading to a large search space, especially as the number of users and items increases. Multi-task evolutionary optimization can improve global search capabilities and accelerate convergence through knowledge transfer between related tasks. Therefore, a multi-objective recommendation method based on multi-task evolutionary optimization is proposed, which can provide users with higher-quality combinations of recommendation lists while also achieving time optimization.

[0003] Current work in the field of multi-objective recommendation can be mainly divided into the following two categories:

[0004] (1) General Multi-Objective Recommendation Methods. General multi-objective recommendation methods typically begin by using traditional recommendation algorithms, such as Probs and UCF, to predict user ratings for items. These ratings are then used to calculate accuracy metrics. Finally, multi-objective optimization algorithms are employed to optimize both accuracy and inaccuracy metrics, resulting in a balanced recommendation list across all objectives. These multi-objective evolutionary optimization-based recommendation algorithms have demonstrated good performance in recommendation systems. However, because general multi-objective recommendation methods typically recommend to all users and use matrix encoding, most of these methods cannot quickly obtain the final recommendation list as the number of users and items increases.

[0005] (2) Multi-objective recommendation methods. Multi-objective recommendation methods generally model the recommendation problem as a multi-objective optimization problem, then propose their own objective function, and finally introduce a multi-objective evolutionary algorithm into the recommendation system to solve the problem of too many objectives in the recommendation. However, most multi-objective recommendation methods lack analysis of the recommendation problem during optimization and simply apply the multi-objective evolutionary algorithm. Summary of the Invention

[0006] To overcome the shortcomings of existing technologies, this invention provides a multi-objective recommendation method based on multi-task evolutionary optimization. It constructs a simple and related auxiliary task and uses knowledge transfer between tasks to help solve complex original tasks, thereby meeting the needs of solving practical problems.

[0007] In one aspect of the present invention, a multi-objective recommendation method based on multi-task evolutionary optimization is proposed. According to an embodiment of the present invention, the method includes the following steps:

[0008] Step 1: Simplify the original task at two different levels, users and items, to obtain an auxiliary task, which is to make recommendations to users at the cluster center;

[0009] Step 2: Initialize the original task and auxiliary task populations;

[0010] Step 3: Evolve and interact with the initial population obtained in Step 2 to obtain a set of offspring individuals. Use the set of offspring individuals to realize the knowledge transfer from the auxiliary task to the original task and form a new population.

[0011] Step 4, Environment Selection: Based on the objective function value, the non-dominated sorting algorithm and the crowding distance algorithm are used to sort all individuals in the new population respectively. The optimal set of recommended items is selected from all individuals in the first frontier of the sorted population and output.

[0012] In addition, the multi-objective recommendation method based on multi-task evolutionary optimization according to the above embodiments of the present invention may also have the following additional technical features:

[0013] In some embodiments of the present invention, step 1, which simplifies the original task at the user level, includes the following steps:

[0014] The K-Means clustering algorithm is used to preprocess users' historical behavior information, group users into groups, and select the users closest to the cluster center in each group as the cluster center users. The purpose of the auxiliary task is to recommend only to these cluster center users.

[0015] When using the K-Means clustering algorithm, the elbow method is used to determine the value of K, and cosine similarity is used to measure the similarity between two users i and j. i,j The calculation formula is:

[0016]

[0017] Where, r i and r j They are u i and u j The rating vector for all items, ui Let u represent the i-th user. j This represents the j-th user;

[0018] In some embodiments of the present invention, step 1, which simplifies the original task at the item level, includes the following steps:

[0019] The Probs algorithm is used to predict ratings for all users, and the N items with the highest predicted ratings for each user are obtained, where N represents the length of the candidate list, calculated as follows: Where m represents the total number of items and L represents the length of the recommendation list, then for each cluster center user, the intersection of the N items with the highest predicted scores of each user in the group other than the cluster center user is selected, denoted as Set1; if |Set1|>N, then the N items with the highest predicted scores are selected and added to the candidate recommendation list of the cluster center user; otherwise, the N-|Set1| items with the highest predicted scores are selected from the set of unrated items remaining in the cluster center user's collection, denoted as Set2, and Set1∪Set2 is added to the candidate recommendation list.

[0020] In some embodiments of the present invention, step 2, the initialization of the original task and auxiliary task populations, specifically includes the following steps:

[0021] Step 2.1, for user u i Set the recommended list length L = 10, u i The candidate recommendation list is O i Set the population size to popsize, and let popsize = 100;

[0022] Step 2.2: Initialize the original population using an extreme point-guided approach;

[0023] Step 2.3: Initialize the auxiliary population using the extreme point-guided method.

[0024] In some embodiments of the present invention, the initial population initialization method in step 2.2 is specifically as follows:

[0025] Step 2.2.1: Initialize an extreme point individual. For each user in the original task, select the top 10 items based on the predicted score to initialize the recommendation list in the individual.

[0026] Step 2.2.2: Initialize the remaining individuals using a randomization method. Randomly select different items from the candidate recommendation list to initialize the remaining individuals.

[0027] Step 2.2.3: Combine the one individual determined in Step 2.2.1 with the remaining individuals selected using the method in Step 2.2.2 to form the initial population Pop for the original task.o .

[0028] In some embodiments of the present invention, the auxiliary population initialization method in step 2.3 is specifically as follows:

[0029] Step 2.3.1: Initialize an extreme point individual. For each cluster center user in the auxiliary task, select the top 10 items based on the predicted score to initialize the recommendation list in the individual.

[0030] Step 2.3.2: Initialize the remaining individuals using a randomization method. Randomly select different items from the candidate recommendation list to initialize the remaining individuals.

[0031] Step 2.3.3: Combine the one individual determined in Step 2.3.1 with the remaining individuals selected using the method in Step 2.3.2 to form the initial population Pop for the auxiliary task. h .

[0032] In some embodiments of the present invention, step 3, population evolution and interaction specifically includes the following steps:

[0033] Step 3.1: Initialize the number of iterations G = 0, the maximum number of iterations maxGen = 100, and the original population P. o =Pop o , auxiliary population P h =Pop h ;

[0034] Step 3.2, from the original population P o In the process, two individuals are randomly selected and crossover mutation is performed to obtain a descendant individual. This process is repeated 100 times to obtain a set of 100 such descendant individuals (OP). o From the auxiliary population P h In the process, two individuals are randomly selected and crossover mutation is performed to obtain a descendant individual. This process is repeated 100 times to obtain a set of 100 such descendant individuals (OP). h ;

[0035] Step 3.3, Knowledge Transfer:

[0036] Step 3.3.1, for OP h Each individual in the process achieves knowledge transfer from the auxiliary task to the original task in two steps: the first step is from the OP... h Each row extracted from individuals will be expanded to the rows of other users in the same cluster; the second step is to adjust the preliminary results obtained in the first step, removing items that have already been rated by users by replacing them with other items that are highly similar to these previously rated items. The similarity between items is calculated using cosine similarity, as follows:

[0037]

[0038] Where, r i R is the rating vector for item i. j It is the rating vector of item j;

[0039] For OP h Each individual in the process is transformed according to the method described above to obtain the OP. h_o ;

[0040] Step 3.3.2, realizing knowledge transfer from the original task to the auxiliary task, is based on the frequency of item occurrence: calculate the frequency of each item appearing in the recommendation list of the same cluster user, then select the top 10 most frequently occurring items according to their frequency, and add these items to the recommendation list of the cluster center user. For OP... o Each individual in the process is transformed according to the above method to obtain OP. o_h ;

[0041] Step 3.4: Put population P o And the 100 newly generated offspring individuals OP o And individual OPs that migrated from the auxiliary population h_o They combine to form a new population TP o ;Put the population P h And the 100 newly generated offspring individuals OP h And individual OPs that migrated from the original population o_h They combine to form a new population TP h .

[0042] In some embodiments of the present invention, step 4, the environment selection specifically includes the following steps:

[0043] Step 4.1: Calculate TP using the following formula. o and TP h For each individual in the dataset, there are two objective functions: Pre for accuracy and Div for diversity of the recommendation list.

[0044]

[0045]

[0046]

[0047] Where U is the user set, L u It is user u's recommendation list; pr u,iIt represents the predicted rating of user u for item i; L represents the length of the recommendation list; |t i | is the number of topics contained in item i; L represents the recommended list u The set of topics; T is the total number of topics in the entire recommendation system. L represents the recommended list u A collection of different themes, q j This indicates that topic j is in the recommendation list L. u Frequency of occurrence in;

[0048] Step 4.2: Based on the objective function value, use the non-dominated sorting algorithm and the crowding distance algorithm to sort the population TP. o and TP h All individuals are sorted to obtain a candidate population with multiple frontiers; the top 100 individuals are selected and retained for the next generation, thus updating the population P. o and P h Then, set the iteration count G = G + 1 until the iteration count G > maxGen; otherwise, proceed to step 3.2.

[0049] Step 4.3: Select all individuals from the first frontier of the sorted population as the optimal set of recommended items and output it.

[0050] Compared with existing technologies, the beneficial effects of this invention are reflected in:

[0051] 1. Compared with general multi-objective recommendation methods, this invention proposes a method for dividing auxiliary tasks based on user rating information. This simplifies the original multi-objective recommendation problem by obtaining simple and relevant auxiliary tasks. By using relevant auxiliary tasks to assist the original task, search efficiency can be greatly improved, and better results can be obtained more quickly.

[0052] 2. This invention proposes an effective knowledge transfer mechanism, including two strategies: knowledge transfer from auxiliary tasks to the original task and knowledge transfer from the original task to auxiliary tasks. This enables positive transfer between tasks and reduces the occurrence of negative transfer. Attached Figure Description

[0053] Figure 1 This is an algorithm flowchart of a multi-objective recommendation method based on multi-task evolutionary optimization in an embodiment of the present invention;

[0054] Figure 2 This is a schematic diagram illustrating the simplification of the original task at the user level in step 1.1 of this embodiment of the invention;

[0055] Figure 3 This is a schematic diagram illustrating the simplification of the original task at the item level in step 1.2 of this embodiment of the invention;

[0056] Figure 4 This is a schematic diagram of the knowledge transfer from the original task to the auxiliary task in step 3.3.1 of this embodiment of the invention;

[0057] Figure 5 This is a schematic diagram of the knowledge transfer from the original task to the auxiliary task in step 3.3.2 of this embodiment of the invention. Detailed Implementation

[0058] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only a part of the embodiments of the present invention, and not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those of ordinary skill in the art without creative effort are within the scope of protection of the present invention.

[0059] This example proposes a multi-objective recommendation method based on multi-task evolutionary optimization, characterized as follows: Figure 1 As shown, specifically, it is done according to the following steps:

[0060] Define a recommender system as RS(U, I, R), where U = {u1, u2, ..., u...} i , ..., u n} represents the set of all users in the recommendation system, u i Let i represent the i-th user, and n be the total number of users; I = {i1, i2, ..., i...} j , ..., i m} represents the set of all items in the recommendation system, i j Let R represent the j-th item, and m be the total number of items; R = {r i，j |i = 1, 2, ..., n; j = 1, 2, ..., m} represents the rating matrix in the recommendation system, where r i，j Indicates user u i For item i j The rating, if r i，j If r ≠ 0, then i，j The record is user u i For item i j The actual rating score, if r i，j =0, which means user u i Not yet associated with item i j Establishing a connection also represents item i j In user u i It is among the candidate recommendation lists.

[0061] Step 1: Auxiliary task generation. The original task is simplified at two different levels: user and item, to obtain auxiliary tasks.

[0062] Step 1.1: Simplify the original task at the user level: Use the K-Means clustering algorithm to preprocess the user's historical behavior information, group the users, and select the user closest to the cluster center in each group as the cluster center user. The purpose of the auxiliary task is to recommend only to these cluster center users.

[0063] Here, the elbow method is used to determine the K value when employing the K-Means clustering algorithm, and cosine similarity is used to measure the similarity between two users i and j. i，j The calculation formula is:

[0064]

[0065] Where, r i and r j They are u i and u j Rating vector for all items.

[0066] For example Figure 2 As shown, assume there are 7 users and 25 items. Using the K-means algorithm, the 7 users are first divided into 2 groups. Finally, u1 is the user closest to the cluster center in the first group, and u5 is the user closest to the cluster center in the second group. Therefore, u1 and u5 are selected as the cluster center users.

[0067] Step 1.2: Simplify the original task at the item level: Use the Probs algorithm to predict the ratings of all users, and obtain the N items with the highest predicted ratings for each user, where N represents the length of the candidate list, calculated as follows: Where m represents the total number of items and L represents the length of the recommendation list, then for each cluster center user, the intersection of the N items with the highest predicted scores of each user in the group other than the cluster center user is selected, denoted as Set1; if |Set1|>N, then the N items with the highest predicted scores are selected and added to the candidate recommendation list of the cluster center user; otherwise, the N-|Set1| items with the highest predicted scores are selected from the set of unrated items remaining in the cluster center user's collection, denoted as Set2, and Set1∪Set2 is added to the candidate recommendation list.

[0068] For example Figure 3As shown, assume that u2, u5, and u7 are users in the same group, where u5 is the cluster center user, and the candidate list length is 5. First, the Probs algorithm is used to predict the ratings of all users, obtaining 5 item sets for u2 and u7 respectively. Taking their intersection, we get Set1 = {1, 4, 8}. At this time, N - |Set1| = 2, so we select the 2 items with the highest predicted ratings from u5, Set2 = {2, 5}. Finally, the candidate recommendation list for u5 is Set = {1, 4, 8, 2, 5}.

[0069] Step 2, Population initialization for the primary and auxiliary tasks:

[0070] Step 2.1, for user u i Set the recommended list length L = 10, u i The candidate recommendation list is O i Set the population size to popsize, and let popsize = 100;

[0071] Step 2.2 Initialization of the original population:

[0072] Step 2.2.1: Initialize an extreme point individual. For each user in the original task, select the top 10 items based on the predicted scores to initialize the recommendation list in the individual;

[0073] Step 2.2.2: Initialize the remaining 99 individuals using a randomization method. Randomly select different items from the candidate recommendation list to initialize the remaining individuals;

[0074] Step 2.2.3: Combine the one individual determined in Step 2.2.1 with the 99 individuals selected using the method in Step 2.2.2 to form the initial population Pop for the original task. o .

[0075] Step 2.3 Assisted population initialization:

[0076] Step 2.3.1: Initialize an extreme point individual. For each cluster center user in the auxiliary task, select the top 10 items based on the predicted scores to initialize the recommendation list in the individual;

[0077] Step 2.3.2: Initialize the remaining 99 individuals using a randomization method. Randomly select different items from the candidate recommendation list to initialize the remaining individuals;

[0078] Step 2.3.3: Combine the one individual determined in Step 2.3.1 with the 99 individuals selected using the method in Step 2.3.2 to form the initial population Pop for the auxiliary task. h ;

[0079] Step 3, Population Evolution and Interaction:

[0080] Step 3.1: Initialize the number of iterations G = 0, the maximum number of iterations maxGen = 100, and the original population P. o =Pop o , auxiliary population P h =Pop h ;

[0081] Step 3.2, from the original population P o In the process, two individuals are randomly selected and crossover mutation is performed to obtain a descendant individual. This process is repeated 100 times to obtain a set of 100 such descendant individuals (OP). o From the auxiliary population P h In the process, two individuals are randomly selected and crossover mutation is performed to obtain a descendant individual. This process is repeated 100 times to obtain a set of 100 such descendant individuals (OP). h .

[0082] Step 3.3, Knowledge Transfer:

[0083] Step 3.3.1, for OP h Each individual entity in the process achieves knowledge transfer from the auxiliary task to the original task in two steps: the first step is a simple extension. From OP... h Each row extracted from the individuals is expanded to include rows belonging to other users within the same cluster. The second step adjusts the preliminary results obtained in the first step, primarily to eliminate items already rated by users. This is achieved by replacing these previously rated items with other items that have high similarity to them. The similarity between items is calculated using cosine similarity, as follows:

[0084]

[0085] Where, r i R is the rating vector for item i. j It is the rating vector of item j;

[0086] For OP h Each individual in the process is transformed according to the method described above to obtain the OP. h_o .

[0087] For example Figure 4 As shown in the diagram. In the first step, the recommendation results of u1 and u5 are copied to the remaining users in the same cluster. Then, in the second step, the recommendation results are adjusted according to each user's candidate recommendation list. For example, u2 has already interacted with i5, so i5 is not in u2's candidate recommendation list. Therefore, i7, which is most similar to i5, is selected from the candidate recommendation list to replace i5.

[0088] Step 3.3.2, realizing knowledge transfer from the original task to the auxiliary task, is based on the frequency of item occurrence: calculate the frequency of each item appearing in the recommendation list of the same cluster user, then select the top 10 most frequently occurring items based on their frequency, and add these items to the recommendation list of the cluster center user. For OP o Each individual in the process is transformed according to the method described above to obtain the OP. o_h .

[0089] For example Figure 5 As shown. First, calculate the frequency of items appearing in the recommendation list of individuals {u1, u3, u4, u6} from the original task, and then sort them in descending order of frequency. Since 5 items need to be selected, the top 5 most frequent items {i1, i5, i6, i8, i3} can be easily selected from the frequency table.

[0090] Step 3.4: Put population P o And the 100 newly generated offspring individuals OP o And individual OPs that migrated from the auxiliary population h_o They combine to form a new population TP o ;Put the population P h And the 100 newly generated offspring individuals OP h And individual OPs that migrated from the original population o_h They combine to form a new population TP h .

[0091] Step 4: Environment Selection

[0092] Step 4.1: Calculate TP using equations (3) and (4). o and TP h For each individual in the dataset, there are two objective functions: Pre for accuracy and Div for diversity of the recommendation list.

[0093]

[0094]

[0095]

[0096] Where U is the user set, L u It is user u's recommendation list; pr u，i It represents the predicted rating of user u for item i; L represents the length of the recommendation list; |t i | is the number of topics contained in item i; L represents the recommended list uThe set of topics; T is the total number of topics in the entire recommendation system. L represents the recommended list u A collection of different themes, q j This indicates that topic j is in the recommendation list L. u Frequency of occurrence in;

[0097] Step 4.2: Based on the objective function value, use the non-dominated sorting algorithm and the crowding distance algorithm to sort the population TP. o and TP h All individuals are sorted to obtain a candidate population with multiple frontiers; the top 100 individuals are selected and retained for the next generation, thus updating the population P. o and P h Then, set the iteration count G = G + 1 until the iteration count G > maxGen; otherwise, proceed to step 3.2.

[0098] Step 4.3: Select all individuals from the first frontier of the sorted population as the optimal set of recommended items and output it.

[0099] The above description is merely an example and illustration of the structure of the present invention. Those skilled in the art can make various modifications or additions to the specific embodiments described, or use similar methods to replace them, as long as they do not deviate from the structure of the present invention or exceed the scope defined in the claims, all of which should fall within the protection scope of the present invention.

Claims

1. A multi-objective recommendation method based on multi-task evolutionary optimization, characterized in that, Includes the following steps: Step 1: Simplify the original task at two different levels, users and items, to obtain an auxiliary task, which is to make recommendations to users at the cluster center; Simplifying the original task at the user level includes the following steps: The K-Means clustering algorithm is used to preprocess users' historical behavior information, group users into groups, and select the users closest to the cluster center in each group as the cluster center users. The purpose of the auxiliary task is to recommend only to these cluster center users. When using the K-Means clustering algorithm The value is determined using the elbow method, while cosine similarity is used to measure the similarity between the two users. and Similarity between The calculation formula is: ， in, and They are and Rating vector for all items, Indicates the first One user, Indicates the first One user; Simplifying the original task at the item level includes the following steps: The Probs algorithm is used to predict ratings for all users, and the highest predicted rating for each user is obtained. Items, among which The length of the candidate list is represented by the following method: ,in, Indicates the total number of items. This indicates the length of the recommendation list. Then, for each cluster center user, select the user with the highest predicted score among all users in the group except the cluster center user. The intersection of these items is denoted as . ;if Then select the one with the highest predicted score. Items are added to the cluster center user's candidate recommendation list; otherwise, the item with the highest predicted rating is selected from the remaining unrated items set of the cluster center user. An item, denoted as ,Will Add to the candidate recommendation list; Step 2: Initialize the original task and auxiliary task populations; Step 3: Evolve and interact with the initial population obtained in Step 2 to obtain a set of offspring individuals. Use the set of offspring individuals to realize the knowledge transfer from the auxiliary task to the original task and form a new population. Population evolution and interaction specifically include the following steps: Step 3.1: Initialize the number of iterations Maximum number of iterations primitive population Assisted population ; Step 3.2, from the original population Two individuals are randomly selected and crossover mutation is performed to obtain a descendant individual. This process is repeated 100 times to obtain a set of 100 such descendant individuals. From auxiliary population Two individuals are randomly selected and crossover mutation is performed to obtain a descendant individual. This process is repeated 100 times to obtain a set of 100 such descendant individuals. ; Step 3.3, Knowledge Transfer: Step 3.3.1, for Each individual in the process achieves knowledge transfer from the auxiliary task to the original task in two steps: the first step is from... Each row extracted from individuals will be expanded to the rows of other users in the same cluster; the second step is to adjust the preliminary results obtained in the first step, removing items that have already been rated by users by replacing them with other items that are highly similar to these previously rated items. The similarity between items is calculated using cosine similarity, as follows: ， in, It is an item The rating vector, It is an item The rating vector; for Each individual in the process is transformed according to the method described above, resulting in... ; Step 3.3.2, realizing knowledge transfer from the original task to the auxiliary task, is based on the frequency of item occurrence: calculate the frequency of each item appearing in the recommendation list of the same cluster user, then select the top 10 most frequently occurring items according to their frequency, and add these items to the recommendation list of the cluster center user. Each individual in the process is transformed according to the above method, resulting in... ; Step 3.4: Population and the 100 newly generated offspring individuals And individuals that migrated from the auxiliary population They combine to form a new population ; to the population and the 100 newly generated offspring individuals And individuals that migrated from the original population They combine to form a new population ; Step 4, Environment Selection: Based on the objective function value, the non-dominated sorting algorithm and the crowding distance algorithm are used to sort all individuals in the new population respectively. The optimal set of recommended items is selected from all individuals in the first frontier of the sorted population and output.

2. The multi-objective recommendation method based on multi-task evolutionary optimization according to claim 1, characterized in that, Step 2, the initialization of the original task and auxiliary task populations, specifically includes the following steps: Step 2.1, for users Set the length of the recommended list. , The candidate recommendation list is Set the population size to ,make ; Step 2.2: Initialize the original population using an extreme point-guided approach; Step 2.3: Initialize the auxiliary population using the extreme point-guided method.

3. The multi-objective recommendation method based on multi-task evolutionary optimization according to claim 2, characterized in that, In step 2.2, the initial population initialization method is as follows: Step 2.2.1: Initialize an extreme point individual. For each user in the original task, select the top 10 items based on the predicted score to initialize the recommendation list in the individual. Step 2.2.2: Initialize the remaining individuals using a randomization method. Randomly select different items from the candidate recommendation list to initialize the remaining individuals. Step 2.2.3: Combine the one individual determined in Step 2.2.1 with the remaining individuals selected using the method in Step 2.2.2 to form the initial population for the original task. .

4. The multi-objective recommendation method based on multi-task evolutionary optimization according to claim 2, characterized in that, In step 2.3, the auxiliary population initialization method is as follows: Step 2.3.1: Initialize an extreme point individual. For each cluster center user in the auxiliary task, select the top performers based on the predicted scores. Use one item to initialize the recommendation list in an individual; Step 2.3.2: Initialize the remaining individuals using a randomization method. Randomly select different items from the candidate recommendation list to initialize the remaining individuals. Step 2.3.3: Combine the one individual determined in Step 2.3.1 with the remaining individuals selected using the method in Step 2.3.2 to form the initial population for the auxiliary task. .

5. The multi-objective recommendation method based on multi-task evolutionary optimization according to claim 1, characterized in that, Step 4, the environment selection specifically includes the following steps: Step 4.1: Calculate using the following formula. and For each individual in the dataset, there are two objective functions, including the accuracy of the recommendation list. and diversity : ， ， ， in, It is a collection of users. User Recommended list; User For items Predicted score; Indicates the length of the recommendation list; It is an item The number of topics included; This refers to the recommended list. A collection of themes; It represents the total number of topics in the entire recommendation system. This refers to the recommended list. A collection of different themes, Indicate topic In the recommended list Frequency of occurrence in; Step 4.2: Based on the objective function value, use the non-dominated sorting algorithm and the crowding distance algorithm to sort the population respectively. and All individuals are sorted to obtain a candidate population with multiple frontiers; the top 100 individuals are selected and retained for the next generation, thus updating the population. and Then make the number of iterations... until the number of iterations... Until then, otherwise, proceed to step 3.2; Step 4.3: Select all individuals from the first frontier of the sorted population as the optimal set of recommended items and output it.

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