Personalized Learning Path Generation Method Based on Meta-Heuristic Algorithm

Abstract

The present invention discloses a personalized learning path generation method based on a meta-heuristic algorithm, which relates to the technical field of personalized learning path generation, and includes initializing a candidate solution population; constructing a multi-objective fitness function based on a concept coverage function, a time penalty function, and a style matching function to comprehensively score the candidate solutions; based on expert guidance and a memetic mechanism, locally updating each candidate solution in the population and updating the expert age, and then globally updating the candidate solution population through a dynamic control and migration mechanism; when the set number of iterations is reached, calculating and sorting the priority scores of learning materials according to the optimal candidate solution, and generating a personalized learning sequence through a weighted pooling method. Therefore, by adopting the above-mentioned personalized learning path generation method based on a meta-heuristic algorithm, the problems of local optimality and instability can be improved, and at the same time, more efficient and accurate personalized learning path generation can be achieved under multi-objective optimization.

Description

Technical Field

[0001] The present invention relates to the technical field of personalized learning path generation, and particularly to a personalized learning path generation method based on metaheuristic algorithms. Background Art

[0002] With the rapid development of online learning and personalized education, how to design the most suitable learning path for students has become a key research topic in the education field. As a multi-objective optimization problem, personalized learning path generation involves student models, learning material parameters, and the correlation constraints between knowledge points. Currently, existing technologies usually generate personalized learning paths based on genetic algorithms, particle swarm optimization, or single bionic optimization algorithms. However, when dealing with large-scale learning materials, high-dimensional search spaces, and complex educational constraints, the optimization effect is often reduced due to local optimal traps, unstable convergence, and insufficient personalized adaptability.

[0003] Therefore, there is an urgent need for a new optimization method that can achieve a good balance between global optimization and local development, suppress local optimality while ensuring the stability of solutions, and take into account multiple constraint conditions and personalized needs to solve technical problems. Summary of the Invention

[0004] The purpose of the present invention is to provide a personalized learning path generation method based on metaheuristic algorithms, which can overcome the local optimal problem through expert guidance and meme mechanisms, and at the same time take into account multi-objective constraint optimization to improve convergence stability and computational efficiency.

[0005] To achieve the above purpose, the present invention provides a personalized learning path generation method based on metaheuristic algorithms, including the following steps:

[0006] S1. Based on the student set and the learning material set, generate an initial candidate solution population through uniform random distribution, where the candidate solutions are represented by a decision matrix, and the matrix elements identify the selection relationship between students and learning materials;

[0007] S2. Based on the concept coverage function, time penalty function, and style matching function, construct a multi-objective fitness function to comprehensively score the candidate solutions in the population;

[0008] S3. Based on expert guidance and meme mechanisms, perform iterative solution by setting the expert age of the candidate solutions, calculate the expert influence weight using the expert age, then determine the expert solutions based on the probabilistic selection mechanism of the expert influence weight, locally update each candidate solution in the population, and then globally update the candidate solutions in the population through dynamic control and migration mechanisms;

[0009] S4. When the set iteration condition is reached, based on the obtained optimal candidate solution, perform priority sorting according to the priority scores of the learning materials, and use the weighted pooling method to generate a personalized learning sequence.

[0010] Preferably, the student set is represented as , the learning material set is represented as , and the decision matrix of the candidate solution is represented as ;

[0011] where, for student selecting material , ; otherwise, ;

[0012] The initialized candidate solution population is represented as , representing the population size.

[0013] Preferably, in step S2, the expression of the multi-objective fitness function is as follows:

[0014] ;

[0015] In the formula, is the multi-objective fitness, is the concept coverage function, is the time penalty function, is the style matching function, , , are the weights of the corresponding functions;

[0016] where,

[0017] ;

[0018] ;

[0019] ;

[0020] In the formula, represents the number of elements in the set of concepts not covered in the candidate solution, represents the number of elements in the set of redundant concepts in the candidate solution, represents the redundant penalty factor, represents the cumulative learning time of the learning materials selected in the candidate solution, represents the maximum allowed learning time, represents student in dimension ideal learning style index, represents the average style index under the candidate solution.

[0021] Preferably, in step S3, a candidate solution is set with an initial expert age of . The expert age is updated each time an iteration is completed as follows:

[0022] ;

[0023] In the formula, represents the current time step. When the candidate solution is selected as a local optimum or sub-optimum, the expert age is set to zero.

[0024] Preferably, in step S3, according to the expert age, the expert influence weight is calculated using an exponential decay function as follows:

[0025] ;

[0026] In the formula, is the decay rate, is the allowable age factor, is the set maximum number of iterations.

[0027] Preferably, in step S3, for each non-expert solution , a potential expert set is defined, which contains candidate solutions with multi-objective fitness superior to . Then, an expert solution is determined using a probabilistic selection mechanism based on the expert influence weight as follows:

[0028] ;

[0029] In the formula, represents the probability of selecting as the expert solution, represents corresponding expert influence weight, represents the expert set the th candidate solution in

[0030] According to the selection probabilities of each candidate solution in the expert set , an expert solution is selected, and the non-expert solution is updated as follows:

[0031] ;

[0032] In the formula, is the random perturbation factor.

[0033] Preferably, in step S3, the candidate solutions in the population are updated through a dynamic control and migration mechanism, including reflecting the risk degree of the current search through a danger signal, and the expression is:

[0034] ;

[0035] In the formula, is the danger signal, is a fixed constant offset, is a regulation parameter;

[0036] When the danger signal exceeds the preset threshold , a migration operation is introduced to update the current candidate solution as follows:

[0037] ;

[0038] In the formula, is the migration intensity, and are two candidate solutions randomly selected from the population.

[0039] Preferably, in step S3, the candidate solutions in the population are updated through a dynamic control and migration mechanism, including balancing local exploitation and global search through a safety signal, as follows:

[0040] The expression of the safety signal is:

[0041] ;

[0042] In the formula, controls the steepness of the curve, is the phase offset parameter;

[0043] When , the safety signal dominates, and the population is divided into high-fitness individuals, medium individuals, and offspring individuals. Among them, the high-fitness individuals use the Halton sequence for global exploration, and the medium individuals perform local exploitation around the current optimal solution;

[0044] When and , the danger signal triggers the migration mechanism;

[0045] When and , the comprehensive optimal solution and sub-optimal solution are updated as follows:

[0046] ;

[0047] ;

[0048] ;

[0049] In the formula, is the optimal candidate solution for the -th iteration, is the sub-optimal candidate solution for the -th iteration, , are respectively the candidate solutions for the , -th iteration, , , , are all random numbers within the range, represents the element-wise absolute value operation.

[0050] Preferably, in step S4, the priority score of the learning material has the following expression:

[0051] ;

[0052] In the formula, , and are indicator functions for identifying the category to which the learning material belongs, , and are the weight coefficients of the corresponding indicator functions.

[0053] Therefore, the personalized learning path generation method based on the meta-heuristic algorithm adopted by the present invention has the following technical effects:

[0054] (1) Overcoming the local optimum problem: By adopting expert guidance and meme mechanism, the diversity of the population can be continuously stimulated through dynamically determining the expert weight and selection mechanism during the search process, effectively improving the ability to jump out of the local optimum.

[0055] (2) Improving the convergence stability and computational efficiency: By introducing dynamic control signals (hazard signal and safety signal) to balance global exploration and local exploitation, the optimization process becomes more stable, the convergence is more stable, and thus the overall computational efficiency is improved.

[0056] (3) Taking into account multi-objective constraint optimization: By simultaneously considering factors such as concept coverage, time constraint, and learning style matching inside the algorithm, a three-layer priority mechanism is designed to achieve personalized regulation of the sorting of learning materials. The generated personalized learning path is superior to the traditional method in terms of difficulty progression, concept integrity, and constraint satisfaction.

[0057] The technical solution of the present invention will be further described in detail below with reference to the accompanying drawings and embodiments. Description of the Drawings

[0058] Figure 1 It is a flowchart of a personalized learning path generation method based on meta - heuristic algorithms. Specific implementation manners

[0059] The present invention can be more detailedly explained through the following embodiments. The purpose of disclosing the present invention is to protect all changes and improvements within the scope of the present invention. The present invention is not limited to the following embodiments.

[0060] Embodiment 1

[0061] As Figure 1 shown, the present invention provides a personalized learning path generation method based on meta - heuristic algorithms, which mainly involves the initialization of candidate solutions, the construction of fitness functions, the update based on expert guidance, the regulation of dynamic control signals, and the generation of the final personalized learning path, etc. They form a closed - loop dynamic search process, including the following steps:

[0062] S1. Define the student set as and the learning material set as . The candidate solutions are represented by a binary decision matrix as follows:

[0063] , where when student selects material , ; otherwise, .

[0064] Generate an initial candidate solution population through a uniform random distribution, represents the population size, and boundary handling techniques are used to ensure that each is a feasible solution. In addition, initialize the iteration counter and specify the maximum number of iterations .

[0065] S2. In each iteration, perform a comprehensive scoring on each candidate solution . Based on the concept coverage function, time penalty function, and style matching function, construct a multi - objective fitness function to provide an evaluation basis for the entire iteration process as follows:

[0066] ;

[0067] where,

[0068] ;

[0069] ;

[0070] ;

[0071] Wherein, is the concept coverage function, is the time penalty function, is the style matching function, , , are the weights of the corresponding functions, represents the number of elements in the set of concepts not covered in the candidate solution, represents the number of elements in the set of redundant concepts in the candidate solution, represents the redundancy penalty factor, represents the cumulative learning time of the learning materials selected in the candidate solution, represents the maximum allowable learning time, represents the student at the ideal learning style index in the dimension, represents the average style index under the candidate solution. , , and are all preset by the problem expert in advance.

[0072] S3. At each iteration time step , for the candidate solutions in the population, update through the expert guidance mechanism, and the specific operations are as follows:

[0073] For each candidate solution set the expert age, and the initial expert age is , and update the expert age to after each iteration. When the candidate solution is selected as the local optimal or sub - optimal, that is, is the smallest or the second smallest, the expert age is set to zero.

[0074] Based on the expert age, calculate the expert influence weight through the exponential decay function as follows:

[0075] ;

[0076] Wherein, is the decay rate, is the allowable age factor, is the set maximum number of iterations.

[0077] Then, determine the expert solution based on the probabilistic selection mechanism of the expert influence weight. The specific operation is: for each non - expert solution , define the potential expert set , including candidate solutions with multi-objective fitness superior to ; define the probability of selecting from the set as the expert solution to be proportional to its expert influence weight , that is, the probability of selecting as the expert solution is , where represents corresponding expert influence weight, represents the expert set in the th candidate solution corresponding expert influence weight. This probabilistic selection mechanism based on expert influence weights not only ensures the trend of learning from high-quality solutions but also avoids premature convergence to a single solution through the age mechanism, effectively maintaining population diversity.

[0078] In addition, to balance global search (exploration) and local exploitation, a dynamic control signal is introduced in each iteration, and the candidate solutions in the population are updated through the dynamic control and migration mechanism. The specific steps are as follows:

[0079] According to the current iteration number and the maximum iteration number , define the danger signal as:

[0080] ;

[0081] In the formula, is the danger signal, is a fixed constant offset, is a regulation parameter.

[0082] When the danger signal exceeds the preset threshold , introduce a migration operation to update the current candidate solutions as follows:

[0083] ;

[0084] In the formula, is the migration intensity, and are two candidate solutions randomly selected from the population.

[0085] At the same time, the safety signal is smoothly adjusted using the Sigmoid function and defined as:

[0086] ;

[0087] In the formula, controls the steepness of the curve, is the phase offset parameter.

[0088] When When the safety signal dominates, the population is divided into high - fitness individuals, medium individuals, and offspring individuals. Among them, the high - fitness individuals use the Halton sequence for global exploration, and the medium individuals conduct local exploitation around the current optimal solution.

[0089] When and the danger signal triggers the migration mechanism.

[0090] When and the comprehensive optimal solution and the sub - optimal solution are updated as follows:

[0091] ;

[0092] ;

[0093] ;

[0094] In the formula, is the optimal candidate solution of the th iteration; is the sub - optimal candidate solution of the th iteration; , are the candidate solutions of the , th iteration respectively; , , , are all random numbers within the range; represents the element - wise absolute value operation. Here, is a matrix, and the update operation is calculated element - wise to ensure that remains a matrix.

[0095] Through local exploitation, fine - grained search is realized in the discovered high - quality regions, improving the quality and convergence speed of the solution, and making the learning path more accurately match the needs of students. Global search is used to explore the unknown solution space, avoid falling into local optima, and enhance the algorithm's ability to adapt to different learning needs. The comprehensive safety signal mechanism dynamically balances these two search strategies, ensuring that the algorithm can both discover innovative learning path combinations and guarantee the pedagogical rationality of these paths.

[0096] S4. When the set number of iterations is reached or other termination conditions are met, the iteration is completed.

[0097] Among them, the other termination conditions specifically include:

[0098] Fitness convergence condition: For consecutive The fitness threshold change of the optimal candidate solution in the current iteration is less than the preset threshold , that is , is the preset number of consecutive iterations.

[0099] Solution vector convergence condition: The solution vector of the optimal candidate solution changes very little in consecutive multiple iterations, that is , where is the distance threshold of the preset vector.

[0100] Concept coverage integrity condition: The current optimal candidate solution completely covers all the concepts that students need to learn, that is , indicating that all the necessary concepts have been covered.

[0101] At this time, based on the current optimal candidate solution , the learning materials are graded and inspected as follows:

[0102] (1) High-priority materials: Completely cover the required concepts and meet the prerequisite knowledge requirements.

[0103] (2) Medium-priority materials: Partially cover and match the learning time.

[0104] (3) Challenging materials: Slightly higher in difficulty but meet the time limit.

[0105] Then, calculate the priority scores of each material, perform priority sorting, and use the weighted pooling method to form the final personalized learning sequence , ensuring that the expected goals are achieved in terms of concept coverage, difficulty progression, and time distribution of the learning materials, so as to meet the personalized needs of students. Among them, the priority score is defined as:

[0106] ;

[0107] In the formula, , and are indicator functions indicating the category to which the learning material belongs, , and are the weight coefficients of the corresponding indicator functions.

[0108] Embodiment 2

[0109] To verify the technical effect of the Memetic Walrus Optimizer (MWO) proposed in the present invention based on the expert-guided strategy in the problem of generating personalized learning paths, in this embodiment, four existing technologies, namely the traditional Walrus algorithm (WO), the Skill Optimization Algorithm (SOA), the Sand Cat Swarm Optimization Algorithm (SCSO), and the Preschool Education Optimization Algorithm (PEOA), are used as comparative examples to analyze their performance in terms of different problem scales and the quality of generated learning paths. Specifically, it includes:

[0110] (1) Dataset and basic configuration: Based on the publicly available Online University Learning Dataset (OULAD), multiple test scenarios containing 100 to 180 learning materials are selected, and the numbers of the student set and the learning material set are set to 30 and 150 - 180 respectively, covering a total of 20 knowledge points.

[0111] (2) Algorithm parameters: The initial population size is set to 30, and the maximum number of iterations is taken as 500.

[0112] (3) Evaluation metrics: In this embodiment, two metrics, namely "Average Fitness Value (Avg)" and "Standard Deviation (Std)", are mainly used to evaluate the overall optimization effect of the algorithm; at the same time, path quality metrics such as "concept coverage rate", "difficulty progression rate", and "difficulty matching rate" are used to verify the quality of the generated personalized learning paths.

[0113] As shown in Table 1, under the conditions of different numbers of learning materials (such as 100, 150, 180), the MWO algorithm reaches the lowest average fitness value, which indicates that on the premise of meeting various educational constraints (such as concept coverage, time limit, and learning style matching), the solutions generated by MWO can achieve a better sorting effect; moreover, the standard deviation of MWO is much lower than that of the comparable algorithms of the same kind. Especially in the scenario of 150 learning materials, its standard deviation is only 18.02, which is significantly reduced compared with other methods, verifying the significant role of expert guidance and dynamic signal control in jumping out of local optima and maintaining convergence stability. In addition, as the number of learning materials increases (from 100 to 180), MWO not only can maintain a lower fitness value but also shows a slight improvement trend, further demonstrating the superiority of MWO in dealing with large-scale optimization problems.

[0114] Table 1 Precision of each algorithm under different numbers of materials

[0115] ;

[0116] On the other hand, in order to intuitively understand the effect of MWO in generating personalized learning paths, the paths of representative students were randomly selected for comparative analysis.

[0117] Table 2 Comparison of recommended learning material paths

[0118] ;

[0119] As shown in Table 2, all algorithms achieve the required 100% concept coverage, but at the level of material sorting, MWO can reasonably distribute key knowledge points to ensure the continuity of subsequent learning. At the same time, the difficulty advancement rate of MWO is as high as 90.7%, and the difficulty completely matches the student's ability (100% matching rate), which means that MWO is better than other comparison algorithms in terms of smooth transition and hierarchical connection between materials; while the existing WO, SOA, SCSO and PEOA methods all have certain connection imbalances.

[0120] In general, the MWO algorithm significantly improves the local optimal trap and convergence instability problems in the adaptive course sorting problem by relying on expert guidance, dynamic danger signal control, and multi-layer priority sorting mechanism, while achieving efficient processing of multi-objective constraints. In addition, MWO can generate personalized course paths that not only meet the overall concept coverage, but also have smooth difficulty progression and match students' learning abilities, providing excellent technical and application support for intelligent teaching in the field of online education.

[0121] WO is a newly proposed nature-inspired meta-algorithm with the characteristics of fewer parameters and lower computational complexity. However, when dealing with complex problems containing a large number of local optimal solutions, it is easy to fall into local optimality and has insufficient convergence stability.

[0122] SOA is designed for multi-objective optimization problems. In some practical applications, it can consider multiple constraints simultaneously. However, it converges slowly during the optimization process and has limited global exploration capabilities for complex search spaces.

[0123] SCSO is inspired by swarm intelligence and realizes global search through group collaboration. However, in large-scale problems or under multi-objective constraints, its stability and convergence effects are still difficult to meet the needs of personalized learning sequence recommendation.

[0124] PEOA focuses on optimization in the teaching field and realizes the sorting of knowledge points through simulating educational scenarios. It has certain effects in solving specific educational problems, but it has obvious disadvantages in algorithm efficiency and complex problem-solving capabilities.

[0125] Therefore, the present invention adopts the above-mentioned personalized learning path generation method based on meta-heuristic algorithms. Through the overall optimization strategy, it not only improves the solution to local optimum and instability problems, but also realizes more efficient and accurate personalized learning path generation under multi-objective optimization, with significant technical and application advantages.

[0126] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and are not intended to limit them. Although the present invention has been described in detail with reference to the preferred embodiments, those of ordinary skill in the art should understand that they can still modify or equivalently replace the technical solutions of the present invention, and these modifications or equivalent replacements cannot make the modified technical solutions deviate from the spirit and scope of the technical solutions of the present invention.

Claims

1. A personalized learning path generation method based on a meta-heuristic algorithm, characterized in that: The following steps are involved: S1. Based on the student set and the learning material set, a population of initialized candidate solutions is generated through uniform random distribution, where the candidate solutions are represented by a decision matrix, and the matrix elements identify the selection relationship between students and learning materials; S2. Based on the concept coverage function, time penalty function and style matching function, a multi-objective fitness function is constructed to comprehensively score the candidate solutions in the population; S3, based on expert guidance and meme mechanism, iterative solution is performed by setting the expert age of candidate solutions, and the expert influence weight is calculated using the expert age. Then, the expert solution is determined based on the probabilistic selection mechanism of the expert influence weight, and each candidate solution in the population is locally updated; then the candidate solutions in the population are globally updated through dynamic control and migration mechanism: The risk level of the current search is reflected by the danger signal, and the expression is: ； In the formula, As a danger signal, is a fixed constant offset, To adjust the parameters, represents the current time step, is the maximum number of iterations set; When the danger signal exceeds the preset threshold When , the migration operation is introduced to update the current candidate solution; Balance local development and global search through safety signals as follows: The expression of the safety signal is: ； In the formula, Controls the steepness of the curve. is the phase shift parameter; when When , the safety signal dominates, and the population is divided into high-fitness individuals, medium-fitness individuals, and offspring individuals. High-fitness individuals use the Halton sequence for global exploration, and medium-fitness individuals perform local development around the current optimal solution. when and When, danger signals trigger migration mechanisms; when and When , the optimal solution and the suboptimal solution are updated; S4. When the set iteration conditions are met, based on the obtained optimal candidate solution, the learning materials are prioritized according to their priority scores, and a weighted pooling method is used to generate a personalized learning sequence.

2. The method for generating a personalized learning path based on a meta-heuristic algorithm according to claim 1, characterized in that: The student set is represented as , the learning material set is represented as , the decision matrix of the candidate solution is expressed as: ; in, ; The population of initialized candidate solutions is expressed as , Indicates the population size.

3. The method for generating a personalized learning path based on a meta-heuristic algorithm according to claim 1, characterized in that: In step S2, the expression of the multi-objective fitness function is as follows: ； In the formula, is the multi-objective fitness, is the concept coverage function, is the time penalty function, is the style matching function, , , is the weight of the corresponding function; in, ； ； ； In the formula, represents the number of elements in the concept set not covered by the candidate solution, represents the number of elements in the redundant concept set in the candidate solution, represents the redundancy penalty factor, represents the cumulative learning time of the learning materials selected from the candidate solutions, Indicates the maximum learning time allowed, Indicates students exist Ideal learning style indicators in terms of dimensions, Represents the average style index under the candidate solutions.

4. The method for generating a personalized learning path based on a meta-heuristic algorithm according to claim 3, characterized in that: In step S3, set the candidate solution The initial expert age is , each time an iteration is completed, the expert age is updated as follows: ； In the formula, Indicates the current time step, when the candidate solution When selected as a local optimum or suboptimal solution, the expert age is set to zero.

5. The method for generating a personalized learning path based on a meta-heuristic algorithm according to claim 4, characterized in that: In step S3, the expert influence weight is calculated using an exponential decay function according to the expert age. ,as follows: ； In the formula, is the attenuation rate, is the allowed age factor, The maximum number of iterations set.

6. The method for generating a personalized learning path based on a meta-heuristic algorithm according to claim 5, characterized in that: In step S3, for each non-expert solution , define the set of potential experts , including multi-objective fitness better than The candidate solutions are then selected using a probabilistic selection mechanism based on expert influence weights, as follows: ； In the formula, Indicates selection As the probability of the expert solution, express The corresponding expert influence weight, Represents a set of experts Middle The expert influence weight corresponding to each candidate solution; According to the expert collection The probability of selecting each candidate solution in the equation is used to select an expert solution. , and explain it to non-experts Update as follows: ； In the formula, is the random disturbance factor.

7. The method for generating a personalized learning path based on a meta-heuristic algorithm according to claim 5, characterized in that: In step S3, a migration operation is introduced to update the current candidate solution as follows: ； In the formula, is the migration intensity, and are two candidate solutions randomly selected from the population.

8. The method for generating a personalized learning path based on a meta-heuristic algorithm according to claim 7, characterized in that: In step S3, the optimal solution and the suboptimal solution are updated as follows: ； ； ； In the formula, For the The best candidate solution for the iteration, For the The suboptimal candidate solution of the iteration, , Respectively , The candidate solution of the iteration, , , , Both A random number in the range, Represents an element-wise absolute value operation.

9. The method for generating a personalized learning path based on a meta-heuristic algorithm according to claim 1, characterized in that: In step S4, the priority score of the learning material The expression is as follows: ； In the formula, , and is the indicator function that identifies the category to which the learning material belongs, , and is the weight coefficient of the corresponding indicator function.

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