Personalized learning path generation method based on meta-heuristic algorithm

Abstract

The invention discloses a personalized learning path generation method based on a meta-heuristic algorithm, and relates to the technical field of personalized learning path generation, and the method comprises the steps: initializing a candidate solution population; constructing a multi-target fitness function based on a concept coverage function, a time penalty function and a style matching function, and comprehensively scoring candidate solutions; on the basis of expert guidance and a memetic mechanism, locally updating each candidate solution in the population, updating the age of an expert, and globally updating the candidate solution population through a dynamic control and migration mechanism; and when a set number of iterations is reached, calculating and sorting the priority scores of the learning materials according to the optimal candidate solution, and generating a personalized learning sequence through a weighted pooling method. Therefore, by the adoption of the personalized learning path generation method based on the meta-heuristic algorithm, the problems of local optimum and instability can be solved, and meanwhile more efficient and accurate personalized learning path generation is achieved under multi-objective optimization.

Description

Technical Field

[0001] The present invention relates to the technical field of personalized learning path generation, and in particular to a personalized learning path generation method based on a meta-heuristic algorithm. Background Art

[0002] With the rapid development of online learning and personalized education, designing the most appropriate learning paths for students has become a key research topic in the field of education. Personalized learning path generation, as a multi-objective optimization problem, involves student models, learning material parameters, and the constraints associated with knowledge points. Currently, existing technologies typically generate personalized learning paths using 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, optimization effectiveness is often compromised due to local optimality 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 and ensure the stability of the solution, and take into account multiple constraints and personalized needs to solve technical problems. Summary of the Invention

[0004] The purpose of this invention is to provide a personalized learning path generation method based on a metaheuristic algorithm, which can overcome the local optimal problem through expert guidance and memetic mechanism, while taking into account multi-objective constrained optimization and improving convergence stability and computational efficiency.

[0005] To achieve the above object, the present invention provides a method for generating a personalized learning path based on a meta-heuristic algorithm, comprising the following steps: S1. Based on the student set and the learning material set, a population of initialized candidate solutions is generated through uniform random distribution. 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 mechanisms, the solution is iterated by setting the expert age of candidate solutions, and the expert influence weight is calculated using the expert age. The expert solution is then determined based on the probabilistic selection mechanism of the expert influence weight. Each candidate solution in the population is locally updated, and then the candidate solutions in the population are globally updated through dynamic control and migration mechanisms. 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.

[0006] Preferably, the student set is represented as , the learning material set is represented as , the decision matrix of the candidate solution is expressed as ; Among them, students Select Materials hour, ;otherwise, ; The population of initialized candidate solutions is expressed as , Indicates the population size.

[0007] Preferably, in step S2, the expression of the multi-objective fitness function is as follows: ; Where, 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, ; ; ; Where, 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 solution.

[0008] Preferably, 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: ; Where, Indicates the current time step, when the candidate solution When selected as a local optimum or suboptimal, the expert age is set to zero.

[0009] Preferably, in step S3, the expert influence weight is calculated using an exponential decay function according to the expert's age. ,as follows: ; Where, is the attenuation rate, is the allowed age factor, The maximum number of iterations is set.

[0010] Preferably, 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: ; Where, 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 expert collection The selection probability of each candidate solution is selected, and an expert solution is selected , and explain it to non-experts Update as follows: ; Where, is the random disturbance factor.

[0011] Preferably, in step S3, the candidate solutions in the population are updated through dynamic control and migration mechanisms, including reflecting the risk level of the current search through danger signals, which are expressed as: ; Where, A danger signal. is a fixed constant offset, To adjust the parameters; When the danger signal exceeds the preset threshold When , the migration operation is introduced to update the current candidate solution as follows: ; Where, is the migration intensity, and are two candidate solutions randomly selected from the population.

[0012] Preferably, in step S3, the candidate solutions in the population are updated through dynamic control and migration mechanisms, including balancing local development and global search through safety signals, as follows: The expression of the safety signal is: ; Where, Controls the steepness of the curve, is the phase offset 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 as follows: ; ; ; Where, For the The best candidate solution of 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.

[0013] Preferably, in step S4, the priority score of the learning material The expression is as follows: ; Where, 、 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.

[0014] Therefore, the present invention adopts the above-mentioned personalized learning path generation method based on the meta-heuristic algorithm, which has the following technical effects: (1) Overcoming the local optimal problem: Using expert guidance and meme mechanisms, the diversity of the population can be continuously stimulated by dynamically determining expert weights and selection mechanisms during the search process, effectively improving the ability to escape the local optimal state.

[0015] (2) Improve convergence stability and computational efficiency: By introducing dynamic control signals (danger signals and safety signals) to balance global exploration and local development, the optimization process becomes smoother and the convergence becomes more stable, thereby improving the overall computational efficiency.

[0016] (3) Taking into account multi-objective constraint optimization: The algorithm simultaneously considers factors such as concept coverage, time constraints, and learning style matching, and designs a three-level priority mechanism to achieve personalized control of the sorting of learning materials. The generated personalized learning path is superior to traditional methods in terms of difficulty progression, concept completeness, and constraint satisfaction.

[0017] The technical solution of the present invention is further described in detail below through the accompanying drawings and embodiments. BRIEF DESCRIPTION OF THE DRAWINGS

[0018] Figure 1 This is a flowchart of the personalized learning path generation method based on meta-heuristic algorithm. DETAILED DESCRIPTION

[0019] The present invention can be explained in more detail by the following examples. 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 examples.

[0020] Example 1 like Figure 1 As shown, the present invention provides a personalized learning path generation method based on a metaheuristic algorithm, which mainly involves the initialization of candidate solutions, the construction of fitness functions, expert-guided updates, the regulation of dynamic control signals, and the generation of the final personalized learning path. These form a closed-loop dynamic search process, including the following steps: S1. Define the student set as , the learning material set is , the candidate solution is represented by a binary decision matrix as follows: , among which students Select Materials hour, ;otherwise, .

[0021] Generate an initial candidate solution population through uniform random distribution , Indicates the population size, and uses boundary processing technology to ensure that each is a feasible solution. In addition, initialize the iteration counter , and specify the maximum number of iterations .

[0022] S2. In each iteration, for each candidate solution Comprehensive scoring is performed based on concept coverage function, time penalty function and style matching function to construct a multi-objective fitness function , providing an evaluation basis for the entire iterative process, as follows: ; in, ; ; ; Where, is the concept coverage function, is the time penalty function, is the style matching function, 、 、 is the weight of the corresponding function, 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 solution. 、 、 and All are pre-set by problem experts.

[0023] S3, at each iterative time step In the ensemble, the candidate solutions within the population are updated through the expert guidance mechanism. The specific operations are as follows: For each candidate solution Set the expert age. The initial expert age is , each time an iteration is completed, the expert age is updated to When the candidate solution When it is selected as the local optimum or suboptimal, At the minimum or second hour, the expert age is set to zero.

[0024] Based on the expert's age, the expert's influence weight is calculated using an exponential decay function as follows: ; Where, is the attenuation rate, is the allowed age factor, The maximum number of iterations is set.

[0025] Then, the expert solution is determined based on the probabilistic selection mechanism of expert influence weights. The specific operation is: for each non-expert solution , define the set of potential experts , including multi-objective fitness better than Candidate solutions of Select The probability of being an expert solution and its expert influence weight Proportional, that is, choose The probability of being an expert solution is ,in express The corresponding expert influence weight, Represents a set of experts Middle The expert influence weights corresponding to candidate solutions are calculated. This probabilistic selection mechanism based on expert influence weights not only ensures the tendency to learn from high-quality solutions, but also avoids premature convergence to a single solution through the age mechanism, effectively maintaining population diversity.

[0026] In addition, to balance global search (exploration) and local development (utilization), a dynamic control signal is introduced in each iteration to update the candidate solutions in the population through dynamic control and migration mechanisms. The specific steps are as follows: According to the current iteration number and the maximum number of iterations , define danger signals as: ; Where, A danger signal. is a fixed constant offset, is the adjustment parameter.

[0027] When the danger signal exceeds the preset threshold When , the migration operation is introduced to update the current candidate solution as follows: ; Where, is the migration intensity, and are two candidate solutions randomly selected from the population.

[0028] At the same time, the safety signal is smoothed using the Sigmoid function, which is defined as: ; Where, Controls the steepness of the curve, is the phase offset parameter.

[0029] when When the safety signal dominates, 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.

[0030] when and When danger signals trigger migration mechanisms.

[0031] when and When , the optimal solution and the suboptimal solution are updated as follows: ; ; ; Where, For the The best candidate solution of the iteration; For the The suboptimal candidate solution of the iteration; 、 Respectively 、 Candidate solutions for iterations; 、 、 、 Both A random number in a range; Represents the element-level absolute value operation, here For matrices, the update operation is calculated element-wise, ensuring Still The matrix of .

[0032] Through local development, a refined search is conducted within discovered high-quality areas, improving solution quality and convergence speed, enabling learning paths to more precisely match student needs. Global search is used to explore the unknown solution space, avoiding local optima and enhancing the algorithm's ability to adapt to diverse learning needs. An integrated safety signal mechanism dynamically balances these two search strategies, ensuring the algorithm discovers innovative learning path combinations while ensuring the pedagogical rationality of these paths.

[0033] S4. When the set number of iterations is reached or other termination conditions are met, the iteration is completed.

[0034] Other termination conditions include: Fitness convergence condition: continuous The fitness threshold change of the optimal candidate solution of the iteration is less than the preset threshold ,Right now , is the preset number of consecutive iterations.

[0035] Solution vector convergence condition: the solution vector of the optimal candidate solution changes very little in multiple consecutive iterations, that is, ,in The distance threshold of the preset vector.

[0036] Concept coverage completeness condition: current optimal candidate solution Complete coverage of all concepts that students need to learn, i.e. , indicating that all necessary concepts have been covered.

[0037] At this time, according to the current optimal candidate solution , conduct graded examinations on the learning materials: (1) High-priority material: fully covers the required concepts and satisfies the prerequisite knowledge requirements.

[0038] (2) Medium priority material: Partial coverage and matching study time.

[0039] (3) Challenging materials: slightly more difficult but within the time limit.

[0040] Then, the priority score of each material is calculated and prioritized, and the weighted pooling method is used to form the final personalized learning sequence. , ensuring that the concept coverage, difficulty progression and time distribution of the learning materials meet the expected goals, thereby meeting the individual needs of students. Defined as: ; Where, 、 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.

[0041] Example 2 To verify the technical effectiveness of the expert-guided Memetic Walrus Optimizer (MWO) algorithm proposed in this invention for generating personalized learning paths, this example uses four existing technologies, including the traditional Walrus Algorithm (WO), the Skill Optimization Algorithm (SOA), the Sand Cat Colony Optimization Algorithm (SCSO), and the Preschool Education Optimization Algorithm (PEOA), as comparative examples to analyze their performance in terms of different problem sizes and learning path generation quality. Specifically, the following are the results: (1) Dataset and basic configuration: Based on the open Online University Learning Dataset (OULAD), we selected a variety of test scenarios containing 100 to 180 learning materials, and set the number of student sets and learning material sets to 30 and 150 to 180, respectively, covering a total of 20 knowledge points.

[0042] (2) Algorithm parameters: The initial population size is set to 30, and the maximum number of iterations is 500.

[0043] (3) Evaluation indicators: This embodiment mainly uses the two indicators of "Average Fitness Value (Avg)" and "Standard Deviation (Std)" to evaluate the overall optimization effect of the algorithm; at the same time, the quality of the generated personalized learning path is verified through path quality indicators such as "concept coverage", "difficulty advancement rate" and "difficulty matching rate".

[0044] As shown in Table 1, the MWO algorithm achieves the lowest average fitness values ​​for different numbers of learning materials (e.g., 100, 150, and 180). This indicates that, while satisfying various educational constraints (such as concept coverage, time limits, and learning style matching), the solutions generated by MWO can achieve superior ranking results. Furthermore, MWO's standard deviation is significantly lower than that of similar comparison algorithms. In particular, in the scenario with 150 learning materials, its standard deviation is only 18.02, significantly lower than that of other methods. This demonstrates the significant role of expert guidance and dynamic signal control in escaping local optima and maintaining convergence stability. Furthermore, as the number of learning materials increases (from 100 to 180), MWO not only maintains a low fitness value but also shows a slight improvement trend, further demonstrating its superiority in handling large-scale optimization problems.

[0045] Table 1 Accuracy of each algorithm under different material quantities ;

[0046] 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.

[0047] Table 2 Comparison of recommended learning material paths ;

[0048] As shown in Table 2, all algorithms achieved the required 100% concept coverage. However, in terms of material sequencing, MWO was able to rationally distribute key knowledge points, ensuring the continuity of subsequent learning. Furthermore, MWO achieved a high difficulty progression rate of 90.7%, with a perfect match between the difficulty levels and student abilities (100% match rate). This indicates that MWO outperformed the other compared algorithms in terms of smooth transitions between materials and layered connections. Existing methods such as WO, SOA, SCSO, and PEOA all exhibited some uneven connectivity.

[0049] Overall, the MWO algorithm, through its expert guidance, dynamic danger signal control, and multi-layered priority sorting mechanism, significantly mitigates the local optimality trap and convergence instability issues in the adaptive course sequencing problem, while also efficiently handling multi-objective constraints. Furthermore, MWO generates personalized course paths that ensure comprehensive concept coverage, smoothly progress in difficulty, and match student learning abilities, providing excellent technical and application support for intelligent teaching in the online education sector.

[0050] WO is a recently 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 prone to falling into local optimality and has insufficient convergence stability.

[0051] 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 in complex search spaces.

[0052] SCSO is inspired by swarm intelligence and achieves global search through group collaboration. However, under large-scale problems or multi-objective constraints, its stability and convergence effects are still difficult to meet the needs of personalized learning sequence recommendation.

[0053] PEOA focuses on optimization in the teaching field and realizes the sorting of knowledge points through simulated educational scenarios. It has certain effects in solving specific educational problems, but it has obvious disadvantages in algorithm efficiency and complex problem-solving capabilities.

[0054] Therefore, the present invention adopts the above-mentioned personalized learning path generation method based on the meta-heuristic algorithm. Through the overall optimization strategy, it not only improves the solution of local optimality and instability problems, but also realizes more efficient and accurate personalized learning path generation under multi-objective optimization, which has significant technical and application advantages.

[0055] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention rather than to limit the same. Although the present invention has been described in detail with reference to the preferred embodiments, those skilled in the art should understand that they can still modify or replace the technical solutions of the present invention with equivalents, and these modifications or equivalent replacements cannot cause the modified technical solutions to 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. The expert solution is then 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; 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: ; Among them, students Select Materials hour, ;otherwise, ; 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 2, 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, the candidate solutions in the population are updated through dynamic control and migration mechanisms, including reflecting the risk level of the current search through danger signals, expressed as: ； In the formula, As a danger signal, is a fixed constant offset, To adjust the parameters; When the danger signal exceeds the preset threshold When , the 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 candidate solutions in the population are updated through dynamic control and migration mechanisms, including balancing 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 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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