Error correction task optimization method based on adaptive crow search

Abstract

The application discloses an error correction task optimization method based on adaptive crow search, and comprises the following steps: constructing an adaptive function, initializing a search population, and obtaining an adaptive degree; introducing a memory forgetting mechanism, dynamically calculating a forgetting threshold according to the adaptive degree distribution of the current crow population, removing the crow individuals with the adaptive degree lower than the forgetting threshold, and obtaining a screened candidate task combination set; performing error factor and knowledge point neighborhood search on the screened candidate task combination set, updating the continuous positions in the neighborhood through a golden sine mode, and obtaining a candidate task combination set after neighborhood updating; applying an adaptive step and a perception probability control strategy, automatically adjusting the flight step and the neighborhood updating trigger probability with the iteration number, and obtaining an adaptively updated candidate task combination set; directional variation and feasible solution repair are performed to obtain a candidate optimal task combination set of the current iteration; and the optimal solution of the current population and the global optimal solution are cyclically iterated and updated.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of online education, in particular to a correction task optimization method based on adaptive crow search. BACKGROUND

[0002] In the online learning and examination training environment, there are two common pain points for students: first, the error types are concentrated and repeated, and many students will repeatedly make similar mistakes in multiple-choice question training, such as concept confusion, incomplete question review, or formula misuse. Although the system can identify the wrong questions, it is difficult to provide targeted correction strategies in the task recommendation level of problem solving. Second, the learning time is limited and scattered, and the students' disposable online learning time is usually only a few minutes every day, so the platform must push a group of tasks that can truly reduce the error rate within a short time.

[0003] Currently, the core problem is to automatically select a group of tasks that can most reduce the error rate of students, not exceed the time limit, and not repeat from hundreds of candidate micro-tasks, including explanations, examples, tests, and wrong questions, within the time budget and prerequisite constraints. This problem is essentially a high-dimensional, multi-constrained, and nonlinear combination optimization problem. Currently, the common algorithms for learning task recommendation and question pushing in online education mainly include greedy or simple heuristic methods, MAB algorithms (Multi-Armed Bandit), traditional recommendation algorithms, and knowledge tracking algorithms (such as BKT and DeepKT). Among them, the greedy or simple heuristic method is the most common approach, which ranks tasks according to time improvement or error rate reduction contribution, and then selects them from high to low. This method is easy to develop, but it ignores the relationship between tasks. Therefore, once there are prerequisites, time conflicts, or content repetition, the greedy algorithm may be biased, resulting in a combination that may exceed the time limit, be in the wrong order, or have repeated themes, which cannot guarantee the overall optimality. MAB algorithms and traditional recommendation algorithms mainly solve the problem of recommending tasks one by one, but in actual teaching, teachers or students generally want to complete a whole group of tasks within a fixed time period. MAB algorithm recommendation has no global planning ability and cannot see the total time, so it cannot balance the proportion of different task types such as explanation, practice, and test, which may result in learning a lot of fragmented content but not solving the main error problem. Finally, the knowledge tracking algorithm mainly predicts the change of students' mastery, which is a model layer judgment tool. The knowledge tracking algorithm itself cannot provide an executable task combination, nor can it find a group of tasks with the strongest error cause and the highest benefit within a given time budget.

[0004] Therefore, it is urgent to propose a correction task optimization method based on adaptive crow search that is simple, accurate, and reliable. SUMMARY

[0005] In view of the above problems, the purpose of the present application is to provide an adaptive crow search based error correction task optimization method, and the technical scheme adopted by the present application is as follows:

[0006] The intelligent error correction task optimization method based on adaptive crow search comprises the following steps:

[0007] A fitness function is constructed, and the expected error rate reduction benefit of the candidate task, the matching degree with the examination target, the time budget deviation, the cognitive load and the content redundancy are taken as evaluation dimensions;

[0008] A search population is initialized, and crow individuals are generated, and the fitness of any crow individual corresponding to the task combination is obtained; any crow individual comprises a continuous position vector and a memory state;

[0009] A memory forgetting mechanism is introduced, the forgetting threshold is dynamically calculated according to the distribution of the fitness of the current crow population, the crow individuals with a fitness lower than the forgetting threshold are removed, and a screened candidate task combination set is obtained;

[0010] Error factor and knowledge point neighborhood search are performed on the screened candidate task combination set, and the continuous positions in the neighborhood are updated through the golden sine method, and a neighborhood updated candidate task combination set is obtained;

[0011] An adaptive step and perception probability control strategy is applied to the neighborhood updated candidate task combination set, so that the flight step and the neighborhood update triggering probability are automatically adjusted with the iteration number, and an adaptively updated candidate task combination set is obtained;

[0012] Directional variation and feasible solution repair are performed on the adaptively updated candidate task combination set, and a candidate optimal task combination set of the current iteration is obtained;

[0013] The maximum iteration number or the iteration change amplitude threshold is preset, and the optimal solution of the current population and the global optimal solution are cyclically iterated and updated.

[0014] Compared with the prior art, the present application has the following beneficial effects:

[0015] By constructing a unified objective function, the present application quantitatively models the multi-dimensional factors such as the expected error rate reduction benefit of the candidate task, the matching degree with the examination target, the time budget deviation, the cognitive load and the content redundancy, and realizes the multi-objective integrated evaluation of the task combination. In addition, the present application introduces a “error factor-knowledge point neighborhood search mechanism”, and through semantic and knowledge graph dual-channel similarity calculation, the search space is limited to the task area related to the main error type of the student, and invalid disturbance is avoided.

[0016] The adaptive step length and perception probability control strategy is adopted to dynamically adjust the flight step length and the neighborhood update triggering probability of the candidate task combination set after neighborhood update according to the iteration number, so that the algorithm has a wide range of exploration ability in the early stage, and gradually narrows the search range and focuses on the high value area in the later stage. The strategy effectively avoids premature convergence and improves the ability to obtain the global optimal solution.

[0017] The application performs directional variation on the candidate task combination set updated adaptively, introduces an adaptive forgetting mechanism, dynamically removes historical low-yield memories, and concentrates computing resources in a high-quality solution space. At the same time, the trend determination variable automatically determines the direction of task increase and decrease, and performs directional variation combined with the cost performance index, improving the interpretability and rationality of the search direction, and significantly improving the combination quality.

[0018] The application introduces a feasibility repair mechanism to automatically handle constraint conflicts such as time overrun and missing pre-repair, ensures that the output task combination can be directly issued for execution, adapts to the actual deployment needs of the online teaching platform, and improves the practicality and landing ability of the system.

[0019] In summary, the application has the advantages of simple logic, accuracy and reliability, and has high practical value and promotion value in the field of online education technology. BRIEF DESCRIPTION OF DRAWINGS

[0020] In order to more clearly illustrate the technical solutions of the embodiments of the application, the following will briefly introduce the drawings needed in the embodiments. It should be understood that the following drawings only show some embodiments of the application, and therefore should not be regarded as limiting the scope of protection. Other related drawings can be obtained by those skilled in the art without creative labor.

[0021] Figure 1 The logic flowchart of the application. DETAILED DESCRIPTION

[0022] In order to make the purpose, technical scheme and advantages of the present application more clear, the following will further illustrate the application combined with the drawings and embodiments. The embodiments of the application include but are not limited to the following embodiments. Based on the embodiments in the present application, all other embodiments obtained by those skilled in the art without creative labor are within the scope of protection of the present application.

[0023] In this embodiment, the term "and / or" is only used to describe the association relationship of the associated objects, which means that there can be three kinds of relationships, for example, A and / or B, which can represent three cases of A alone, A and B together, and B alone.

[0024] The terms "first" and "second" and the like in the description and claims of the application are used for distinguishing between similar elements and not necessarily for describing a particular sequential or chronological order. For example, the first target object and the second target object are used for distinguishing between two different target objects and do not imply that the first target object is before the second target object in any way.

[0025] In the present application, the word "exemplary" or "for example" is used to illustrate, exemplify, or describe, not to prefer or advocate. Any embodiment or design scheme described as "exemplary" or "for example" in the present application should not be interpreted as more preferred or more advantageous than other embodiments or design schemes. In fact, the use of "exemplary" or "for example" is intended to present the relevant concept in a specific manner.

[0026] In the description of the embodiments of the present application, unless otherwise specified, "a plurality of" means two or more. For example, a plurality of processing units means two or more processing units; a plurality of systems means two or more systems.

[0027] As shown in Figure 1 The present embodiment provides an error correction task optimization method based on adaptive crow search, which adopts four core steps: first, a unified evaluation standard is established, and a single objective function is used to quantify several factors affecting task effectiveness, and the algorithm can consider the benefits and costs comprehensively, and no longer rely on manual trade-off. Second, three key improvements are made to the improved adaptive crow search algorithm according to the actual characteristics of the learning task of online education: (1) memory forgetting mechanism, the algorithm will automatically discard the historical task combination with low return in each iteration, making the search more focused and efficient; (2) error factor-knowledge point neighborhood search, the algorithm does not blindly jump in the entire task space, but "fine digging" in the knowledge point neighborhood related to the main error factor of the student, significantly improving the hit rate; (3) adaptive step and perception control, the search is more bold in the early stage (large step, wide exploration), and more fine in the later stage (small step, deep focus), balancing global exploration and local optimization. Third, the feasibility repair mechanism is added: if the task combination generated by the algorithm violates the time limit or the pre-repair sequence during the search process, it needs to be repaired, removing the overtime task, filling in the missing pre-repair content, etc., to ensure that the output result can be directly executed. Fourth, when the number of candidate tasks is particularly large, the tasks can be divided into several subspaces according to "error factor x knowledge point", each subspace evolves independently, and the final result is obtained through elite combination. This approach can greatly reduce the computational load, making the algorithm still stable and efficient in large-scale scenarios.

[0028] Specifically, the error correction task optimization method based on adaptive crow search includes the following steps:

[0029] The first step is to construct a fitness function, using the expected error rate reduction benefit of candidate tasks, the degree of matching with the exam objectives, the time budget deviation, cognitive load, and content redundancy as evaluation dimensions.

[0030] Here, the fitness function is expressed as: in, Represents the fitness function; This indicates the weight of the error rate reduction term, which controls the proportion of error correction benefits in the overall objective; This represents the total number of candidate tasks, i.e., the number of all currently available error correction tasks. An indicator that the i-th task is selected, with a value of 0 or 1; Indicates task The expected decrease in error rate, i.e., the expected decrease in the error rate after the task is completed; This indicates the weight of the target matching item, which is used to control the importance of the match between the task and the exam target; This indicates the weight of the time deviation penalty, which is used to control the degree of impact of the deviation between the total time and the time budget; This represents the weight of the cognitive load penalty term, which is used to control the impact of excessive task load on fitness. This represents the weight of the redundancy penalty term, which is used to control the intensity of the penalty for duplicate content; Indicates task Matching coefficient with exam objectives; degree of alignment between task and exam objectives; Indicates task The estimated time; This indicates the time budget for the current learning round; Indicates task Cognitive load coefficient; Indicates task Content redundancy measures the degree of overlap between the content and other selected tasks in terms of knowledge points or question types.

[0031] Here, by inputting a set of candidate error correction tasks To determine whether each task is selected for this round of learning, use a binary variable. Indicates that if a task is selected... ,but If no selection is made, then .

[0032] The second step is to use a group of individual crows to explore multiple task combinations simultaneously: assuming a total of... There are 10 individual crows, each representing a task combination, which is a vector z consisting of 0s and 1s. Each individual crow contains two core states: (1) individual position. (1) is a continuous vector used to generate the probability of each task being selected; (2) and memory state m, which stores the best combination of tasks encountered by the individual so far.

[0033] During initialization, assume there are a total of Individual crows, based on the number of candidate tasks Randomly generate a length of continuous vectors And use the sigmoid function to transform continuous vectors Mapping to the interval [0,1], we obtain the probability that the task for any individual crow is selected, expressed as:

[0034] ;

[0035] in, This represents the probability that the task corresponding to the i-th crow individual is selected; This represents the position vector of the i-th individual crow; This represents the slope parameter of the Sigmoid function.

[0036] A random number is generated using a uniform random sampling method. , ;when When the i-th crow is selected, set a flag indicating whether the task corresponding to the i-th crow has been selected. Otherwise, set a flag indicating whether the task corresponding to the i-th crow individual has been selected. An initial task combination vector z is formed using the tags indicating whether the task for each crow individual was selected. After generating the initial combination for all crow individuals, a fitness function is applied. Calculate its fitness and use it as the starting point for the search.

[0037] The third step involves introducing a memory forgetting mechanism: automatically clearing low-value memories during the evolutionary process to avoid repeated calculations near poor solutions. This requires calculating an adaptive forgetting threshold for each generation based on the fitness distribution of the population. If a solution's score in the memory bank falls below this threshold, it is removed from the memory bank. By concentrating computational resources on more promising regions, model convergence can be accelerated. Specifically:

[0038] The forgetting threshold is dynamically calculated based on the fitness distribution of the contemporary population, and its expression is: in, This represents the forgetting threshold of generation t; Let represent the minimum value of the fitness set in generation t; This represents the maximum value of the fitness set in generation t; This indicates the preset maximum number of iterations; e represents the base of the natural logarithm function.

[0039] When a crow's memory fitness At that time, remember this memory Remove from memory set.

[0040] Fourth, error cause-knowledge point neighborhood search: In each round of updates, the search no longer jumps around randomly, but is limited to the neighborhood of the main error cause—related knowledge points. The neighborhood similarity of each candidate task for the current globally optimal combination is calculated, and only tasks with similarity thresholds are allowed to be perturbed in this round. For those dimensions that are allowed to be perturbed, a directed, continuous position update is performed using the golden sine wave method, and then mapped to selection probabilities and binary selection.

[0041] Specifically, when performing a neighborhood search on the filtered set of candidate task combinations, the i-th candidate error correction task is calculated. Overall similarity Its expression is:

[0042] ;

[0043] ;

[0044] in, Represents the i-th candidate error correction task The comprehensive similarity is used to determine whether the task belongs to the "error cause-knowledge point neighborhood". It uses the dual-channel similarity of semantics and knowledge graph to define the neighborhood, and only allows tasks that are highly related to the current optimal solution and the main error cause clusters to participate in the update, thereby reducing invalid perturbation from the source. This represents the i-th candidate error correction task; This represents the weighting coefficient of the semantic similarity channels, controlling the proportion of semantic features in neighborhood determination, and its value range is... ; This represents the weighting coefficient for the similarity channels of the knowledge graph, controlling the proportion of knowledge structure features in neighborhood determination, and its value range is... ; This represents the set of tasks selected from the globally optimal task combination obtained in the t-th iteration, which serves as the reference set for the current neighborhood computation. Represents the i-th candidate error correction task The set of tasks selected from the globally optimal task combination obtained in the t-th iteration semantic similarity; This represents the main error cluster—a cluster of knowledge points—obtained through statistical analysis at the t-th iteration. Represents the i-th candidate error correction task The main error clusters obtained through statistical or analytical analysis at the t-th iteration—knowledge point clusters Knowledge graph similarity is calculated using knowledge point path distance or graph structure, and normalized to... ; This represents the neighborhood indicator variable for the i-th task in the t-th iteration; Indicates the neighborhood threshold; This indicates an indicator function that outputs 1 if the condition within the parentheses is true, and 0 otherwise.

[0045] Here, the neighborhood indicator variable for the i-th task in the t-th iteration is... Performed under control, if the following conditions are met If the search is updated according to the golden sine neighborhood, it will be updated; otherwise, it will remain in its original position. This strategy avoids wasting search energy in irrelevant areas and allows the search to perform targeted and detailed mining around the main error clusters, significantly reducing blindness and redundancy.

[0046] Here, the expression for the golden sine neighborhood update is: in, This represents the continuous position value of the crow individual in the (t+1)th generation in the i-th dimension, which is the input for this update; This represents the continuous position value of a crow individual in the t-th generation in the i-th dimension; Let represent the continuous position value of the currently globally optimal crow individual in the t-th generation in the i-th dimension; The angle factor represents the t-th generation golden sinusoidal perturbation, which is used to drive the periodic perturbation of position updates. It is generally obtained by random sampling in the interval (0, 2π). The amplitude factor represents the t-th generation golden sinusoidal perturbation, used to control the perturbation intensity along the globally optimal direction, and is generally obtained by random sampling in the interval (0, π).

[0047] Step 5, Adaptive Step Size and Perception Probability: In the early stages of the search, a larger step size is needed to broadly explore different task combinations in the task space. As convergence approaches, the step size automatically decreases and the perception probability increases, making the search more focused and stable. Two parameters that dynamically change with the number of iterations are introduced: flight step size and perception probability, used to control the exploration range and the triggering frequency of neighborhood updates, respectively. Specifically:

[0048] ;

[0049] ;

[0050] in, This represents the flight step size in generation t; Indicates the initial flight step size; Let represent the perceptual probability of the t-th generation; This represents the initial perception probability.

[0051] In the early stages of the search, the flight step size of generation t. The probability of perception is relatively large and in the t-th generation. Because the size is relatively small, individual crows primarily explore large areas to avoid getting trapped in local optima. As the number of iterations increases, the flight step size in generation t... The probability of perception gradually decreases in generation t. Gradually increasing the search range, it naturally transitions from "global search" to local refinement, achieving adaptive control of the search scope from broad to precise.

[0052] Step 6, Targeted Mutation and Feasible Solution Repair: Here, the sequence of trend determination → targeted mutation → constraint repair prevents the search from stopping at a local optimum or generating timed-out or missing prerequisite solutions. In this step, the second-order difference of the selected proportion is used to determine whether the current solution is increasing or decreasing with increasing selection. If it tends to increase with increasing selection and the total time approaches the upper limit, it is deleted from the task with the lowest cost-effectiveness; otherwise, it is added from the task with the highest cost-effectiveness. If the time or prerequisite constraints are still violated after mutation, feasibility repair is performed, deleting timed-out solutions and adding prerequisite solutions according to the rules to ensure that the result can be directly executed.

[0053] Specifically, it includes:

[0054] Defining "cost-effectiveness" and candidate pool:

[0055] The adaptively updated set of candidate task combinations is sorted according to the task's unit-time benefit, resulting in a bottom candidate pool and a top candidate pool. The bottom candidate pool is... The top candidate pool is: ;in, Let represent the adaptively updated set of candidate task combinations in the t-th iteration; This indicates taking the bottom of the sorted results. A proportional combination of candidate tasks; This means taking the top of the sorted results. A proportional combination of candidate tasks.

[0056] The bottom candidate pool To calculate the cost-effectiveness per unit time Sort in ascending order and take values ​​less than the preset bottom threshold. A partial combination; the top candidate pool To calculate the cost-effectiveness per unit time Sort in descending order and take values ​​greater than the preset top threshold. A partial combination; among which, The cost-effectiveness per unit time; The expression is:

[0057] ;

[0058] in, Represents the i-th candidate error correction task The expected decrease in error rate; Represents the i-th candidate error correction task The estimated time.

[0059] (62) Trend Determination and Selection Ratio: The second difference of the selection ratio is used to determine the trend of the search direction. The expression is as follows:

[0060] ;

[0061] ;

[0062] in, This represents the second-order trend of the selection ratio of candidate task combinations in generation t. It is used to determine the trend of the number of selected tasks in the current iteration. The positive or negative sign of the value reflects whether the selection ratio is accelerating, slowing down, or decreasing. This represents the percentage of tasks selected in generation t, i.e., the number of tasks marked as 1 in the candidate task combinations of that generation out of the total number of tasks. The proportion. This represents the percentage of tasks selected in the (t-1)th generation; A flag indicating whether the i-th task in generation t is selected; that is, if the task is selected... Otherwise, it is 0.

[0063] (621) When the selection ratio of the candidate task combination in generation t is a second-order trend quantity When ≥0 and the total duration of the t-th generation candidate task combination is close to the time budget limit, the following condition is met: Then select from the bottom candidate pool. Cost-effectiveness per unit time Select several tasks in ascending order to form a reduction set. It satisfies: .

[0064] (622) Otherwise, select from the top candidate pool Select several units of time benefit-cost ratio The highest task composition supplementary set It satisfies: .

[0065] In this embodiment, Represents the definite pruning set in generation t; Let represent the definitive supplementary set for generation t; This represents the total duration of the t-th candidate task combination; This indicates the time tolerance for determining when the value is close to the upper limit.

[0066] (63) Feasible solution repair includes:

[0067] (631) Time restoration: The total learning time of the selected task in the candidate task combination after targeted mutation in generation t. Then, for the selected task in the candidate task combination after targeted mutation, its cost-effectiveness per unit time is calculated. Sorted from smallest to largest, based on cost-effectiveness per unit of time. The identifier indicating whether the i-th task in generation t is selected, in ascending order. Set to 0 until the condition is met: .

[0068] (632) Pre-correction: The i-th candidate error correction task The corresponding prerequisite tasks are Its pre-edited image is defined as: ;

[0069] If there exists an i-th candidate error correction task in the candidate task combination after directional mutation in generation t... It has been selected, that is However, the i-th candidate error correction task Corresponding prerequisite tasks Not selected, satisfied but Then for the i-th candidate error correction task The missing parts are filled in, including:

[0070] Calculate the condition that satisfies the i-th candidate error correction task The set of the smallest prior closures required by the prior requirements Its expression is:

[0071] ;

[0072] The constraints are: ;

[0073] Where C represents a subset of candidate prerequisite tasks selected from the task set U; Indicates the priority task The estimated learning time.

[0074] Satisfying all i-th candidate error correction tasks From the set of prerequisites, select the set of tasks with the minimum total learning time as the minimum time prerequisite closure set. Start with the minimum duration closure set. Cost-effectiveness per unit time Tasks are added sequentially from largest to smallest, up to the i-th candidate error correction task. With the i-th candidate error correction task Corresponding prerequisite tasks Priorities must be met.

[0075] Step 7, Iteration and Termination:

[0076] The contemporary optimal solution update is performed in the t-th iteration, obtaining the task selection vector for the k-th crow individual in the t-th generation. And calculate its fitness, which is expressed as:

[0077] ;

[0078] in, Represents the fitness function;

[0079] Choosing the individual with the highest fitness score as the optimal solution for generation t, we have: in, Let represent the task selection vector corresponding to the crow individual with the highest fitness score in generation t; Let represent the fitness score of the crow individual that is the best solution in the current generation (t-th generation).

[0080] Global optimal solution update: Compare the current optimal solution of generation t with the current optimal solution of the previous generation to obtain the global optimal solution, which is:

[0081]

[0082] in, Represents the globally optimal task selection vector in generation t; This represents the fitness score corresponding to the global optimal solution in generation t; This represents the globally optimal task selection vector for the (t-1)th generation; This represents the fitness score corresponding to the global optimal solution in generation t-1.

[0083] In this embodiment, the convergence determination condition is: ;in, This represents the range of change in the global optimal score over two consecutive generations.

[0084] When continuous The convergence requirement is considered met when all iterations satisfy the following condition:

[0085] ;

[0086] in, Indicates the relative improvement threshold (e.g.) ); Indicates the absolute improvement threshold (e.g.) ).

[0087] When the number of iterations reaches its maximum value If the convergence requirement is met, then the current global optimal solution is output.

[0088] The above embodiments are merely preferred embodiments of the present invention and are not intended to limit the scope of protection of the present invention. Any changes made based on the design principles of the present invention, or any non-creative modifications made thereon, shall fall within the scope of protection of the present invention.

Claims

1. An optimization method for error correction tasks based on adaptive crow search, characterized in that, Includes the following steps: Construct a fitness function and use the expected error rate reduction benefit of candidate tasks, the degree of matching with the exam objectives, the time budget deviation, cognitive load, and content redundancy as evaluation dimensions. Initialize the search population and generate Given a set of crows, calculate the fitness of any crow for the corresponding task combination; each crow consists of a continuous position vector and a memory state. A memory forgetting mechanism is introduced. The forgetting threshold is dynamically calculated based on the fitness distribution of the contemporary crow population. Crow individuals with fitness below the forgetting threshold are removed to obtain a set of candidate task combinations after screening. Perform error cause and knowledge point neighborhood search on the filtered candidate task combination set, and update the continuous positions in the neighborhood using the golden sine method to obtain the candidate task combination set after neighborhood update. An adaptive step size and perception probability control strategy is applied to the candidate task combination set after the neighborhood update, so that the flight step size and the neighborhood update trigger probability are automatically adjusted with the number of iterations, and an adaptively updated candidate task combination set is obtained. The candidate task combination set that has been adaptively updated is subjected to targeted mutation and feasible solution repair to obtain the candidate optimal task combination set for the current iteration; The maximum number of iterations or the threshold for the magnitude of iteration change is preset, and the optimal solution of the current population and the global optimal solution are updated iteratively. The step of performing error cause and knowledge point neighborhood search on the filtered candidate task combination set includes: When performing a neighborhood search on the filtered set of candidate task combinations, the i-th candidate error correction task is calculated. Overall similarity Its expression is: ; ; Based on the i-th candidate error correction task Overall similarity Construct a neighborhood indicator variable, the expression of which is: in, This represents the i-th candidate error correction task; Represents the weighting coefficients for semantic similarity channels; This represents the weighting coefficient for the similarity channels in the knowledge graph; Let represent the set of tasks selected from the globally optimal task combination obtained in the t-th iteration; Represents the i-th candidate error correction task The set of tasks selected from the globally optimal task combination obtained in the t-th iteration semantic similarity; This represents the main error cluster—a cluster of knowledge points—obtained through statistical analysis at the t-th iteration. Represents the i-th candidate error correction task The main error clusters obtained through statistical analysis at the t-th iteration—knowledge point clusters The knowledge graph similarity is calculated by the path distance between knowledge points and normalized to [0,1]. This represents the neighborhood indicator variable for the i-th task in the t-th iteration; Indicates the neighborhood threshold; This indicates an indicator function.

2. The error correction task optimization method based on adaptive crow search according to claim 1, characterized in that, The expression for the fitness function is: ; ,in, Represents the fitness function; Indicates the weight of the error rate reduction term; This indicates the total number of candidate tasks; An indicator showing whether the i-th task is selected; Indicates task The expected decrease in error rate; Indicates the weight of the target match; Indicates the weight of the time deviation penalty term; This represents the weight of the cognitive load penalty term; Indicates the weight of the redundancy penalty term; Indicates task Matching coefficient with the exam objectives; Indicates task The estimated time; This indicates the time budget for the current learning round; Indicates task Cognitive load coefficient; Indicates task Content redundancy.

3. The error correction task optimization method based on adaptive crow search according to claim 2, characterized in that, Initialize the search population and generate Given a set of crows, calculate the fitness of any given crow for any given task combination, including: Assume there is a total Individual crows, based on the number of candidate tasks Randomly generate a length of continuous vectors And use the sigmoid function to transform continuous vectors Mapping to the interval [0,1], we obtain the probability that the task for any individual crow is selected, expressed as: ； in, This represents the probability that the task corresponding to the i-th crow individual is selected; This represents the position vector of the i-th individual crow; The slope parameter represents the sigmoid function; A random number is generated using a uniform random sampling method. , ;when When the i-th crow is selected, set a flag indicating whether the task corresponding to the i-th crow has been selected. Otherwise, set a flag indicating whether the task corresponding to the i-th crow individual has been selected. The initial task combination vector z is formed by using the flags indicating whether the task corresponding to each individual crow has been selected. The fitness of any crow individual for any task combination is obtained using a fitness function.

4. The error correction task optimization method based on adaptive crow search according to claim 2 or 3, characterized in that, The forgetting threshold is calculated based on the distribution dynamics of fitness in contemporary crow populations, and its expression is as follows: in, This represents the forgetting threshold of generation t; Let represent the minimum value of the fitness set in generation t; This represents the maximum value of the fitness set in generation t; This indicates the preset maximum number of iterations; e represents the base of the natural logarithm function.

5. The error correction task optimization method based on adaptive crow search according to claim 4, characterized in that, The position of the crow in generation t is updated using the golden sine neighborhood update method, and its expression is: in, This represents the continuous position value of the crow individual in the (t+1)th generation in the i-th dimension; This represents the continuous position value of a crow individual in the t-th generation in the i-th dimension; Let represent the continuous position value of the currently globally optimal crow individual in the t-th generation in the i-th dimension; This represents the angle factor of the t-th generation golden sinusoidal perturbation; This represents the amplitude factor of the t-th generation golden sinusoidal perturbation.

6. The error correction task optimization method based on adaptive crow search according to claim 5, characterized in that, The expression for the flight step size is: in, This represents the flight step size in generation t; Indicates the initial flight step size; The expression for the neighborhood update trigger probability is: ； in, Let represent the perceptual probability of the t-th generation; This represents the initial perception probability.

7. The error correction task optimization method based on adaptive crow search according to claim 6, characterized in that, The adaptively updated candidate task combination set is subjected to targeted mutation to obtain the targeted mutation candidate task combination, which includes: The adaptively updated set of candidate task combinations is sorted according to the unit time benefit of the task to obtain the bottom candidate pool and the top candidate pool. The bottom candidate pool is The top candidate pool is: ;in, Let represent the adaptively updated set of candidate task combinations in the t-th iteration; This indicates taking the bottom of the sorted results. A proportional combination of candidate tasks; This means taking the top of the sorted results. A proportional combination of candidate tasks; The bottom candidate pool To calculate the cost-effectiveness per unit time Sort in ascending order and take values ​​less than the preset bottom threshold. A partial combination; the top candidate pool To calculate the cost-effectiveness per unit time Sort in descending order and take values ​​greater than the preset top threshold. A partial combination; among which, The cost-effectiveness per unit time The expression is: ； in, Represents the i-th candidate error correction task The expected decrease in error rate; Represents the i-th candidate error correction task The estimated time; The second-order difference of the selected proportion is used to determine the trend of the search direction, and its expression is: ； ； in, This represents the second-order trend quantity indicating the selection proportion of candidate task combinations in generation t; This represents the percentage of tasks selected in generation t; This represents the percentage of tasks selected in the (t-1)th generation; A flag indicating whether the i-th task in generation t is selected; that is, if the task is selected... Otherwise, it is 0; The second-order trend of the selection ratio of candidate task combinations in generation t When ≥0 and the total duration of the t-th generation candidate task combination is close to the time budget limit, the following condition is met: From the bottom candidate pool Select several units of time benefit-cost ratio Minimum task composition reduction set It satisfies: ; Otherwise, select from the top candidate pool. Select several units of time benefit-cost ratio The highest task composition supplementary set It satisfies: ;in, Represents the definite pruning set in generation t; Let represent the definitive supplementary set for generation t; This represents the total duration of the t-th candidate task combination; This indicates the time tolerance for determining when the value is close to the upper limit.

8. The error correction task optimization method based on adaptive crow search according to claim 7, characterized in that, The feasible solution repair includes: Time Fixing: The total learning time of the selected task among the candidate task combinations after targeted mutation in generation t. Then, for the selected task in the candidate task combination after targeted mutation, its cost-effectiveness per unit time is calculated. Sorted from smallest to largest, based on cost-effectiveness per unit of time. The identifier indicating whether the i-th task in generation t is selected, in ascending order. Set to 0 until the condition is met: ; First, repair: the i-th candidate error correction task The corresponding prerequisite tasks are Its pre-edited image is defined as: If there exists an i-th candidate error correction task in the candidate task combination after targeted mutation in generation t; It has been selected, that is However, the i-th candidate error correction task Corresponding prerequisite tasks Not selected, satisfied but Then for the i-th candidate error correction task The missing parts are filled in during the repair process, including: Calculate the condition that satisfies the i-th candidate error correction task The set of the smallest prior closures required by the prior requirements Its expression is: ； The constraints are: ; Where C represents a subset of candidate prerequisite tasks selected from the task set U; Indicates the priority task The estimated learning time; Satisfying all i-th candidate error correction tasks From the set of prerequisites, select the set of tasks with the minimum total learning time as the minimum time prerequisite closure set. Start with the minimum duration closure set. Cost-effectiveness per unit time Tasks are added sequentially from largest to smallest, up to the i-th candidate error correction task. With the i-th candidate error correction task Corresponding prerequisite tasks Priorities must be met.

9. The error correction task optimization method based on adaptive crow search according to claim 8, characterized in that, A preset maximum number of iterations or a threshold for the magnitude of iteration change is used to iteratively update the current population's optimal solution and the global optimal solution, including: The contemporary optimal solution update is performed in the t-th iteration, obtaining the task selection vector for the k-th crow individual in the t-th generation. And calculate its fitness, which is expressed as: Choosing the individual with the highest fitness score as the optimal solution for generation t, we have: in, Let represent the task selection vector corresponding to the crow individual with the highest fitness score in generation t; Let represent the fitness score of the crow individual that is the best solution in the current generation (t-th generation). Global optimal solution update: Compare the current optimal solution of generation t with the current optimal solution of the previous generation to obtain the global optimal solution, which is: ;in, Represents the globally optimal task selection vector in generation t; This represents the fitness score corresponding to the global optimal solution in generation t; Represents the globally optimal task selection vector for the (t-1)th generation; This represents the fitness score corresponding to the global optimal solution in generation t-1.

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