Sprint learning path optimization method based on improved beluga whale optimization algorithm

Abstract

The application discloses a sprint learning path optimization method based on an improved beluga whale optimization algorithm, and solves the problem that existing sprint path planning is unreliable. The method comprises the following steps: constructing a total learning cost target function; adopting a random key coding algorithm based on chaotic mapping to represent a learning path in a sequence manner, and adopting serial scheduling to obtain a plurality of candidate sprint learning paths; introducing an adaptive weight mechanism, an examination-driven offset term and a Gaussian disturbance term, and adopting an improved beluga whale optimization algorithm to iteratively optimize the candidate sprint learning paths, so as to obtain a plurality of iteratively optimized sprint learning paths; in any iteration optimization, if the current candidate sprint learning path violates a prerequisite relationship in the learning path, or / and a time window, or / and a daily learning time length budget, then the current candidate sprint learning path is repaired for feasibility; the iteratively optimized sprint learning paths are subjected to neighborhood local search based on a forgetting risk index; and an optimal sprint learning path is output.

Description

Technical Field

[0001] This invention relates to the field of learning path optimization technology, and in particular to a sprint learning path optimization method based on an improved white whale optimization algorithm. Background Technology

[0002] In online teaching scenarios, besides regular instruction, a crucial element is the short-term "intensive study" before exams. This intensive study must be completed within a limited number of days and a strict daily schedule. The actual study plan not only needs to meet the constraints of the actual course schedule, regular mock exams, and the final official exam, but also needs to consider the prerequisite relationships of reviewed knowledge points, daily student study time, and student fatigue. If intensive study relies solely on a "practice makes perfect" approach, it often leads to short-term memory buildup, resulting in rapid forgetting and even a dislike for learning, ultimately leading to unsatisfactory exam results.

[0003] Currently, existing technologies, such as the "Artificial Intelligence English Learning Platform" (publication number CN108694867A), only mention modules for identifying and reinforcing learning gaps, without demonstrating how to optimize learning paths. Furthermore, existing solutions rarely consider review, quizzes, or breaks. Even in offline scenarios, they often rely on the teacher's experience, lacking unified optimization of learning time, time windows, and review effectiveness. This can easily lead to student fatigue or insufficient review, thus reducing the overall effectiveness of the intensive review phase. Moreover, current mainstream methods are based on the number of knowledge points covered or the algorithmic planning of knowledge difficulty matching, ignoring the individual forgetting patterns of students during the learning process. This results in students completing learning tasks according to the planned learning scheme, but due to insufficient memory retention, their actual performance is unsatisfactory.

[0004] Therefore, there is an urgent need to propose a sprint learning path optimization method based on the improved white whale optimization algorithm that can balance learning coverage and memory retention in a short time. Summary of the Invention

[0005] To address the aforementioned problems, the purpose of this invention is to provide a sprint learning path optimization method based on an improved beluga optimization algorithm. The technical solution adopted by this invention is as follows:

[0006] The sprint learning path optimization method based on the improved beluga optimization algorithm includes the following steps:

[0007] Construct the objective function for the total learning cost and obtain several learning paths;

[0008] A random key encoding algorithm based on chaotic mapping is used to represent the learning path in a sequential manner, and several candidate sprint learning paths are obtained by serial scheduling.

[0009] An improved white whale optimization algorithm is used to iteratively optimize the candidate sprint learning paths, resulting in several iteratively optimized sprint learning paths. The iterative optimization introduces an adaptive weight mechanism, an exam-driven offset term, and a Gaussian perturbation term.

[0010] In any iteration of optimization, if the current candidate sprint learning path violates the prerequisite relationships and / or time window and / or daily learning duration budget in the learning path, then the feasibility of the current candidate sprint learning path is repaired.

[0011] Based on the forgetting risk index, a neighborhood local search is performed on the iteratively optimized sprint learning path.

[0012] The iteration termination condition is preset; when the iteration optimization meets the iteration termination condition, the optimal sprint learning path is output.

[0013] Compared with the prior art, the present invention has the following beneficial effects:

[0014] This invention establishes a total learning cost objective function and introduces learning time, forgetting loss, feasibility penalty, reactivation node cost, and activity switching cost, thereby avoiding the problems of relying on experience-based insertion or handling them separately, and realizing a unified optimization framework.

[0015] This invention employs a random key encoding algorithm based on chaotic mapping to represent the learning path in a sequential manner, and uses serial scheduling to obtain several candidate sprint learning paths. It establishes a representation of "candidate solutions" through encoding, which facilitates the algorithm's search in the solution space. Through decoding and scheduling, the encoding results are restored to a specific learning schedule, thereby enabling direct evaluation of its learning cost.

[0016] This invention introduces an adaptive weighting mechanism, an exam-driven bias term, and a Gaussian perturbation term, and employs an improved White Whale Optimization algorithm to iteratively optimize candidate sprint learning paths. By introducing weights that gradually change with the iteration process, the early update phase focuses more on analyzing different path combinations, while the later phase leans towards refining existing solutions. Furthermore, a moderate perturbation (Gaussian perturbation term) is added during the update process to prevent all candidate solutions from prematurely concentrating on a single path. In this way, the entire algorithm can enter a "generation, decoding, repair, update" loop, continuously producing differentiated candidate paths and gradually converging to a reasonable sprint learning arrangement that conforms to practical constraints.

[0017] This invention combines inverse learning in chaotic initialization to improve population diversity and suppress premature convergence; it takes into account both feasibility repair and neighborhood search, which can significantly improve the feasible solution rate and the quality of later convergence, and solve the strong constraint characteristics of short-cycle sprint.

[0018] In summary, this invention has the advantages of simple logic and high accuracy and reliability, and has high practical and promotional value in the field of learning path optimization technology. Attached Figure Description

[0019] To more clearly illustrate the technical solutions of the embodiments of the present invention, the accompanying drawings used in the embodiments will be briefly introduced below. It should be understood that the following drawings only show some embodiments of the present invention and should not be regarded as a limitation on the scope of protection. For those skilled in the art, other related drawings can be obtained based on these drawings without creative effort.

[0020] Figure 1 This is a logic flowchart of the present invention. Detailed Implementation

[0021] To make the objectives, technical solutions, and advantages of this application clearer, the present invention will be further described below with reference to the accompanying drawings and embodiments. The embodiments of the present invention include, but are not limited to, the following embodiments. All other embodiments obtained by those skilled in the art based on the embodiments in this application without inventive effort are within the scope of protection of this application.

[0022] In this embodiment, the term "and / or" is merely a description of the relationship between related objects, indicating that there can be three relationships. For example, A and / or B can represent three situations: A exists alone, A and B exist simultaneously, and B exists alone.

[0023] The terms "first" and "second," etc., used in the specification and claims of this embodiment are used to distinguish different objects, not to describe a specific order of objects. For example, "first target object" and "second target object," etc., are used to distinguish different target objects, not to describe a specific order of target objects.

[0024] In the embodiments of this application, the terms "exemplary" or "for example" are used to indicate that something is an example, illustration, or description. Any embodiment or design that is described as "exemplary" or "for example" in the embodiments of this application should not be construed as being more preferred or advantageous than other embodiments or design. Specifically, the use of the terms "exemplary" or "for example" is intended to present the relevant concepts in a specific manner.

[0025] In the description of the embodiments in this application, unless otherwise stated, "multiple" means two or more. For example, multiple processing units means two or more processing units; multiple systems means two or more systems.

[0026] like Figure 1As shown, this embodiment provides a sprint learning path optimization method based on the improved beluga optimization algorithm, which includes the following steps:

[0027] The first step is to construct the total learning cost objective function and derive several learning paths. Here, the expression for the total learning cost objective function J(π) is: Where π represents the candidate sprint learning path, which is the sorting and scheduling result of each learning activity (including review, quizzes, rest and other recharge nodes) in the total set of activities U; U represents the total set of all learning activities. Indicates learning activities Indicator variables included in the current sprint learning path; Indicates learning activities The duration of study; This represents the weight of forgetting loss, which controls the importance of memory retention in the overall goal. It can be set based on the sensitivity of improving simulated test scores. For example, a 10% decrease in forgetting loss is equivalent to a 15-minute reduction in study time. It is generally set to 0.3–0.6. This represents the loss value of mastery of all knowledge points from the candidate sprint learning path π to the exam. This represents the feasibility penalty weight, which ensures that the generated learning path meets hard constraints such as prerequisites, time windows, and budget, and is fitted using historical scheduling data. If the feasibility rate of the plan is below 95%, it is appropriately increased, usually set to 0.8–1.0, the largest among the four weights, to ensure that executability takes priority. The feasibility penalty item represents the degree of violation of the core hard constraints of the candidate sprint learning path π, including prerequisites, time windows, and daily budgets. This represents the cost weight of the recovery node, which measures the balance between the "cost" and "benefit" of review, quizzes, or rest. It combines learning time statistics and teacher and student feedback, such as "each additional quiz increases learning time by 15 minutes", and is usually taken as 0.1–0.3. Represents a rechargeable node The equivalent cost; This represents the switching cost weight, which reflects the additional cognitive overhead of frequently switching between different subjects or activities, and is generally between 0.05 and 0.2. Indicates from learning activities To learning activities The time switching overhead, i.e., the minutes consumed; This represents a set of recharge nodes, including review sessions, quizzes, and rest periods. This represents the set of all adjacent activity pairs in the candidate sprint learning path π.

[0028] In this embodiment, The actual duration of all learning activities is the basic cost of path calculation. Forgetting loss measures the decline in knowledge mastery between learning and testing. As a feasibility penalty, it is used to constrain prerequisites, time windows, and daily learning budgets. The cost of the recovery node includes time expenditure for processes such as review, testing, and rest. This is a cost for activity switching, used to suppress excessive switching across subjects or modules.

[0029] In this embodiment, the mastery loss value of all knowledge points from the candidate sprint learning path π to the exam is... The expression is: ; ;in, Representing knowledge points During the exam The degree of mastery; This indicates that exam e refers to the knowledge points. The weights; Representing knowledge points The degree of mastery of t at the time of the exam; This indicates the rate of knowledge forgetting (refer to the Ebbinghaus forgetting curve, generally between 0.05 and 0.2). It is the most recent time when you studied or reviewed this knowledge point.

[0030] In this embodiment, the feasibility penalty item The expression is: ;in, This indicates a prior relationship penalty; Indicates time window penalty; This indicates a daily budget penalty.

[0031] Punishment for prior relationship repair The expression is: Where P represents the set of prior relations; Indicates the end time of activity i; This indicates the start time of activity j.

[0032] Time window penalty The expression is: ;in,[ , The allowed time window for activity u; , The actual start and end times of activity u.

[0033] Daily budget penalty The expression is: ,in, This represents the total actual study time on day d; This represents the time budget for day d.

[0034] The second step, encoding and decoding process: A random key encoding algorithm based on chaotic mapping is used to represent the learned path as a sequence, and serial scheduling is used to generate { , , The initial calculated total learning cost objective function J(π) is used as the baseline. Here, the learning path is represented sequentially: first, a weight value is generated for each learning activity; then, the order of these weight values ​​is determined to form a complete learning path. This allows for a unified structure to describe the learning tasks of different students, enabling the algorithm to compare, adjust, and optimize the path order, ultimately obtaining a learning arrangement that meets time constraints and prerequisite requirements. Specifically, during the initialization phase, several random key vectors are randomly generated, and after decoding using serial scheduling rules, several feasible learning paths are formed, each path corresponding to a candidate solution.

[0035] In this embodiment, the encoding (sequential representation) defines the random key vector. For random key vectors The activity sequence is obtained by sorting in ascending order. ;

[0036] Use serial scheduling for the active sequence We place each activity one by one to obtain candidate sprint learning paths π. Here, placement refers to scheduling the activity to the earliest feasible time while satisfying prerequisite and time window constraints. For each... When the prerequisite relationship and activity window are satisfied [ , Under the premise of not exceeding the daily budget Prioritize and select the earliest feasible start time. And record At this point, if a conflict arises, feasibility repairs will be carried out in the order of "1. Prioritize repairs, 2. Time window, 3. Budget." If placement is still not possible within the planned period, then... .

[0037] The third step, chaotic initialization, is used to generate the initial solution set for the algorithm. In sprint learning path optimization, in general population evolution optimization algorithms, if the initial solutions are too concentrated—for example, multiple candidate solutions differ only slightly in activity order or timing—the algorithm often has to repeatedly adjust between local solutions during the subsequent search process. This results in a lack of diversity in the learning path arrangement, making it difficult to find a better solution. Therefore, by using chaotic mapping to generate initial solutions, candidate solutions can be more evenly distributed within the feasible range, ensuring greater diversity among initial solutions. This increases the possibility of exploring multiple path combinations during subsequent optimization and obtaining a more reasonable learning arrangement.

[0038] Here, an initial value is selected within the interval [0,1]. The Bernoulli chaotic map is used to generate random sequences, and its expression is: in, Indicates the chaos control parameters; This represents the chaotic value generated in the t-th iteration; This represents the chaotic value generated in the (t+1)th iteration; This indicates the modulo operation.

[0039] The fourth step, reverse learning reinforcement: After the chaotic initialization in the previous step, the initial solution settling can be avoided. During the iterative process of sprint learning path optimization, as the search gradually converges, candidate solutions may converge, limiting the room for further improvement. This step constructs a reverse solution from the existing solutions and combines it with segment reversal operations to create structural differences while maintaining feasibility. This allows the search process to continuously generate new candidate paths, thus avoiding getting stuck on overly similar solutions.

[0040] Specifically, for learning activities The corresponding random key vector The expression for reverse learning enhancement is: in, Indicates learning activities The corresponding random key vector of the reverse candidate solution.

[0041] Step 5, Feasibility Repair (Optional): After decoding candidate learning paths, violations of time windows, prerequisite relationships, or daily learning time budgets may occur. Directly discarding these solutions will lead to a decrease in the proportion of feasible solutions and reduce optimization stability. This step uses a layered repair strategy to adjust the activity order or insert necessary nodes without disrupting the overall structure, thereby improving the feasible solution rate and ensuring that the generated learning paths can be executed in real-world scenarios.

[0042] For example: (1) Prerequisite relationship: When a learning activity violates the prerequisite relationship, such as activity j being scheduled before activity i, but activity i is a prerequisite for activity j, the order of activities should be adjusted, either by bringing the prerequisite activity forward or postponing the subsequent activity, until the prerequisite constraint is met.

[0043] (2) Time window repair: If the end time of an activity > or start time < If the position is not feasible, it will be adjusted to the nearest feasible position on the same day; if no feasible position is available on the same day, it will be moved across days.

[0044] (3) Budget Adjustment: When the total study time on a certain day exceeds the daily budget. If so, the excess activities will be postponed to the next feasible day.

[0045] (4) Reactivation: When the continuous learning duration exceeds the threshold gather Insert a short-term recharge node or force a rest activity to alleviate fatigue and improve learning retention.

[0046] Step 6: The improved White Whale Optimization Algorithm is used to iteratively optimize the candidate sprint learning paths, resulting in several iteratively optimized sprint learning paths. The iterative optimization incorporates an adaptive weighting mechanism, an exam-driven offset term, and a Gaussian perturbation term. In this embodiment, after iterative updates using the improved White Whale Optimization Algorithm, each candidate learning path in the population is updated once, thus obtaining the same number of iteratively optimized learning paths after each iteration.

[0047] In the iterative process of sprint learning path optimization, candidate learning paths already possess basic representations, diverse initial distributions, differential iterative preservation mechanisms, and feasibility repair guarantees. The task of this step is to drive the population to continuously update during the iteration process, thereby gradually improving the candidate solutions. This step introduces weights that gradually change with the iteration process, allowing the early update phase to focus more on analyzing different path combinations, while the later phase focuses more on refining existing solutions. Furthermore, appropriate perturbations are added during the update process to prevent all candidate solutions from prematurely concentrating on a single path. This allows the entire algorithm to enter a "generation, decoding, repair, update" loop, continuously producing differentiated candidate paths and gradually converging to a reasonable sprint learning arrangement that conforms to practical constraints. Specifically: the preset population size for the sprint learning paths is... And the maximum number of iterations is ;

[0048] Adaptive weight updates using a linear decreasing method are expressed as follows: in, Represents the adaptive weights of generation t; This represents the initial adaptive weights; This represents the minimum value of the adaptive weights. Here, , As the number of iterations gradually decreases, the early stages tend to favor global search, while the later stages focus more on local convergence.

[0049] In continuous random key vectors In the learning space, the improved white whale optimization algorithm is used to update the candidate sprint learning paths, and its expression is: in, Represents the random key vector of the (t+1)th generation individual; Represents the random key vector of an individual in the t-th generation; This indicates that the beluga whale is updating its operator; Let represent the globally optimal individual in generation t; Represents the exam-driven weights, typically taking... ; Indicates exam-driven items; Represents the set of exams; Indicates the amplitude of the Gaussian perturbation; This represents a Gaussian noise vector with zero mean and covariance equal to an identity matrix.

[0050] Step 7 involves performing a neighborhood local search on the iteratively optimized sprint learning path based on the forgetting risk index. After step 6, while the overall quality of candidate solutions is high, local arrangements may still contain redundancy or inappropriateness. This step refines the elite individuals through a specialized fine-tuning strategy targeting regenerating nodes, further reducing learning costs and improving the rationality of path execution.

[0051] Here, the risk indicator of forgetting The expression is: in, Indicates from learning activities Completion Time Until the next time with knowledge points Effective intervals between relevant consolidation moments; Indicates learning activities The completion time; Indicates the time of exam e; This indicates that exam e refers to the knowledge points. The weights; Indicates learning activities Knowledge points Review weights; This indicates that the learning activities will be followed closely within the current learning path. Then and related to knowledge points The start time of the next related learning activity; Indicates knowledge points The rate of forgetting; It is a set of knowledge points, and the knowledge points Belongs to a collection of knowledge points .

[0052] Here, reactivation is fine-tuned based on proximity, and a forgetting risk index is calculated for each activity. For example: the longer the interval between learning and exams, the higher the risk; the adjustment strategy is as follows: if activities The risk of forgetting exceeds the threshold Then try in Inserting or moving reactivation nodes forward or backward Ensure its duration does not exceed the duration of the reactivation node r. And it does not violate budget constraints; the assessment is updated, the cost function is recalculated, including the decrease in forgetting loss and the increase in rehabilitation costs. If the overall cost is reduced, the adjustment is retained; otherwise, it is revoked.

[0053] Improved retention mechanism: For each locally adjusted path, calculate the total learning cost objective function J(π). If the total learning cost of the locally adjusted path is greater than the total learning cost of the path before adjustment, then retain the path before adjustment; otherwise, use the adjusted path.

[0054] Step 8: Preset the iteration termination condition; when the iteration optimization meets the iteration termination condition, output the optimal sprint learning path.

[0055] Termination condition: If the total learning cost objective function is continuous (Maximum number of generations allowed for continuous stagnation) The rate of decline within each generation is less than the improvement threshold. For example, if the actual learning cost is 1% (since fluctuations in performance during the practice phase are less significant than 1%, hence the 1% threshold), the solution is considered stable, and the process terminates early. For system safety, a maximum iteration limit is also set for the project, defining the maximum allowed number of iterations. The value can be determined by system runtime or hardware conditions. For example, 100 or 200 iterations are common engineering settings. When the number of iterations reaches... When this happens, the iteration is forcibly stopped to prevent excessive consumption of computing resources.

[0056] Output: Output J(π) optimal activity sequence And its optimal scheduling, giving the corresponding set of start and end times. It then outputs a learning path description, including daily learning, review, quizzes, and rest schedules, which can be directly used in the teaching plan for the sprint stage.

[0057] 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. A sprint learning path optimization method based on an improved beluga optimization algorithm, characterized in that, Includes the following steps: Construct the objective function for the total learning cost and obtain several learning paths; The expression for the total learning cost objective function J(π) is: ;in, This represents the candidate sprint learning path; U represents the set of all learning activities. Indicates learning activities Indicator variables included in the current sprint learning path; Indicates learning activities The duration of study; Indicates the weight of the forgetting loss; This represents the loss value of mastery of all knowledge points from the candidate sprint learning path π to the exam. Indicates the feasibility penalty weight; Indicates a feasible penalty item; Indicates the cost weight of the reactivation node; Represents a rechargeable node The equivalent cost; Indicates the switching cost weight; Indicates from learning activities To learning activities Time switching overhead; Represents the set of reactivated nodes; This represents the set of all adjacent activity pairs in the candidate sprint learning path π; A random key encoding algorithm based on chaotic mapping is used to represent the learning path in a sequential manner, and several candidate sprint learning paths are obtained by serial scheduling. An improved white whale optimization algorithm is used to iteratively optimize the candidate sprint learning paths, resulting in several iteratively optimized sprint learning paths. The iterative optimization introduces an adaptive weight mechanism, an exam-driven offset term, and a Gaussian perturbation term. In any iteration of optimization, if the current candidate sprint learning path violates the prerequisite relationships and / or time window and / or daily learning duration budget in the learning path, then the feasibility of the current candidate sprint learning path is repaired. Based on the forgetting risk index, a neighborhood local search is performed on the iteratively optimized sprint learning path. The iteration termination condition is preset; when the iteration optimization meets the iteration termination condition, the optimal sprint learning path is output.

2. The sprint learning path optimization method based on the improved beluga optimization algorithm according to claim 1, characterized in that, A random key encoding algorithm based on chaotic mapping is used to represent the learning path as a sequence, and several candidate sprint learning paths are obtained by serial scheduling, including the following steps: Define a random key vector For random key vectors The activity sequence is obtained by sorting in ascending order. ; Use serial scheduling for the active sequence By placing them one by one, we obtain candidate sprint learning paths π.

3. The sprint learning path optimization method based on the improved beluga optimization algorithm according to claim 2, characterized in that, The random key encoding algorithm based on chaotic mapping includes the following steps: Select an initial value within the interval [0, 1]. The Bernoulli chaotic map is used to generate random sequences, and its expression is: ;in, Indicates the chaos control parameters; This represents the chaotic value generated in the t-th iteration; This represents the chaotic value generated in the (t+1)th iteration; This indicates the modulo operation.

4. The sprint learning path optimization method based on the improved beluga optimization algorithm according to claim 3, characterized in that, It also includes: learning activities The corresponding random key vector The expression for reverse learning enhancement is: in, Indicates learning activities The corresponding random key vector of the reverse candidate solution.

5. The sprint learning path optimization method based on the improved beluga optimization algorithm according to claim 3 or 4, characterized in that, An improved white whale optimization algorithm is used to iteratively optimize candidate sprint learning paths, resulting in several iteratively optimized sprint learning paths, including the following steps: The population size for the preset sprint learning path is And the maximum number of iterations is ; Adaptive weight updates using a linear decreasing method are expressed as follows: ;in, Represents the adaptive weights of generation t; This represents the initial adaptive weights; This represents the minimum value of the adaptive weights; In continuous random key vectors In the learning space, the improved white whale optimization algorithm is used to update the candidate sprint learning paths, and its expression is: ;in, Represents the random key vector of the (t+1)th generation individual; Represents the random key vector of an individual in the t-th generation; This indicates that the beluga whale is updating its operator; Let represent the globally optimal individual in generation t; Indicates the exam-driven weights; Indicates exam-driven items; Represents the set of exams; Indicates the amplitude of the Gaussian perturbation; This represents a Gaussian noise vector with zero mean and covariance equal to an identity matrix.

6. The sprint learning path optimization method based on the improved beluga optimization algorithm according to claim 5, characterized in that, The forgetting risk indicator The expression is: ; ;in, Indicates from learning activities Completion Time Until the next time with knowledge points Effective intervals between relevant consolidation moments; Indicates learning activities The completion time; Indicates the time of exam e; This indicates that exam e refers to the knowledge points. The weights; Indicates learning activities Knowledge points Review weights; This indicates that the learning activities will be followed closely within the current learning path. Then and related to knowledge points The start time of the next related learning activity; Indicates knowledge points The rate of forgetting; This represents a set of knowledge points.

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