Improved crayfish optimization algorithm-based three-expert collaborative scheduling method and system
By improving the crayfish optimization algorithm, a multi-objective optimization objective function and a two-layer coding were constructed, which solved the robustness problem of the three-teacher collaborative scheduling system in the senior year of high school. A stable and reliable three-teacher resource scheduling scheme was generated, which can adapt to the countdown to the college entrance examination and changes in students' learning conditions, and reduce manual adjustments.
Patent Information
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- SICHUAN QIMINGDAREN TECH CO LTD
- Filing Date
- 2026-03-09
- Publication Date
- 2026-07-10
AI Technical Summary
Existing technologies lack robustness in the three-teacher collaborative scheduling system during the senior year of high school, cannot effectively handle uncertain events, and fail to reasonably allocate teacher resources and the intervention of AI learning partners, resulting in unstable scheduling schemes and frequent manual adjustments.
An improved crayfish optimization algorithm (ICOA-S) is adopted. By constructing a multi-objective optimization objective function and a two-layer encoding method, combined with a robust correction term, the collaborative scheduling strategy of three teachers is optimized, generating an executable scheduling matrix that can cope with uncertain events.
Driven by the countdown to the college entrance examination and the changing trends in student learning, the system enables the efficient and rational allocation of resources from the three types of teachers, generating stable and reliable scheduling plans, reducing manual intervention, and improving the scheduling's resilience to disruptions and the continuity of teaching.
Smart Images
Figure CN122366902A_ABST
Abstract
Description
Technical Field
[0001] This invention relates to the field of educational learning technology during the sprint stage, and in particular to a three-teacher collaborative scheduling method and system based on an improved crayfish optimization algorithm. Background Technology
[0002] Currently, in high schools, especially during the final year of high school, schools generally introduce a three-teacher collaborative teaching service model: subject teachers, homeroom teachers (or moral education teachers), and AI learning companions. Subject teachers are responsible for answering questions about key and difficult points, providing in-depth topic analysis, and conducting group lectures; homeroom teachers and moral education teachers are responsible for tracking learning progress, providing psychological support, and facilitating communication between home and school; and AI learning companions (teaching agents based on large models) are responsible for explaining test questions, knowledge points, grading homework, and data analysis.
[0003] In practice, schools face numerous fragmented time slots and intervention tasks daily and weekly. Students with different risk levels require different frequencies and types of interventions. Teachers and homeroom teachers have limited time, needing to ensure lesson preparation and rest. While AI learning companions theoretically have sufficient computing power, the intervention ratio needs to be controlled based on product strategy and student acceptance. Schools have a crucial timeline for the final year of high school: the closer to the major exam, the more explicit the adjustments need to be made to the intervention pace and the allocation of resources among the three types of teachers. Therefore, how to rationally allocate the three types of teacher resources and intervention tasks to each time slot within a given time window becomes a complex collaborative scheduling problem, rather than simply a matter of "scheduling a timetable."
[0004] Currently, existing scheduling systems and algorithms only consider class time and classroom resources, or occasionally teachers' free time. They rarely incorporate student learning risks, intensive study strategies, and the degree of AI resource intervention into the same scheduling model. Furthermore, existing technologies ignore uncertainty and lack robustness; teachers taking leave unexpectedly, students being absent unexpectedly, and school events such as grade-level assemblies or physical examinations can all disrupt scheduling. Existing systems mostly rely on manual emergency adjustments, lacking robust scheduling methods that have a certain tolerance for uncertain events.
[0005] Therefore, there is an urgent need to propose a simple, accurate, and reliable three-teacher collaborative scheduling method and system based on an improved crayfish optimization algorithm. Summary of the Invention
[0006] To address the aforementioned problems, the purpose of this invention is to provide a collaborative scheduling method and system for three teachers based on an improved crayfish optimization algorithm. The technical solution adopted by this invention is as follows: The first part of this technology provides a collaborative scheduling method for three teachers based on an improved crayfish optimization algorithm, which includes the following steps: Step S1: Construct a multi-objective optimization objective function and impose scheduling feasibility constraints; Step S2: Obtain the basic data required for scheduling, and initialize the population using a two-layer encoding method based on the improved crayfish optimization algorithm to obtain the initial generation population; Step S3: Decode any individual in the current generation of the population and convert the double-layer encoded vector into a scheduling matrix; Step S4: Calculate the comprehensive objective value of the decoded scheduling matrix using the multi-objective optimization objective function, and combine it with the robust correction term to obtain the corresponding fitness value, forming the fitness sequence of the current generation of the population; Step S5: Based on the fitness sequence, update and determine the optimal individual of the current generation from the current generation population; Step S6: Based on the improved crayfish optimization algorithm, update the position of any individual in the current generation population to generate the next generation population; Step S7: Determine whether the preset termination condition has been met. The termination condition includes reaching the maximum number of iterations or the change in fitness of the population over multiple consecutive generations being less than a preset threshold. If the termination condition is met, output the scheduling matrix corresponding to the best individual in the current generation and use it as the final scheduling result. Otherwise, take the next generation population as the new current generation population and return to step S3 to continue iterating.
[0007] The second part of this technology provides a system employing a three-teacher collaborative scheduling method based on an improved crayfish optimization algorithm, which includes: The objective function construction module constructs a multi-objective optimization objective function and applies scheduling feasibility constraints. The data access and preprocessing module obtains the basic data required for scheduling, and uses a two-layer encoding method based on the improved crayfish optimization algorithm to initialize the population and obtain the initial generation population. The decoding module, connected to the data access and preprocessing module, decodes any individual in the current generation of the population, converting the two-layer encoded vector into a scheduling matrix. The fitness calculation module is connected to the objective function construction module and the decoding module. It uses the multi-objective optimization objective function to calculate the comprehensive objective value of the decoding scheduling matrix, and combines it with the robust correction term to obtain the corresponding fitness value, forming the fitness sequence of the current generation of the population. The optimal solution module is connected to the fitness solution module. Based on the fitness sequence, it updates and determines the optimal individual of the current generation from the current generation population. The position update module, connected to the optimal solution module, uses an improved crayfish optimization algorithm to update the position of any individual in the current generation of the population and generate the next generation of the population. The iteration determination module, connected to the position update module and the data access and preprocessing module, determines whether a preset termination condition has been met. The termination condition includes reaching the maximum number of iterations or the change in fitness of the population over multiple consecutive generations being less than a preset threshold. If the termination condition is met, the scheduling matrix corresponding to the best individual in the current generation is output and used as the final scheduling result. Otherwise, the next generation population is used as the new current generation population, and the iteration continues.
[0008] Compared with the prior art, the present invention has the following beneficial effects: (1) This invention defines all the constraints of tasks, teachers, AI learning partners, students and time slots as mathematical models, and drives the weight switching through the countdown to the college entrance examination and the trend of changes in learning situation, so as to ensure that the scheduling strategy is consistent with the actual teaching rhythm of the senior year.
[0009] (2) This invention uses the improved crayfish optimization algorithm (ICOA-S) as the solver, which merges the overall strategy parameters of the three-teacher collaboration in this cycle with the specific executable scheduling matrix into the same candidate solution vector, achieving one-time overall optimization, rather than the fragmented process of determining the strategy first and then scheduling separately. This invention uses the improved crayfish optimization algorithm (ICOA-S) to efficiently search for the minimum value of the comprehensive objective function within the feasible region. This invention adopts integrated optimization of strategy and scheduling, reducing manual intervention. The double-layer coding allows the overall collaboration strategy and the specific scheduling table to be optimized simultaneously, avoiding the fragmentation of determining the strategy first and then scheduling, and greatly reducing repeated manual debugging.
[0010] (3) The present invention decodes the initial population, which contains all the information of the strategy layer and the scheduling layer, and converts it into an executable three-teacher scheduling matrix. The comprehensive score of the scheme is calculated according to the core total objective function and used to guide the next round of search.
[0011] (4) The present invention uses an improved crayfish optimization algorithm to update the position of the optimal solution in the current iteration. By combining the inertia term, the global optimal guiding term and the empirical prior guiding term, each candidate scheduling scheme can move steadily and controllably towards a better direction. The search strategy is automatically adjusted according to the learning situation and risk, thereby ensuring that the final generated scheduling scheme is both feasible.
[0012] (5) The present invention adopts a robust scenario sampling mechanism to calculate the expected default cost of each candidate scheme in multiple possible scenarios, so that the algorithm prioritizes those schemes that do not need to be significantly adjusted even if unexpected situations occur, thereby improving the anti-disturbance ability of the scheduling, reducing the maintenance burden of front-line teachers and academic affairs staff, and making the output scheduling scheme have continuous stability and engineering implementation.
[0013] 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 education and learning technology during the sprint stage. Attached Figure Description
[0014] 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.
[0015] Figure 1 This is a logic flowchart of the present invention. Detailed Implementation
[0016] 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.
[0017] like Figure 1 As shown, this embodiment provides a three-teacher collaborative scheduling method based on an improved crayfish optimization algorithm. It strictly models the three-teacher collaborative scheduling as a constrained multi-objective optimization problem, clearly defining the student set, teachers and AI resources, time slots, intervention tasks, scheduling decision variables and all feasibility constraints, and constructs a comprehensive objective function that simultaneously considers intervention coverage for high-risk students, teacher load balancing, resource fairness and execution robustness.
[0018] In this embodiment, the improved crayfish optimization algorithm (ICOA-S) is used as the solver. The overall collaborative strategy parameters and the specific scheduling matrix are uniformly encoded using a two-layer encoding method of strategy layer + scheduling layer. By using mechanisms such as chaotic initialization, empirical prior vector, adaptive weight, and dynamic stage adjustment, the search process is guided to be more in line with the real teaching rules.
[0019] Specifically, this three-teacher collaborative scheduling method based on an improved crayfish optimization algorithm includes the following steps: The first step is data preparation and parameter initialization, which involves obtaining the basic data required for scheduling. This basic data includes the student set. The collection of all executable entities All time slots set All task sets ,Task Risk weight of the corresponding student Teacher's available time The i-th student The maximum acceptable number of interventions or total duration within this period. Countdown to the College Entrance Examination Population size and maximum number of iterations .
[0020] (11) Student assembly The expression is: ;in, This indicates the total number of students.
[0021] (12) The collection of all executors The expression is: ;in, Represents a set of subject teachers; This indicates that the homeroom teacher and moral education teacher have gathered. This refers to an intelligent teaching system, specifically a set of AI learning companion execution agents.
[0022] (13) All time slots The expression is: ;in, This indicates the total number of time slots, which includes evening self-study sessions, self-study class sessions, and available time slots on weekends.
[0023] (14) All task sets The expression is: Each task is defined as a triple. ;in, Indicates task The corresponding students; Indicates task Types include, for example, homeroom teacher talks, subject-specific Q&A, and AI-assisted Q&A; Indicates task Discipline to which you belong.
[0024] (15) Scheduling decision variables, the expression of which is: .
[0025] The second step is to construct the scheduling feasibility constraints and the multi-objective optimization objective function: Here, feasibility constraints are imposed on scheduling to avoid unreasonable situations such as conflicts, overload, or overlapping student time slots. These scheduling feasibility constraints include: constraints on the number of times tasks can be assigned, the number of tasks that can be executed in the same time slot, the number of tasks that can be assigned to students in the same time slot, the available time of the executor, and the upper limit of intervention that students can tolerate.
[0026] (21) The expression for the task scheduling frequency constraint is: ; Here, the task scheduling frequency constraint ensures that an intervention task will only be scheduled in one time slot of one executor, avoiding duplicate scheduling. This constraint guarantees that tasks will not be repeatedly assigned, while also preventing unrealistic scheduling structures from arising during the search process, maintaining clear and executable scheduling logic. Indicates task Is the execution body in time slot b? Execution is enabled; if executed, the value is 1, otherwise it is 0. When the execution body... When working as a subject teacher, equal .
[0027] (22) The expression for the constraint on the number of tasks executed in the same time slot is: ; The constraint on the number of tasks executed in the same time slot ensures that teachers or AI learning partners can only execute one task at a time, avoiding conflicts and overload. This ensures that teacher scheduling does not conflict, AI learning partner tasks do not stack, and that each executor in the scheduling matrix maintains a single-task state in any time slot, allowing for conflict-free deployment.
[0028] (23) The expression for the upper limit constraint on student intervention tolerance is: ; The constraint on the number of tasks assigned to students in the same time slot is to ensure that a single student does not have multiple conflicting tasks assigned to them within the same time slot. This represents the set of time slots that are allowed to schedule tasks within the current period; Represents the i-th student The maximum number of interventions or total duration that is acceptable within this period is the maximum number of interventions or total duration preset according to the teaching management rules.
[0029] (24) The expression for the available time constraint of the executor is: ; Among these measures, the available time constraint for the executor ensures that the workload of each teacher or AI learning partner does not exceed their capacity throughout the entire scheduling cycle. This avoids unreasonable scheduling situations such as excessive overtime for teachers, overload for moral education teachers, and abnormal load on AI agents, providing a fundamental guarantee for the health of the scheduling plan. Indicates the execution body The total available time is the actual data of the project.
[0030] (25) The expression for the constraint on the number of tasks assigned to students in the same time slot is: ; This ensures that no single student will have multiple conflicting intervention tasks in the same time slot. This prevents students from having two different interventions scheduled simultaneously, such as Q&A and conversation, aligning with school management practices and ensuring the effectiveness of the scheduling logic.
[0031] Based on the above scheduling task elements and scheduling feasibility constraints, decision variables are given. The range of values and feasible solution space of are defined. Here, a multi-objective function is constructed to evaluate the merits of scheduling schemes, focusing on the same decision variable. Objectives are given from three aspects: intervention coverage for high-risk students, teacher workload balance, and resource equity among students, and then synthesized through dynamic weights. The expression for the multi-objective optimization objective function is as follows: in, Indicates the weight of the intervention coverage target for high-risk students; The weights representing the teacher workload balancing objectives; Indicates the weight of the goal of resource equity among students; This represents the objective function for intervention coverage of high-risk students; Represent the objective function for balancing teacher workload; The objective function for resource equity among students is defined as follows: The high-risk student intervention coverage objective function represents the degree to which the scheduling scheme covers intervention tasks for high-risk students. This is obtained by weighted summation of all task risk weights and scheduling decision variables. Risk weights are calculated by the learning analysis system based on indicators such as student performance change rate, homework completion, and knowledge mastery. The teacher workload balance objective function represents the degree of balance in the allocation of teacher workload in the scheduling scheme. This is calculated by comparing the deviation between each teacher's actual workload and their available upper limit. The student resource equity objective function represents the degree of balance in the intervention resources received by different students within the scheduling cycle. This is obtained by statistically analyzing the total intervention time received by students and calculating its standard deviation.
[0032] Here, the intervention coverage target for high-risk students is to ensure that high-risk students are given priority in effective interventions during class scheduling, thereby improving the overall effectiveness of teaching interventions. Its expression is: in, This represents the objective function for intervention coverage of high-risk students; Indicates task The corresponding risk weight for the student; Indicates task Whether the scheduling decision is executed by subject teacher j in time slot b is a binary variable. If it is executed, the value is 1; otherwise, the value is 0.
[0033] In addition, the objective function for balancing teacher workload The expression is: ; To avoid overburdening some teachers and ensure a more even distribution of workload between homeroom teachers and subject teachers, this implementation uses the squared difference to measure the degree of workload deviation; the more even the workload distribution, the smaller this term. This indicates the actual workload of subject teacher j during scheduling; This represents the maximum available workload for subject teacher j, which is preset by the school's scheduling system. This represents the average workload rate of all subject teachers. This indicates the actual workload of the homeroom teacher (h) in scheduling; This indicates the maximum available workload for class teacher h; This represents the average workload rate of all homeroom teachers.
[0034] Here, the expression for the average workload rate of all subject teachers is: ;in, This indicates the number of subject teachers. The average workload rate of all subject teachers is used to measure the overall workload level of subject teachers.
[0035] Finally, the objective function for resource equity among students. The expression is: ; Here, it is ensured that, while prioritizing high-risk students, the intervention time received by all students does not exhibit extreme disparities. This embodiment uses standard deviation to reflect the fairness of resource allocation, preventing situations where high-risk students receive resources while other students are completely ignored, thus ensuring reasonable resource allocation and educational equity. This indicates the total number of students; This represents the total intervention time received by student s in this cycle, that is, the cumulative time or class hours of all intervention tasks received by the student in the current scheduling cycle; This represents the average intervention duration for all students.
[0036] This embodiment uses the countdown to the college entrance examination and the trend of changes in student learning to drive weight switching, ensuring that the scheduling strategy is consistent with the actual teaching pace of senior high school students. In the time dimension, it is based on the number of days remaining until the college entrance examination. The scheduling strategy is divided into three phases: early, middle, and late. Based on this, this embodiment introduces educational logic-driven phase switching conditions, so that phase switching depends not only on the countdown but also on the changing trends of student learning data, including factors such as the slope of changes in overall student risk, the rate of change in teacher workload, and the rate of change in student fatigue.
[0037] Among them, the slope of the overall risk change for students The expression is: ; In addition, the rate of change in teacher workload The expression is: ; In addition, the rate of change in student fatigue The expression is: ; in, This indicates the number of students participating in the scheduling for this period; The risk index of student S at the end of period t is calculated by the existing learning analysis model based on indicators such as changes in grades, homework completion rate, and knowledge mastery. This represents the risk index of student S at the end of period t-1; This represents the average workload ratio of all executors at the end of period t, i.e., the average workload ratio of all executors (subject teachers, homeroom teachers, and AI agents) at the end of period t. This represents the average load ratio of all actuators at the end of period t-1; The fatigue index of student S at the end of period t can be calculated based on indicators such as study time, amount of homework, and rest. This represents the fatigue index of student S at the end of period t-1.
[0038] The weight in this embodiment varies with the remaining days. Divided into three sections: Early stage ( ): The value is 0.35; The value is 0.4; The value is 0.25.
[0039] Mid-term stage ( ): The value is 0.55; The value is 0.3; The value is 0.15.
[0040] Final stage ( ): The value is 0.7; The value is 0.25; The value is 0.05.
[0041] The third step involves initializing the population using a two-layer encoding method based on an improved crayfish optimization algorithm to obtain the initial generation population, including the following steps: (31) Individual coding: In this embodiment, the overall strategy style of the three teachers working together in this cycle and the allocation details of specific tasks in each time slot are uniformly placed in the same candidate solution for synchronous optimization, avoiding the disconnect problem of first determining the strategy and then arranging the table separately in the traditional method.
[0042] Encode any candidate scheduling scheme into a real-valued vector, the expression of which is: ;in, This represents the two-layer encoding vector of the p-th candidate scheduling scheme individual in the g-th generation population; Let represent the strategy layer vector of the p-th candidate scheduling scheme individual in the g-th generation population; Let represent the scheduling layer vector of the p-th candidate scheduling scheme individual in the g-th generation population. The total dimension of the two-layer encoding vector of the candidate scheduling scheme is denoted by . for: ;in, A fixed dimension representing the strategy layer vector; The dimension of the scheduling layer vector is equal to the total number of intervention tasks multiplied by the total number of time slots.
[0043] (32) Initialization of the Tent chaotic mapping strategy layer: Let the Tent sequence be Its iterative relationship is: ; in, This represents the Tent chaos value generated in the nth iteration; Represents the chaos control coefficient; This represents an independent uniform random number generated in the nth iteration; This represents the maximum number of iterations in the improved crayfish optimization algorithm.
[0044] The initial population generation includes: generating strategy layer initial vectors for several candidate scheduling schemes using Tent chaotic mapping, and generating corresponding random scheduling layer initial vectors for any candidate scheduling scheme under scheduling feasibility constraints; combining the strategy layer initial vectors with the corresponding scheduling layer initial vectors to obtain the initial population. ; in, Indicates the initial generation of the population; This represents the initial two-layer encoding vector for the p-th candidate scheduling scheme; This represents the strategy layer vector of the p-th candidate scheduling scheme individual in the initial generation of the population; This represents the scheduling layer vector of the p-th candidate scheduling scheme individual in the initial generation of the population.
[0045] After initialization, each dimension of the Tent chaos strategy layer will be evenly distributed in [0,1], and then linearly mapped to the actual business range, such as AI accounting for 0%~70%, high-risk intervention intensity 0.3~1.0, etc., which is equivalent to generating dozens of completely different but reasonable collaborative templates at once.
[0046] In this embodiment, a batch of three-teacher collaborative scheduling methods that have performed well in the actual operation of previous sprint camps are compressed into a fixed vector, namely, the educational experience prior pattern vector. ;in, The sub-vectors representing the experience (Tent chaos) strategy layer are derived from the average or weighted statistical results of historical data from multiple sessions, such as the weekly intervention rates of homeroom teachers, subject teachers, and AI for students at each risk level, the resource allocation ratio for each class type, and the frequency of interventions during daily routines. ; ;in, This represents the number of dimensions in the experience strategy layer; This represents the empirical parameter of the i-th policy; This indicates the number of graduating classes from each year of high school used for statistical analysis; Let represent the empirical value of the i-th strategy in the m-th historical sample.
[0047] in addition, This represents the empirical (random) scheduling layer subvector, which quantifies the time distribution patterns of high-quality scheduling from previous years. For example, high-risk students are prioritized for the first half of the evening self-study session, homeroom teacher talks are concentrated on Wednesdays and Saturdays, and AI tutor Q&A sessions are mostly scheduled at noon and during the first evening self-study session. The expression for the empirical (random) scheduling layer subvector is: ;definition: ;in, This indicates the number of experience-based scheduling levels. This represents the k-th scheduling experience parameter; This represents the k-th scheduling experience value in the m-th historical scheduling sample.
[0048] Here, the encoded value of the d-th dimension of the prior pattern vector of educational experience is... Satisfy the following relationship: when hour, ;when hour, Therefore, the empirical prior vector The dimension is consistent with the two-layer encoding vector of the candidate scheduling scheme, which consists of sub-vectors of the empirical strategy layer. and experience scheduling layer subvector It was assembled in a predetermined order.
[0049] The fourth step is to decode any individual in the current generation of the population, converting the double-layer encoded vector into a scheduling matrix: Here, a decoding function is used. The two-layer encoding vector of candidate scheduling schemes in the current generation of the population is decoded, and its expression is: ;in, This represents an element in the scheduling matrix obtained after decoding. This represents the decoding function from a vector to a scheduling matrix, including processes such as specific task sorting, time slot mapping, and teacher resource verification.
[0050] Using the aforementioned scheduling feasibility constraints, the decoding results are verified to obtain the scheduling matrix corresponding to the p-th candidate scheduling scheme: When the executor When being a subject teacher, and equal .
[0051] The fifth step involves using the multi-objective optimization objective function to calculate the comprehensive objective value of the decoded scheduling matrix, and combining it with the robust correction term to obtain the corresponding fitness value, thus forming the fitness sequence of the current generation of the population.
[0052] Specifically, decoding the candidate scheduling scheme individuals in the current generation of the population yields the scheduling matrix corresponding to the p-th candidate scheduling scheme individual. The comprehensive target value is calculated using the following expression: ; This represents the core integrated objective function, used to uniformly measure intervention coverage for high-risk students, teacher workload balance, and resource equity among students.
[0053] In addition, under robust scenario sampling conditions, the expected default cost of individual candidate scheduling schemes is calculated. And as a robustness correction term, its expression is: ;in, This represents the number of pre-defined uncertain events (e.g., teachers taking temporary leave, students being temporarily absent, school affairs temporarily occupying time slots, limited execution resources, etc.) within the current scheduling optimization cycle, and the number of such scenarios within a single scheduling optimization process. It is a fixed value; Represents the scenario of the q-th uncertain event. The probability of occurrence, and satisfying ; This represents the individual with the p-th candidate scheduling scheme in the g-th generation population during the q-th uncertain event scenario. The default adjustment costs.
[0054] In this embodiment, the fitness value of the p-th candidate scheduling scheme individual after adding robustness is obtained through iteration in the g-th generation of the population. To sort, the expression is: ,in, This indicates the robust adjustment weight coefficient.
[0055] The sixth step involves updating the position of any individual in the current generation of the crayfish population based on the improved crayfish optimization algorithm, thereby generating the next generation of the population.
[0056] (61) Let the velocity vector of the p-th candidate scheduling scheme individual in the g-th generation population be... for: ;in, This represents the velocity component of the p-th candidate scheduling scheme individual in the g-th generation population along the d-th encoding dimension; d takes values of 1, 2, ... The The total dimension of the two-layer encoding vector of the candidate scheduling scheme is composed of the strategy layer encoding dimension and the scheduling layer encoding dimension. (62) Update the velocity, the expression is: ; in, Let represent the velocity of the p-th candidate scheduling scheme individual in the g+1-th generation population in the d-th dimension; This represents the inertia weight of the g-th generation population; This represents the guiding coefficient that tends towards the current globally optimal scheduling scheme; The guiding coefficient represents the tendency towards an empirically-based prior scheduling scheme; Indicates the interval The first random number that is uniformly distributed within the range; This represents the encoded value on the d-th dimension of the individual with the globally optimal scheduling scheme in the g-th generation population; This represents the encoded value of the p-th candidate scheduling scheme individual in the g-th generation population on the d-th dimension; Indicates the interval The second random number is uniformly distributed within the range; Represents the empirical prior vector at the th Encoded values in each dimension.
[0057] (63) After the speed is updated, the encoding vector of the candidate scheduling scheme individual is updated in position, and its expression is: ;in, This represents the encoding value of the p-th candidate scheduling scheme individual in the g+1-th generation population on the d-th dimension.
[0058] Step 7: Determine whether a preset termination condition has been met. The termination condition includes reaching the maximum number of iterations or the change in population fitness over multiple consecutive generations being less than a preset threshold. If the termination condition is met, output the scheduling matrix corresponding to the best individual in the current generation. If the current generation population is selected, the next generation population is selected as the new current generation population, and the process returns to step three to continue iterating.
[0059] 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 three-teacher collaborative scheduling method based on an improved crayfish optimization algorithm, characterized in that, Includes the following steps: Step S1: Construct a multi-objective optimization objective function and impose scheduling feasibility constraints; Step S2: Obtain the basic data required for scheduling, and initialize the population using a two-layer encoding method based on the improved crayfish optimization algorithm to obtain the initial generation population; Step S3: Decode any individual in the current generation of the population and convert the double-layer encoded vector into a scheduling matrix; Step S4: Calculate the comprehensive objective value of the decoded scheduling matrix using the multi-objective optimization objective function, and combine it with the robust correction term to obtain the corresponding fitness value, forming the fitness sequence of the current generation of the population; Step S5: Based on the fitness sequence, update and determine the optimal individual of the current generation from the current generation population; Step S6: Based on the improved crayfish optimization algorithm, update the position of any individual in the current generation population to generate the next generation population; Step S7: Determine whether a preset termination condition has been met. The termination condition includes reaching the maximum number of iterations or the change in population fitness over multiple consecutive generations being less than a preset threshold. If the termination condition is met, the scheduling matrix corresponding to the best individual in the current generation is output as the final scheduling result. Otherwise, the next generation population is taken as the new current generation population, and the process returns to step S3 to continue iterating.
2. The three-teacher collaborative scheduling method based on the improved crayfish optimization algorithm according to claim 1, characterized in that, The expression for the multi-objective optimization objective function is: ； ； ； ； in, Indicates the weight of the intervention coverage target for high-risk students; The weights representing the teacher workload balancing target; Indicates the weight of the goal of resource equity among students; This represents the objective function for intervention coverage of high-risk students; Represent the objective function for balancing teacher workload; Represents the objective function for ensuring fairness of resources among students; Indicates task The corresponding risk weight for the student; Indicates task The scheduling decision variable is whether it is executed by subject teacher j in time slot b. If it is executed, the value is 1; otherwise, the value is 0. This indicates the actual workload of subject teacher j during scheduling; This represents the maximum available workload for subject teacher j; This represents the average workload rate of all subject teachers. This indicates the actual workload of the homeroom teacher (h) in scheduling; This indicates the maximum available workload for class teacher h; This represents the average workload rate of all homeroom teachers. This indicates the total number of students; This represents the total intervention duration received by student s during this period; This represents the average intervention duration for all students.
3. The three-teacher collaborative scheduling method based on the improved crayfish optimization algorithm according to claim 2, characterized in that, It also includes: introducing educational logic-driven phase switching conditions, which include the slope of changes in overall student risk, the rate of change in teacher workload, and the rate of change in student fatigue; The slope of the overall student risk change The expression is: ； The teacher workload change rate The expression is: ； The student fatigue rate The expression is: ； in, This indicates the number of students participating in the scheduling for this period; This represents the risk index of student S at the end of period t; This represents the risk index of student S at the end of period t-1; This represents the average load ratio of all actuators at the end of period t. This represents the average load ratio of all actuators at the end of period t-1; This represents the fatigue index of student S at the end of period t. This represents the fatigue index of student S at the end of period t-1.
4. The three-teacher collaborative scheduling method based on the improved crayfish optimization algorithm according to claim 3, characterized in that, The scheduling feasibility constraints include: constraints on the number of times tasks can be assigned, constraints on the number of tasks that can be executed in the same time slot, constraints on the number of tasks that can be assigned to students in the same time slot, constraints on the available time of the executor, and constraints on the upper limit of intervention that students can tolerate. The expression for the constraint on the number of task scheduling attempts is: ； The expression for the constraint on the number of tasks executed in the same time slot is: ； The expression for the constraint on the number of tasks assigned to students in the same time slot is: ； The expression for the available duration constraint of the executor is: ； The expression for the upper limit constraint on student intervention tolerance is: ； in, Indicates task Is the execution body in time slot b? If executed, the value is 1; otherwise, the value is 0. When working as a subject teacher, equal ; This represents the set of all executors, including the set of subject teachers, the set of homeroom teachers and moral education teachers, and the set of AI learning companion execution agents; Represents the set of all time slots; Represents the entire set of tasks; Indicates the i-th student; Indicates task The corresponding students; This represents the set of time slots that are allowed to schedule tasks within the current period; Represents the i-th student The maximum acceptable number of interventions or total duration within this period; Indicates the execution body Total available time.
5. The three-teacher collaborative scheduling method based on the improved crayfish optimization algorithm according to claim 4, characterized in that, Obtain the basic data required for scheduling; the basic data required for scheduling includes a student set. The collection of all executable entities All time slots set All task sets ,Task Risk weight of the corresponding student Teacher's available time The i-th student The maximum acceptable number of interventions or total duration within this period. Countdown to the College Entrance Examination Population size and maximum number of iterations .
6. The three-teacher collaborative scheduling method based on the improved crayfish optimization algorithm according to claim 5, characterized in that, An improved crayfish optimization algorithm employs a two-layer encoding method to initialize the population; the two-layer encoding method includes a Tent chaotic strategy layer and a random scheduling layer; the two-layer encoding method for population initialization includes the following steps: Encode any candidate scheduling scheme into a real-valued vector, the expression of which is: ;in, This represents the two-layer encoding vector of the p-th candidate scheduling scheme individual in the g-th generation population; Let represent the strategy layer vector of the p-th candidate scheduling scheme individual in the g-th generation population; Let represent the scheduling layer vector of the p-th candidate scheduling scheme individual in the g-th generation population; Total dimension of the two-layer encoding vector of the candidate scheduling scheme for: ;in, A fixed dimension representing the strategy layer vector; The dimension of the scheduling layer vector; Initialization is performed using the Tent chaos strategy layer, which includes: Let the Tent sequence be Its iterative relationship is: ； in, This represents the Tent chaos value generated in the nth iteration; Represents the chaos control coefficient; This represents the independent uniform random number generated in the nth iteration; This represents the maximum number of iterations in the improved crayfish optimization algorithm; The initial population generation includes: generating strategy layer initial vectors for several candidate scheduling schemes using Tent chaotic mapping, and generating corresponding random scheduling layer initial vectors for any candidate scheduling scheme under scheduling feasibility constraints; combining the strategy layer initial vectors with the corresponding scheduling layer initial vectors to obtain the initial population. ； in, Indicates the initial generation of the population; This represents the initial two-layer encoding vector for the p-th candidate scheduling scheme; This represents the strategy layer vector of the p-th candidate scheduling scheme individual in the initial generation of the population; This represents the scheduling layer vector of the p-th candidate scheduling scheme individual in the initial generation of the population.
7. The three-teacher collaborative scheduling method based on the improved crayfish optimization algorithm according to claim 6, characterized in that, Decode any individual in the current generation of the population, converting the two-layer encoded vector into a scheduling matrix, including: Use decoding function The two-layer encoding vector of candidate scheduling schemes in the current generation of the population is decoded, and its expression is: ;in, This represents an element in the scheduling matrix obtained after decoding; Using the aforementioned scheduling feasibility constraints, the decoding results are verified to obtain the scheduling matrix corresponding to the p-th candidate scheduling scheme: When the executor When being a subject teacher, and equal .
8. The three-teacher collaborative scheduling method based on the improved crayfish optimization algorithm according to claim 7, characterized in that, The multi-objective optimization objective function is used to calculate the comprehensive objective value of the decoded scheduling matrix, and the corresponding fitness value is obtained by combining it with the robust correction term, forming the fitness sequence of the current generation of the population, including: Decoding the candidate scheduling scheme individuals in the current generation of the population yields the scheduling matrix corresponding to the p-th candidate scheduling scheme individual. The comprehensive target value is calculated using the following expression: ; Under robust scenario sampling conditions, calculate the expected default cost for individual candidate scheduling schemes. And as a robustness correction term, its expression is: ； in, This indicates the number of uncertain event scenarios set within the current scheduling optimization cycle; Represents the scenario of the q-th uncertain event. The probability of occurrence, and satisfying ; This represents the individual with the p-th candidate scheduling scheme in the g-th generation population during the q-th uncertain event scenario. Underlying default adjustment costs; The fitness value of the current generation of the population is obtained by the following expression: ； in, This indicates the robust adjustment weight coefficient.
9. The three-teacher collaborative scheduling method based on the improved crayfish optimization algorithm according to claim 8, characterized in that, Based on an improved crayfish optimization algorithm, the position of any individual in the current generation population is updated to generate the next generation population, including: Let the velocity vector of the p-th candidate scheduling scheme individual in the g-th generation population be... for: ;in, This represents the velocity component of the p-th candidate scheduling scheme individual in the g-th generation population along the d-th encoding dimension; d takes values of 1, 2, ... The The total dimension of the two-layer encoding vectors for the candidate scheduling schemes; The expression for updating the speed is: ； in, Let represent the velocity of the p-th candidate scheduling scheme individual in the g+1-th generation population in the d-th dimension; This represents the inertia weight of the g-th generation population; This represents the guiding coefficient that tends towards the current globally optimal scheduling scheme; The guiding coefficient represents the tendency towards an empirically-based prior scheduling scheme; Indicates the interval The first random number that is uniformly distributed within the range; This represents the encoded value on the d-th dimension of the individual with the globally optimal scheduling scheme in the g-th generation population; This represents the encoded value of the p-th candidate scheduling scheme individual in the g-th generation population on the d-th dimension; Indicates the interval The second random number is uniformly distributed within the range; Represents the empirical prior vector at the th Encoded values in each dimension; After the speed is updated, the encoding vector of each candidate scheduling scheme is updated in position, and the expression is as follows: ;in, This represents the encoding value of the p-th candidate scheduling scheme individual in the g+1-th generation population on the d-th dimension.
10. A system employing the three-teacher collaborative scheduling method based on the improved crayfish optimization algorithm as described in any one of claims 1 to 9, characterized in that, include: The objective function construction module constructs a multi-objective optimization objective function and applies scheduling feasibility constraints. The data access and preprocessing module obtains the basic data required for scheduling, and uses a two-layer encoding method based on the improved crayfish optimization algorithm to initialize the population and obtain the initial generation population. The decoding module, connected to the data access and preprocessing module, decodes any individual in the current generation of the population, converting the two-layer encoded vector into a scheduling matrix. The fitness calculation module is connected to the objective function construction module and the decoding module. It uses the multi-objective optimization objective function to calculate the comprehensive objective value of the decoding scheduling matrix, and combines it with the robust correction term to obtain the corresponding fitness value, forming the fitness sequence of the current generation of the population. The optimal solution module is connected to the fitness solution module. Based on the fitness sequence, it updates and determines the optimal individual of the current generation from the current generation population. The position update module, connected to the optimal solution module, uses an improved crayfish optimization algorithm to update the position of any individual in the current generation of the population and generate the next generation of the population. The iteration determination module, connected to the position update module and the data access and preprocessing module, determines whether a preset termination condition has been met. The termination condition includes reaching the maximum number of iterations or the change in population fitness over multiple consecutive generations being less than a preset threshold. If the termination condition is met, the scheduling matrix corresponding to the best individual in the current generation is output and used as the final scheduling result. Otherwise, the next generation population is taken as the new current generation population, and the iteration continues.