Concurrent beam cluster collaborative optimization mobile class arrangement method and system

Abstract

The invention discloses a mobile class arrangement method and system for concurrent beam cluster collaborative optimization, and belongs to the field of intelligent class arrangement. The method comprises the steps that an anchor point set is generated for a mobile class set; generating a plurality of feasible solutions without hard conflicts from the anchor point set; selecting m optimal solutions to form a cluster; defining five complementary neighborhood operations to form a directive neighborhood set; the directivity neighborhood set and the random disturbance neighborhood jointly form a collaborative neighborhood set; self-adaptive parallel beam cluster searching is carried out; performing dynamic knowledge learning and cluster evolution; when the search is stagnated, backtracking enhancement is triggered. According to the method, the course arrangement quality is remarkably improved, the solving efficiency is greatly improved, the robustness is enhanced, the efficiency bottleneck of serial calculation is overcome, the specific strong coupling constraint of shift shifting can be efficiently processed, the situation that search falls into local optimum is avoided, the quality stability of the solution is improved, and intelligent self-adaption of a search strategy is achieved.

Description

Technical Field

[0001] This invention belongs to the field of intelligent scheduling technology, specifically relating to a method and system for scheduling classes in a flexible class schedule based on concurrent cluster collaborative optimization. Background Technology

[0002] As educational philosophies continue to evolve towards personalization and differentiation, the high school education system, driven by the new 3+1+2 college entrance examination reform, is systematically restructuring its teaching organization. The traditional one-size-fits-all teaching model based on fixed administrative classes is gradually shifting towards a tiered, student-selected subject system. This system requires students to complete three compulsory subjects—Chinese, Mathematics, and English—and then choose one from Physics and History as their first-choice subject, followed by two from Chemistry, Biology, Geography, and Politics as their second-choice subjects, resulting in 12 different subject combinations. While this structural change grants students greater choice, it also presents unprecedented and complex challenges to teaching management, especially curriculum design, primarily in the following aspects: (1) The challenge of scheduling with strong constraints: The scheduling process not only needs to meet basic hard constraints such as no conflicts between teachers, students, and classrooms, but also must ensure that the courses participating in the flexible class scheduling are arranged in the same time period so that students from different administrative classes can move synchronously and complete their flexible class learning. This puts extremely high demands on the coordinated scheduling of high school teaching environments with relatively fixed classroom resources, tight teacher allocation, and complex course structure.

[0003] (2) Challenges of Dynamic Class Assignment and Resource Optimization: Due to the diverse combinations of student course selections, each elective course needs to be dynamically assigned to classes based on the actual number of students enrolled. How to rationally allocate classrooms, match teachers, and arrange time slots to maximize resource utilization while ensuring a balanced number of students in each class and consistent course progress has become an optimization problem that traditional manual scheduling methods cannot systematically solve.

[0004] (3) Challenges in algorithm adaptability and solution efficiency: The class scheduling problem is a typical combinatorial optimization problem with characteristics such as high dimensionality, multiple constraints, and NP-hardness. Although metaheuristic methods, represented by genetic algorithms, have been applied to some extent in this field, they still generally suffer from slow convergence speed, easy getting trapped in local optima, and unstable solution quality when dealing with large-scale, strongly constrained class scheduling scenarios in practice. It is difficult to generate high-quality, executable timetable solutions within a limited time.

[0005] The closest existing technology to this invention is a method for intelligent class scheduling based on genetic algorithms disclosed in Chinese patent CN116468416A. This scheme represents a typical approach to solving class scheduling problems using metaheuristic algorithms, specifically including the following steps: Initialization: An initial timetable is generated through individual optimization and encoded in binary to form an initial population. Fitness evaluation: A comprehensive fitness function is designed to quantify the degree to which the timetable violates various constraints (such as teacher conflicts, class scheduling paths, etc.). Genetic iteration: The fitness of the population is calculated, and the individual with the best fitness is selected. A new generation of the population is generated through crossover (randomly swapping two classes in a class) and mutation (randomly swapping two classes in the same grade at the same time). Termination output: The iteration continues until the fitness of the best individual reaches the expected value, and the output is the final timetable. Analysis reveals the following problems with this scheme: (1) Low search efficiency and difficulty in dealing with large-scale problems: The scheme uses a genetic algorithm that is executed serially, which cannot utilize modern multi-core computing resources. Each iteration can only produce one offspring population, and the computing speed is limited by the performance of a single thread. When facing large-scale scheduling problems with a large number of classes and complex constraints in actual schools, the computing time required to obtain a satisfactory solution is too long, which cannot meet the timeliness requirements of academic affairs work.

[0006] (2) The search strategy is simplistic and blind, resulting in limited optimization: The genetic operations in this scheme only include simple "random exchange" type crossover and mutation, which are generalized, unguided random perturbations. This strategy fails to fully utilize the domain knowledge of the class scheduling problem. The algorithm lacks specific handling for the key coupling constraint that "different levels of elective courses must be taught in the same class at the same time." Instead, it treats this constraint as a general soft constraint and penalizes it. This results in the algorithm spending a lot of random search resources to satisfy the constraint and generating a large number of infeasible solutions during the search process, leading to low efficiency. The lack of specialized and refined neighborhood operations for different optimization objectives (such as balanced teacher workload and course distribution) makes it difficult to coordinate the optimization of multiple competing soft constraints.

[0007] (3) Easily trapped in local optima and lacking global exploration capability: The genetic algorithm used in this scheme relies on population diversity, but it is prone to premature convergence under selection pressure. This scheme lacks an effective global exploration and diversity maintenance mechanism to maintain the diversity of search directions or escape from local optima, resulting in unstable quality of the final solution, which may be far from the global optimum.

[0008] (4) Inadequate resource allocation and failure to utilize modern computing architecture: This scheme adopts a fixed search strategy and parameters, does not involve parallel computing, cannot utilize the currently prevalent multi-core CPUs or computing clusters, cannot dynamically adjust the optimization focus and allocation of computing resources according to the solution process, lacks adaptability to different problem states and solution stages, and has low computing resource utilization. At the same time, the algorithm treats all courses and all constraints equally during execution, failing to intelligently focus computing resources on the most pressing conflicts or the most likely improved search directions.

[0009] (5) Inability to effectively coordinate and optimize multiple conflicting soft constraint objectives: This scheme handles multiple objectives through simple weighted summation, but fails to deeply analyze the hierarchical coupling structure characteristics of the class scheduling problem (the difference between administrative class courses and class scheduling courses, and the strong time coupling within class scheduling courses). It also fails to deeply integrate advanced ideas such as parallelization, adaptive and guided search in modern intelligent optimization algorithms with domain knowledge, making it difficult to systematically balance the requirements of teacher workload, course distribution, classroom utilization, etc., and difficult to generate a timetable with high overall satisfaction. Summary of the Invention

[0010] To address the technical problems of existing technologies, such as low search efficiency, single search strategy, limited optimization effect, susceptibility to local optima, insufficient global exploration capability, and unreasonable resource allocation, this invention provides a concurrent cluster collaborative optimization method and system for flexible class scheduling, achieving the goal of efficiently and effectively solving large-scale, strongly constrained flexible class scheduling problems.

[0011] The technical solution adopted by this invention to solve the technical problem is as follows: The present invention provides a concurrent bundle cluster collaborative optimization method for class scheduling, which mainly includes the following steps: Step S1: Generate an anchor set for the set of elective courses; generate multiple feasible solutions without hard conflicts from the anchor set; select the m optimal solutions to form a bundle; Step S2: Define five complementary neighborhood operations to form a directional neighborhood set; the directional neighborhood set and the random perturbation neighborhood together form a cooperative neighborhood set; Step S3: Adaptive parallel beam cluster search; Step S4: Dynamic knowledge learning and cluster evolution; Step S5: When the search stalls, trigger backtracking enhancement.

[0012] Furthermore, in step S1, the focus is on the set of elective courses. C w generate K A set of anchor points that satisfy the constraint of simultaneous teaching in the same class. A w For each anchor set The time slot was used as an exclusion period for related classes, and the remaining administrative classes were randomly scheduled. C f And fix the hard conflicts, and obtain K A complete feasible solution is found; the solution with the minimum soft constraint cost is selected. m The solutions constitute the initial bundle. B .

[0013] Furthermore, the aforementioned elective course set C w Including the college entrance examination level c g and the level of compliance c d .

[0014] Furthermore, in step S2, the five complementary neighborhood operations include coupling adjustment neighborhood. N C And four criteria for optimizing the neighborhood.

[0015] Furthermore, the four criteria for optimizing neighborhoods are: minimum working days, etc. N 1. Recommended time slot N 2. Class Interval N 3 and teachers continuously N 4.

[0016] Furthermore, in step S3, start L Several parallel search processes, each executing in a loop: (1) Starting point selection: based on the cluster B Ranking of Chinese solutions r Ranking probabilities by non-linearity Choose a starting solution; m The size of the cluster; (2) Adaptive local search: using dynamic probability from { N R}∪ N Select neighborhood operation, where P ( N R )= β , P ( N i )=(1− β ) w i , i ∈{C,1,2,3,4}, β For a fixed probability, w i The neighborhood weights are used; an iterative descent method is performed until a local optimum is reached. (3) Asynchronous update: When a solution better than the global optimum is found, update the bundle optimum solution. B 1. And store the found local optimal solutions into a shared candidate pool. Pool .

[0017] Furthermore, in step S4, the following main process is executed periodically: (1) Merge parallel bundle cluster search results to update the bundle; (2) Adjust the neighborhood set weights based on the statistical neighborhood improvement amount; (3) Synchronize the bundle and neighborhood knowledge to all processes.

[0018] Furthermore, in step S5, the specific triggering and execution methods for backtracking enhancement are as follows: (1) From the current optimal solution of the bundle B Extracting the elective course schedule from 1 A w ∗ ; (2) Arrangement of elective courses A w ∗ Generate random perturbations m -2 new anchor point sets; (3) Replace the lower-ranked solutions in the bundle with solutions based on the new anchor set and reset some weights.

[0019] Furthermore, in step S5, the optimal solution is output when the termination condition is met; otherwise, the process returns to step S3 to continue iterating.

[0020] This invention provides a concurrent bundle cluster collaborative optimization-based class scheduling system, mainly comprising: The bundle management module is used to maintain and evolve bundles; The weight learning module is used to manage dynamic search strategies and dynamically evaluate and adjust the utility weights of each dynamic search strategy. Multiple parallel search modules are configured to select a starting point from the bundle based on utility weights, perform local optimization, and then feed back the results. In other words, multiple parallel search modules perform local optimization in parallel based on the solutions in the bundle.

[0021] The beneficial effects of this invention are: The core innovation of this invention lies in the deep integration of the characteristics of flexible class scheduling, modern parallel computing architecture, and intelligent adaptive search technology. Compared with existing technologies, this invention has the following advantages: (1) Structure-aware neighborhood design for flexible class scheduling coupling constraints (problem feature fusion); Traditional metaheuristic algorithms, such as genetic algorithms, employ general random swapping operations, which are inefficient when dealing with the unique "synchronous class scheduling" constraint of flexible class scheduling. The key point of this invention lies in its in-depth analysis of the hierarchical coupling structure of flexible class scheduling, and for this purpose, it designs a set of structure-aware neighborhood operations.

[0022] Dedicated coupling neighborhood ( N C Unlike general random exchange, this invention designs two operations specifically for adjusting the flexible class schedule while maintaining its coupling relationship: (a) Synchronous movement: Moving different levels of the same course (such as the college entrance examination class and the standard class) as an inseparable whole, fundamentally eliminating the possibility of breaking the constraint of simultaneous learning of the same course.

[0023] (b) Pairing and swapping: Time slots are swapped between two different courses that have established a pairing relationship (such as chemistry and politics), which optimizes resource allocation while maintaining the feasibility of students choosing one of the two courses to attend.

[0024] Four criteria for optimizing neighborhoods: N 1 (minimum working day) N 2 (Recommended time slot) N 3 (Class Interval) N 4 (Teacher Continuity) applies to all courses to optimize soft constraints. The combination of the four standard optimization neighborhoods is the most universally accepted and most important combination of constraints selected from a large number of constraints through methods such as interviews and questionnaires. This combination is more conducive to the efficiency and applicability of course scheduling, rather than simply piling up constraints.

[0025] The structure-aware neighborhood design with this step-by-step coupling constraint allows the search process to always proceed within a subset of highly feasible solutions, avoiding the huge overhead of existing technologies that generate a large number of invalid solutions due to blind operation, and achieving more accurate and efficient search.

[0026] (2) Elite-guided parallel cluster search architecture (parallel computing fusion). To overcome the computational bottleneck of serial algorithms and improve search quality, this invention constructs an elite-guided parallel beam-cluster search architecture.

[0027] Beam management: Maintaining an elite set (beam) of currently optimal solutions as the command center and knowledge base for the global search.

[0028] Nonlinear resource allocation: Based on the ranking of solutions within the cluster, a nonlinear probability formula is used to allocate opportunities as search starting points for each solution. This ensures that high-quality solutions receive more resources for in-depth development, while reserving exploration opportunities for potential solutions, thus intelligently balancing development and exploration.

[0029] Asynchronous parallel collaboration: Multiple search processes select a starting point from the cluster and perform local optimizations in parallel. Once an improvement is found, the global information is updated asynchronously. This loosely coupled parallel mode avoids inter-process waiting, greatly improving the utilization of multi-core CPUs and the overall solution speed.

[0030] (3) Adaptive policy learning mechanism based on historical utility (integration of intelligent technologies); This invention possesses the ability to learn and dynamically adjust itself, which is a core intelligent feature that distinguishes it from fixed-parameter algorithms.

[0031] Dynamic weight learning: A dynamic weight is maintained for each search strategy (neighborhood). The algorithm periodically calculates the average improvement brought by each strategy and updates its weight accordingly. Strategies with better performance receive increased weights and gain more application opportunities.

[0032] Minimum weight guarantee: To prevent certain strategies from being permanently forgotten due to poor short-term performance, a minimum weight is set to forcibly retain a certain exploration probability, thus ensuring the long-term diversity of the search.

[0033] This invention employs dynamic weight learning and a minimum weight guarantee mechanism to autonomously identify the most effective optimization direction in the current problem state and search phase, achieving a leap from a fixed strategy to a context-aware strategy, and significantly enhancing the robustness and adaptability of the algorithm.

[0034] (4) Structure-preserving backtracking enhancement mechanism (global convergence guarantee); To avoid getting trapped in local optima, this invention designs an intelligent exit mechanism based on the problem structure, rather than a simple random restart.

[0035] Anchor point extraction and perturbation: When a search stall is detected, the arrangement structure (anchor point) of the elective course is extracted from the current optimal solution and subjected to controlled, small-amplitude random perturbation.

[0036] Targeted restart: The new arrangement generated after the perturbation replaces some of the inferior solutions in the cluster, thereby injecting new possibilities into the elective course part while retaining most of the currently optimized good structures (such as the administrative class course arrangement).

[0037] This invention employs a low-cost, highly targeted structural perturbation that can effectively help the algorithm escape the valley of local optima and continue to move towards a better solution, while avoiding knowledge loss and efficiency waste caused by completely random restarts.

[0038] In summary, the four key aspects of this invention form a closed-loop technical system: dedicated neighborhoods ensure correct and efficient search direction; parallel cluster architecture provides powerful computing capabilities and quality assurance; adaptive learning enables the search process to continuously self-optimize; and intelligent backtracking ensures global convergence. Together, these elements achieve an efficient and high-quality solution to the large-scale, strongly constrained class scheduling problem. Attached Figure Description

[0039] Figure 1 The flowchart shows a concurrent bundle cluster collaborative optimization method for scheduling classes in a flexible class schedule, which is provided by the present invention.

[0040] Figure 2 This represents the parallel speedup ratio of the present invention under different numbers of cores.

[0041] Figure 3 Adjusting the neighborhood for coupling N C A schematic diagram of synchronous movement operation.

[0042] Figure 4 Adjusting the neighborhood for coupling N C A diagram illustrating the pairing and swapping operation.

[0043] Figure 5 This is a graph showing the dynamic weight evolution. Detailed Implementation

[0044] The present invention will be further described in detail below with reference to the accompanying drawings.

[0045] In a first aspect, the present invention provides a method for scheduling classes in a flexible class schedule based on concurrent bundle cluster collaborative optimization.

[0046] like Figure 1 As shown, the present invention provides a concurrent cluster collaborative optimization method for class scheduling, which mainly includes data flow of three core modules: parallel search, dynamic learning, and backtracking enhancement. Specifically, it includes the following steps: Step S1: Initialization of structure awareness;

[0047] For the set of courses with flexible class scheduling, generate an anchor point set; generate K feasible solutions without hard conflicts from the anchor point set; select the m optimal solutions to form a bundle B.

[0048] Specifically, the set of elective courses C w Mainly includes the college entrance examination level c g and the level of compliance c d For the flexible class scheduling curriculum C w ,generate KA partial arrangement scheme (anchor point set) that satisfies the "same class, same time" constraint. A w For each anchor set The time slot was used as an exclusion period for related classes, and the remaining administrative classes were randomly scheduled. C f And fix the hard conflicts, and obtain K A complete feasible solution is found; the solution with the minimum soft constraint cost is selected. m These solutions constitute the initial elite pool (bundle). B .

[0049] Step S2: Design of collaborative neighborhood set;

[0050] Define five complementary neighborhood operations to form a directional neighborhood set. N The following are examples: Coupling Adjustment Neighborhood N C : Specifically handles the coupling constraints of elective courses. It includes at least one of the following two operations: (1) Synchronous movement, which moves the college entrance examination / passing level of an elective course to a new time slot as a whole; (2) Pairing exchange, which swaps the time slots of two different courses that have established a pairing relationship.

[0051] like Figure 2 and Figure 3 As shown, all courses need to be arranged before the high school entrance examination, but based on the students' choices of subjects for the college entrance examination, courses are divided into college entrance examination level and standard level. When moving classes, courses are paired according to level for the same course and moved simultaneously. The required time slot for the move must be free of classes; if there are classes, the courses for the two classes must be two independent, unpaired courses, or exactly one paired course. Specifically, as... Figure 2 As shown, when a physics class involving flexible scheduling moves from time period a to time period b, the paired college entrance examination class A and the standard-achieving class B must simultaneously move their physics classes. Simultaneously, it is required that the two courses present in target time period b, Chemistry A and Politics B, do not involve flexible scheduling, or are either another pair of courses involving flexible scheduling, such as Chemistry A and Chemistry B. After the high school entrance examination, some courses will no longer be offered if they are not in the class's college entrance examination course combination. Therefore, it is necessary to pair the college entrance examination courses offered by different classes, such as... Figure 3 As shown, pairing class A offers history courses for the college entrance examination but not chemistry, while pairing class B offers chemistry courses. If a student in pairing class A has chemistry in their college entrance examination subject but not history, they will move to pairing class B for chemistry when they have history class in pairing class A. Therefore, the history class times in pairing class A and the chemistry class times in pairing class B must be completely consistent, and the movement requirements are the same as those for pairing courses at different levels within the same subject.

[0052] Four criteria for optimizing neighborhoods: N 1 (minimum working day) N 2 (Recommended time slot) N 3 (Class Interval) N 4 (Teacher Continuity), applied to all courses to optimize soft constraints.

[0053] Random perturbation neighborhood N R Randomly swap the time slots of any two courses to maintain diversity.

[0054] directional neighborhood set N With random perturbation neighborhood N R Together they form a collaborative neighborhood set.

[0055] The purpose of introducing a dedicated neighborhood operation to preserve coupling constraints in this invention is to specifically handle class scheduling synchronization constraints in the adaptive local search process. This neighborhood operation is configured to ensure that the synchronous start-up relationship of related class scheduling courses (such as different levels within a course or paired courses between courses) is not disrupted when performing time period adjustments.

[0056] This invention identifies and classifies the constraints of class scheduling, clearly distinguishing between hierarchical coupling within courses (such as synchronization between college entrance examination classes and standard classes) and pairing coupling between courses (such as two different subjects sharing a time slot), and uses corresponding neighborhood operations to process them in the adaptive local search process.

[0057] Step S3: Adaptive parallel beam cluster search;

[0058] start up L Several parallel search processes, each executing in a loop: (1) Starting point selection: based on the cluster B Ranking of Chinese solutions r (Sorted by soft constraint cost), ranked by nonlinear probability Choose the starting solution; where m For the cluster size, r To solve the ranking in the cluster ( r =1 indicates optimality.

[0059] This invention employs an elite solution selection and evolution mechanism based on nonlinear ranking. When selecting the search starting point from the cluster, a nonlinear probability distribution based on solution ranking is used, which allows high-quality solutions to obtain more optimization resources while retaining a moderate exploration opportunity for lower-quality solutions.

[0060] Furthermore, the cluster evolution strategy can also employ a multi-objective optimization method based on the Pareto front to replace the single-objective ranking of this invention. By constructing a three-dimensional objective space (such as teacher satisfaction, course distribution uniformity, and resource utilization), a non-dominated solution set is maintained as an elite pool, and selection is based on indicators such as crowding distance.

[0061] (2) Adaptive local search: using dynamic probability from { N R}∪ N Select neighborhood operation, where P ( N R )= β , P ( N i )=(1− β ) w i , i ∈{C,1,2,3,4}, β For a fixed probability, w i The neighborhood weights are used; an iterative descent method is performed until a local optimum is reached.

[0062] Furthermore, the neighborhood selection mechanism can also employ reinforcement learning-based Q-learning or Multi-armed Bandit algorithms to replace the simple weighted average method of this invention, dynamically adjusting the neighborhood selection strategy. That is, each neighborhood is regarded as an arm, and the neighborhood selection probability is calculated using formulas such as UCB based on its historical returns (improvement amount).

[0063] (3) Asynchronous update: When a solution better than the global optimum is found, the bundle optimum solution is updated immediately. B 1. And store the found local optimal solutions into a shared candidate pool. Pool .

[0064] The present invention employs an asynchronous communication parallel search collaboration mechanism, which enables multiple parallel search processes to feed back the improved solutions obtained to the shared candidate pool after completing local optimization without waiting for other processes, and immediately start a new round of search based on the latest global information, thereby achieving efficient asynchronous parallel collaboration.

[0065] Step S4: Dynamic knowledge learning and cluster evolution;

[0066] The main process executes periodically: (1) Bundle reassembly: Merge parallel bundle cluster search results to update the bundle, that is, periodically merge shared candidate pools. Pool With the current cluster B Sort by objective function value and retain only the top [values]. m The optimal solutions form a new cluster. Bnew And clear the shared candidate pool. Pool .in B new =Top m ( B ∪ Pool Top m Candidate pool Pool Candidate solutions and current bundle B After merging the elite solutions, the top m optimal solutions are reordered and retained.

[0067] (2) Weight adjustment: Adjust the weight of the neighborhood set by statistical neighborhood improvement, that is, statistically analyze the neighborhood of each neighborhood. N i Average improvement Δ i According to the formula w i ′= max ( w min , Δ i / ∑ j Δ j Update the weights, where, , α For smoothing factors, minimum threshold w min =0.03.

[0068] The specific rules for adaptive weight updates are as follows: In the dynamic weight update method described above, a minimum threshold is set for each weight. w min This ensures that even if a search strategy does not improve in the short term, it still retains the opportunity to be selected, preventing a loss of search diversity.

[0069] (3) Knowledge synchronization: Synchronize the bundle and neighborhood knowledge to all processes, that is, update the bundle. B new and weight w new Broadcast to all processes.

[0070] This invention employs a dynamic adaptive multi-strategy selection mechanism, which assigns dynamic weights to various search strategies (neighborhood operations). By statistically analyzing the historical performance indicators of each strategy during the search process, the weights are periodically adjusted, enabling the algorithm to intelligently allocate computing resources based on the current solution state.

[0071] Step S5: Backtracking Enhancement Mechanism;

[0072] When a search stall is detected, the optimal solution is continuous.U If no improvement is made, backtracking enhancement is triggered, which involves extracting the class schedule from the current optimal solution, subjecting it to controlled perturbation to generate new alternatives, replacing some of the worse solutions in the cluster, and partially resetting the search strategy weights.

[0073] The specific triggering and execution methods for backtracking enhancement are as follows: (1) From the current optimal solution of the bundle B Extracting the elective course schedule from 1 A w ∗ ; (2) Arrangement of elective courses A w ∗ Generate random perturbations m -2 new anchor point sets; (3) Replace the lower-ranked solutions in the bundle with solutions based on the new anchor set and reset some weights.

[0074] The optimal solution is output when the termination condition is met; otherwise, the iteration returns to step S3. The objective function is: ,in, f 1 represents the cost of workday distribution. f 2 represents the cost of time period deviation. f 3 represents the cost of the course interval. f 4. The continuous cost to teachers.

[0075] The backtracking enhancement mechanism can replace the fixed stagnation detection of this invention with a temperature control mechanism in simulated annealing. When the probability of accepting a poor solution is lower than a threshold, the perturbation and reorganization of the elective course is actively carried out, and the perturbation intensity decreases as the temperature decreases.

[0076] Secondly, this invention provides a concurrent bundle cluster collaborative optimization-based flexible class scheduling system. This system is primarily applied to the concurrent bundle cluster collaborative optimization-based flexible class scheduling method provided in the first aspect.

[0077] This invention provides a concurrent bundle cluster collaborative optimization-based flexible class scheduling system, which adopts a flexible class scheduling method framework based on parallel bundle cluster collaborative optimization, and specifically includes the following modules: The cluster management module is mainly used for maintaining and evolving clusters; The weight learning module is mainly used to manage dynamic search strategies and to dynamically evaluate and adjust the utility weights of each dynamic search strategy. Multiple parallel search modules are configured to select a starting point from the bundle based on utility weights, perform local optimization, and then feed back the results. In other words, multiple parallel search modules perform local optimization in parallel based on the solutions in the bundle.

[0078] Alternatively, an island model can be used to replace the master-slave architecture of this invention. The search process is divided into multiple islands, each evolving independently, with superior individuals being migrated periodically. Different neighborhood weight configurations can be used between islands to enhance diversity.

[0079] To verify the actual scheduling quality of this invention, a practical test was conducted at a typical high school in Henan Province, and it was compared with the following existing methods: manual scheduling schemes and three classic metaheuristic algorithms: simulated annealing, tabu search, and genetic algorithm.

[0080] To ensure fairness in the comparison, the running time of all automated algorithms was limited to within 400 seconds. Given the randomness of the algorithms, each algorithm, except for the manual scheduling scheme, was run independently 30 times, and its statistical results were reported. To ensure a fair comparison with the serial algorithms, the CPU usage of this invention was also limited to a single core during runtime. Table 1 summarizes the calculation results of the school's current manual scheduling scheme, simulated annealing, tabu search, genetic algorithm, and this invention, including the optimal solution score (…). f min ), average score of 30 runs ( f ave30 ) and standard deviation ( σ ). Detailed information on all soft constraint violations, total costs, and resource usage is included.

[0081] Table 1 As shown in Table 1, this invention achieves the best average performance across all four soft constraints, with a significantly lower scheduling cost compared to manual scheduling and other comparative algorithms. This demonstrates the effectiveness of this invention in overall optimization. Regarding scheduling performance, all automated algorithms outperform manual scheduling, highlighting the advantages of automated optimization in satisfying resource constraints. Notably, under the same time constraints, the average performance of the population-based genetic algorithm is slightly inferior to that of single-point-based simulated annealing and tabu search. This phenomenon may indicate that in such complex scheduling problems, a strategy of deeply cultivating a local region within a limited time is more likely to yield a high-quality solution than extensive exploration. This also reflects the significant value of the adaptive mechanism in balancing development and exploration in this invention. In summary, this invention significantly improves scheduling quality.

[0082] Regarding solution efficiency, due to the targeted design of asynchronous parallel collaboration, this invention avoids inter-process waiting, greatly improving the utilization of multi-core CPUs and the overall solution speed. For example... Figure 4 As shown, the parallel efficiency (speedup) of this invention is close to linear, demonstrating excellent parallel performance and scalability. In an 8-core environment, the solution task that would take nearly 7 minutes on a single core is reduced to approximately 54 seconds. This efficiency leap transforms this invention from an offline computing model into a practical tool that supports interactive time scheduling planning.

[0083] Regarding robustness, besides completing scheduling tasks faster, parallelization also means higher-quality searches within the same timeframe. As shown in Table 2, in a comparative experiment with a fixed time budget (400 seconds), the 8-core version, with its higher throughput, completed more rounds of iteration and evaluation within the same timeframe, resulting in significantly better average scheduling cost (63.3 vs. 69.4 for the single-core version) and standard deviation (0.9 vs. 1.7 for the single-core version). This reveals the deeper value of parallelization: it substantially expands the search budget of this invention within a limited time, enabling it to perform more diverse and in-depth explorations, thereby directly improving the quality and robustness of the solution. This characteristic is crucial for the deadline constraints commonly present in practical applications.

[0084] Table 2 Performance Comparison in Full Multi-Core State Regarding the manifestation of search intelligence: In each iteration, this invention selects a neighborhood with a fixed probability. β = 0.3 Perform random perturbation neighborhood N R To ensure basic exploration capabilities; with a remaining probability of 1- β = 0.7 Based on the dynamic weight vector from the directional neighborhood set N Select the operation. Figure 5 Displaying the weights of each neighborhood w C , w 1. w 2. w 3. w 4. The changing trend as the search progresses reflects the autonomous learning process of this invention: In the initial stage of the search, the coupling neighborhood weights... w C The value is relatively high (approximately 0.35), and this invention focuses on exploring the overall structure; as the search progresses, the neighborhood weights are specifically optimized. w 1 to w 4. As the sum gradually increases to approximately 0.67, the focus of this invention shifts to local fine-tuning optimization. This process demonstrates the algorithm's intelligent adaptive capability from macroscopic layout to microscopic tuning.

[0085] The above description is only a preferred embodiment of the present invention. It should be noted that for those skilled in the art, several improvements and modifications can be made without departing from the principle of the present invention, and these improvements and modifications should also be considered within the scope of protection of the present invention.

Claims

1. A concurrent bundle cluster collaborative optimization method for flexible class scheduling, characterized in that, Includes the following steps: Step S1: Generate an anchor set for the set of elective courses; generate multiple feasible solutions without hard conflicts from the anchor set; select the m optimal solutions to form a bundle; Step S2: Define five complementary neighborhood operations to form a directional neighborhood set; the directional neighborhood set and the random perturbation neighborhood together form a cooperative neighborhood set; Step S3: Adaptive parallel beam cluster search; Step S4: Dynamic knowledge learning and cluster evolution; Step S5: When the search stalls, trigger backtracking enhancement.

2. The concurrent bundle cluster collaborative optimization method for flexible class scheduling according to claim 1, characterized in that, In step S1, for the set of elective courses... C w generate K A set of anchor points that satisfy the constraint of simultaneous teaching in the same class. A w For each anchor set The time slot was used as an exclusion period for related classes, and the remaining administrative classes were randomly scheduled. C f And fix the hard conflicts, and obtain K A complete feasible solution; Select the one with the lowest soft constraint cost m The solutions constitute the initial bundle. B .

3. The concurrent bundle cluster collaborative optimization method for flexible class scheduling according to claim 2, characterized in that, The set of elective courses C w Including the college entrance examination level c g and the level of compliance c d .

4. The concurrent bundle cluster collaborative optimization method for flexible class scheduling according to claim 1, characterized in that, In step S2, the five complementary neighborhood operations include coupling adjustment neighborhood. N C And four criteria for optimizing the neighborhood.

5. The concurrent bundle cluster collaborative optimization method for flexible class scheduling according to claim 4, characterized in that, The four criteria for optimizing neighborhoods are: minimum working days, etc. N 1. Recommended time slot N 2. Class Interval N 3 and teachers continuously N 4.

6. The concurrent bundle cluster collaborative optimization method for flexible class scheduling according to claim 1, characterized in that, In step S3, start L Several parallel search processes, each executing in a loop: (1) Starting point selection: based on the cluster B Ranking of Chinese solutions r Ranking probabilities by non-linearity Choose a starting solution; m The size of the cluster; (2) Adaptive local search: using dynamic probability from { N R }∪ N Select neighborhood operation, where P ( N R )= β , P ( N i )=(1− β ) w i , i ∈{C,1,2,3,4}, β For a fixed probability, w i Neighborhood weights; Perform iterative descent until a local optimum is reached; (3) Asynchronous update: When a solution better than the global optimum is found, update the bundle optimum solution. B 1. And store the found local optimal solutions into a shared candidate pool. Pool .

7. The concurrent bundle cluster collaborative optimization method for flexible class scheduling according to claim 1, characterized in that, In step S4, the following main process is executed periodically: (1) Merge parallel bundle cluster search results to update the bundle; (2) Adjust the neighborhood set weights based on the statistical neighborhood improvement amount; (3) Synchronize the bundle and neighborhood knowledge to all processes.

8. The concurrent bundle cluster collaborative optimization method for flexible class scheduling according to claim 1, characterized in that, In step S5, the specific triggering and execution methods for backtracking enhancement are as follows: (1) From the current optimal solution of the bundle B Extracting the elective course schedule from 1 A w ∗ ; (2) Arrangement of elective courses A w ∗ Generate random perturbations m -2 new anchor point sets; (3) Replace the lower-ranked solutions in the bundle with solutions based on the new anchor set and reset some weights.

9. The concurrent bundle cluster collaborative optimization method for flexible class scheduling according to claim 1, characterized in that, In step S5, the optimal solution is output when the termination condition is met; otherwise, the process returns to step S3 to continue iterating.

10. A concurrent bundle cluster collaborative optimization scheduling system applied to the concurrent bundle cluster collaborative optimization scheduling method according to any one of claims 1-9, characterized in that, include: The bundle management module is used to maintain and evolve bundles; The weight learning module is used to manage dynamic search strategies and dynamically evaluate and adjust the utility weights of each dynamic search strategy. Multiple parallel search modules are configured to select a starting point from the bundle based on utility weights, perform local optimization, and then feed back the results. In other words, multiple parallel search modules perform local optimization in parallel based on the solutions in the bundle.

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