Multi-target intelligent course arrangement method based on improved lion group optimization algorithm

Abstract

The invention discloses a multi-target intelligent course arrangement method based on an improved lion group optimization algorithm. The method comprises the following steps: S1, acquiring course arrangement information data; s2, establishing a multi-target course arrangement model based on the average non-uniformity of the students and the teachers and the average vacancy rate of the arranged classrooms; s3, inputting course arrangement information data into the multi-target course arrangement model, performing result optimization based on an improved lion group optimization algorithm, and obtaining an optimal solution based on a set optimization target, namely a final course arrangement result; the optimization target is to minimize the average non-uniformity of the students and the teachers and the average vacancy rate of the arranged classrooms. According to the method, the multi-target course arrangement model is constructed, the improved lion group optimization algorithm is introduced, automatic course arrangement is realized based on the method, the course arrangement efficiency and the convergence speed are improved, meanwhile, the resource allocation problem in the course arrangement problem can be flexibly and effectively managed, and efficient and stable multi-target automatic course arrangement is realized.

Description

Technical Field

[0001] The present invention relates to the technical field of intelligent class scheduling, and in particular to a multi-objective intelligent class scheduling method based on an improved lion group optimization algorithm. Background Art

[0002] As a combinatorial optimization problem, the course scheduling problem is still a challenge that universities around the world have to face every semester. At present, most universities still use manual course scheduling, which usually has problems such as low efficiency, lack of flexibility and difficulty in optimization. However, based on the larger and more complex data volume of university course scheduling, current intelligent course scheduling methods such as mathematical methods, heuristic methods and meta-heuristic methods are not suitable for university course scheduling. For example, mathematical methods are based on strict mathematical models and can guarantee the global optimality of solutions in small-scale course scheduling problems. However, as the scale and complexity of the problem increase, mathematical methods are insufficient in terms of computing time and resource consumption, and are prone to dimensionality disasters. Heuristic methods quickly generate feasible solutions through empirical rules and heuristic information of specific problems, without strict reliance on mathematical models, but may fall into local optimal solutions and lack global search capabilities. Meta-heuristic methods simulate evolution or intelligent behavior in nature for global search, which has strong versatility and flexibility, but has high computational cost, slow convergence speed, and cannot solve multi-objective course scheduling problems. Summary of the invention

[0003] The present invention provides a multi-objective intelligent course scheduling method based on an improved lion group optimization algorithm, so as to overcome the technical problem that the traditional course scheduling method is not suitable for multi-objective course scheduling in colleges and universities.

[0004] In order to achieve the above object, the technical solution of the present invention is:

[0005] A multi-objective intelligent class scheduling method based on an improved lion group optimization algorithm, characterized by comprising:

[0006] S1: Get class schedule information data;

[0007] S2: Establish a multi-objective scheduling model based on the average unevenness of students and teachers and the average vacancy rate of the scheduled classrooms;

[0008] S3: inputting the course scheduling information data into the multi-objective course scheduling model, and optimizing the results based on the improved lion group optimization algorithm, and obtaining the optimal solution based on the set optimization goal, which is the final course scheduling result;

[0009] The optimization goal is to minimize the average unevenness of students and teachers and the average vacancy rate of the arranged classrooms.

[0010] Furthermore, in S2, the multi-objective class scheduling model established based on the average unevenness of students and teachers and the average idleness rate of the scheduled classrooms includes the average unevenness model of students and teachers and the average idleness rate model of the scheduled classrooms;

[0011] The average heterogeneity model of students and teachers is expressed as:

[0012] TUni=α s SUni+α l LUni

[0013] Among them, SUni is the average unevenness model of students, LUni is the average unevenness model of teachers, α s is the student average unevenness weight, α l is the average unevenness weight of teachers;

[0014] The average vacancy rate model of the arranged classrooms is expressed as:

[0015]

[0016] Where R is the set of classrooms, and R = {r1, r2, …, r n ,…,r N}, where n, N∈N * And n <N,cap(r n ) indicates classroom r n The number of people that can be accommodated; In the time period p a , classroom n The number of seats actually used in the teaching week; P is the set of classes in the teaching week;

[0017] The constraints of the multi-objective scheduling model are set as follows:

[0018] The same student can only take one course at the same time, which is expressed as:

[0019]

[0020] The same teacher can only teach one course at the same time, which is expressed as:

[0021]

[0022] Among them, U(r) represents the set of teaching tasks selected by role r, where U(r)∈C and r∈S∪L, S is the set of students, and L is the set of all teachers; r∈S∪L means that role r can be any student or any teacher; when r is a student, U(S p ) represents student S p The selected teaching task set; when r is a teacher, U(l q) represents teacher l q The selected set of teaching tasks;

[0023] F(r,c m ,p a ) represents role r, i.e., student s p or teacher l q whether to take course c a during time period p m ,

[0024]

[0025] Only one course can be taken in the same classroom at the same time, which is expressed as:

[0026]

[0027] where S(r n ,c m ,p a ) represents whether classroom r n takes course c a during time period p m , and

[0028]

[0029] The number of seats in the classroom must be greater than or equal to the number of students taking classes in that classroom, which is expressed as:

[0030]

[0031] where std(c m ) represents the number of students selecting teaching task c m ; represents whether teaching task c m is taken in classroom r n , and

[0032]

[0033] Furthermore, the student average non-uniformity model is expressed as:

[0034]

[0035] where S is the set of students, and S = {s1, s2, …, s p , …, s P}, where p, P ∈ N * and p < P, P represents the total number of students; W is the set of teaching weeks, and W = {w1, w2, …, w u , …, w U}, where u, U ∈ N *and \(u < U\), where \(U\) represents the total number of teaching weeks; \(c(s p w u d v ) represents the number of classes of student \(s p in week \(w u on day \(d v ; \(D\) is the set of teaching days per week, and \(D=\{d_1, d_2, \ldots, d v , \ldots, d V \}, where \(v, V\in N * and \(v < V\), \(V\) represents the total number of teaching days per week; \(P\) is the set of class sessions in a teaching week, and \(P = W\times D\times T = W\times Y=\{p_1, p_2, \ldots, p a , \ldots, p A \}, \(A = U\times B\), \(A\) represents the total number of class sessions in a teaching week, and \(B\) represents the total number of class sessions per week; \(T\) is the set of class sessions per day, and \(T=\{t A , t_1, \ldots, t z , \ldots, t Z \}=T s \cup T x \cup T w , where \(z, Z\in N * and \(z < Z\), \(Z\) represents the total number of class sessions per day, and \(T s , T x , T w are the sets of class sessions in the morning, afternoon, and evening respectively; \(Y\) is the set of class sessions per week, and \(Y = D\times T=\{y_1, y_2, \ldots, y b , \ldots, y B \}, \(B = V\times Z\).

[0036] Furthermore, the teacher average non-uniformity model is expressed as:

[0037]

[0038] where \(L\) is the set of teachers, and \(L = \{l_1, l_2, \ldots, l q , \ldots, l Q \}, where \(q, Q\in N * and \(q < Q\); \(Q\) represents the total number of teachers; \(c(l q w u d v ) represents the number of classes of teacher \(l q in week \(w u on day \(d v .

[0039] Furthermore, in S3, the process of inputting the processed course scheduling information data into the multi-objective course scheduling model and performing result optimization based on the improved lion swarm optimization algorithm to obtain the optimal solution based on the set optimization objective is:

[0040] S31: Set the total number of lions in the lion group to K, the maximum number of iterations to J, and each lion represents a class scheduling method;

[0041] S32: Select KF lions as lionesses and KY lions as cubs, where KY=K-KF-1; the proportion of adult lions to the total number of lions is Be;

[0042] Initialize the position of each lion to obtain the initial historical optimal position of each lion, where the initial position of the kth lion, k∈[1,K], is expressed as:

[0043]

[0044] S33: Calculate the fitness value of each lion based on the multi-objective scheduling model, take the lion with the lowest fitness value as the optimal individual, thereby obtaining an initial global optimal position, and take the optimal individual as the lion king;

[0045] S34: updating the position of the k-th lion in sequence, and judging whether the updated position of the k-th lion satisfies the constraint conditions of the multi-objective scheduling model. If so, replacing the position of the k-th lion before the update with the updated position of the k-th lion; otherwise, retaining the position of the k-th lion before the update.

[0046] S35: Update the position of each lion, thereby updating the historical optimal position and the global optimal position;

[0047] S36: Determine whether the maximum number of iterations has been reached. If so, output the global optimal position, i.e., the optimal solution; otherwise, repeat S34-S35.

[0048] Furthermore, in S34 and S35, the process of updating the position of each lion is:

[0049] S351: Determine whether the k-th lion is a lion king, a lioness or a lion cub. If it is a lion king, execute S352; if it is a lioness, execute S353; if it is a lion cub, execute S354;

[0050] S352: From the teaching task set C = {c1, c2, ..., c m ,…,c M}, randomly select K α Teaching tasks, The set of perturbed teaching tasks that constitute the jth iteration of Lion King k is expressed as:

[0051]

[0052] The remaining K βThe teaching tasks constitute the unperturbed teaching task set of Lion King k's jth iteration, expressed as:

[0053]

[0054] Among them, α K is the disturbance coefficient of the Lion King teaching task, and α K =γ, γ is a random number generated according to the normal distribution N(0,1), which is limited to the interval [0,1] by truncation; M is the total number of teaching tasks, and K α +K β =M,

[0055] Set the perturbed class schedule information matrix of Lion King k's jth iteration to:

[0056]

[0057] The unperturbed class schedule information matrix of Lion King k's jth iteration is:

[0058]

[0059] in,

[0060] S353: In the teaching task set C = {c1, c2, ..., c m ,…,c M}, randomly select M α Teaching tasks, The set of perturbed teaching tasks that constitute the jth iteration of lioness k is expressed as:

[0061]

[0062] The remaining M β The teaching tasks constitute the unperturbed teaching task set of Lioness k at the jth iteration:

[0063]

[0064] Among them, α M is the disturbance coefficient of the lioness teaching task, and γ is a random number generated from N(0,1) according to the normal distribution, which is limited to the interval [0,1] by truncation; μ represents the step size factor; M α +M β =M,

[0065] Select Lioness K ′ As a collaborative hunting partner, the perturbed schedule information matrix of lioness k in the jth iteration is set to:

[0066]

[0067] The unperturbed schedule information matrix of Lioness k at the jth iteration is:

[0068]

[0069] in,

[0070] S354: In the teaching task set C = {c1, c2, ..., c m ,…,c M}, randomly select Y α Teaching tasks, The set of perturbed teaching tasks that constitute the jth iteration of cub k is expressed as:

[0071]

[0072] The remaining Y β The teaching tasks constitute the unperturbed teaching task set of the kth iteration of the lion cub:

[0073]

[0074] Among them, α Y is the disturbance coefficient of the lion cub teaching task, and γ is a random number generated from a normal distribution N(0,1), which is restricted to the interval [0,1] by truncation; Y α +Y β =M,

[0075] When the lion cub k follows the lion king to hunt, the perturbed schedule information matrix of the lion cub k's jth iteration is set to:

[0076]

[0077] When the lion cub k follows the lioness k′ to hunt, the perturbed schedule information matrix of the lion cub k at the jth iteration is:

[0078]

[0079] When the lion cub k is far away from the lion king's hunting, the perturbed schedule information matrix of the lion cub k's jth iteration is:

[0080]

[0081] The unperturbed class schedule information matrix of the jth iteration of the young lion k is:

[0082]

[0083] Among them, the position of the k-th lion after the j-th iteration is expressed as:

[0084]

[0085] Furthermore, in S35, the process of updating the historical optimal position and the global optimal position is:

[0086] 1) According to the multi-objective scheduling model, calculate the fitness value of K lions at the current position, that is, the average unevenness of students and teachers TUni k and the average vacancy rate of the classrooms Emp k ;

[0087] 2) Based on the fitness values ​​of the current positions and the historical optimal positions of the K lions, a total matrix is ​​formed, and the Pareto solution set is obtained using the Pareto sorting method. The j-th layer Pareto solution set is Pareto solution The fitness values ​​are and

[0088] 3) Calculate the Pareto solution The congestion degree is calculated as:

[0089]

[0090] In the formula,

[0091]

[0092] Where I is the total number of elements in the Pareto optimal solution set;

[0093] 4) Concentrate the first layer of Pareto solutions, The largest individual is taken as the new global optimal individual, thereby updating the global optimal individual; at the same time, determine whether the number of layers of the Pareto solution set corresponding to the current position of each lion is the same as the number of layers of the Pareto solution set corresponding to the historical optimal position. If they are the same, execute 4), otherwise, the lion position with a smaller number of layers of the Pareto solution set is taken as the new historical optimal position, thereby updating the historical optimal position;

[0094] 5) Determine the crowding degree of each lion’s current position and the crowding degree of the historical optimal position, that is, the corresponding If the congestion degree of the current position is greater, the current position is used as the new historical optimal position, thereby updating the historical optimal position; otherwise, the historical optimal position is not updated.

[0095] Furthermore, in S1, the obtained course schedule information data includes:

[0096] Basic student information, including student ID and name;

[0097] Teacher basic information, including teacher number and teacher name;

[0098] Basic classroom information, including classroom number, building number, classroom type, and number of people it can accommodate;

[0099] Teaching task information, including teaching task number, school year, semester, course number, teacher number, teaching class number, school year / semester, start week, end week, total course hours, whether it is an odd or even week, and weekly hours;

[0100] Course selection information, including teaching task number and student number.

[0101] Beneficial effects: The present invention constructs a multi-objective class scheduling model and introduces an improved lion group optimization algorithm. Based on the multi-objective class scheduling model and the set optimization goal, the optimal solution is obtained, which is the final class scheduling result. The optimization goal is to minimize the average unevenness of students and teachers and the average idle rate of the scheduled classrooms. Based on this method, automatic class scheduling is achieved, and the class scheduling efficiency and convergence speed are improved. The present invention can flexibly and effectively manage the resource allocation problem in the class scheduling problem, and realize efficient and stable multi-objective automatic class scheduling. BRIEF DESCRIPTION OF THE DRAWINGS

[0102] In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the following briefly introduces the drawings required for use in the embodiments or the description of the prior art. Obviously, the drawings described below are some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying creative labor.

[0103] Figure 1 It is a flow chart of a multi-objective intelligent class scheduling method based on an improved lion group optimization algorithm in the present invention;

[0104] Figure 2 The flowchart of the improved lion group optimization algorithm in the embodiment of the present invention. DETAILED DESCRIPTION

[0105] In order to make the purpose, technical solution and advantages of the embodiments of the present invention clearer, the technical solution in the embodiments of the present invention will be clearly and completely described below in conjunction with the drawings in the embodiments of the present invention. Obviously, the described embodiments are part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0106] This embodiment provides a multi-objective intelligent class scheduling method based on an improved lion group optimization algorithm. Figure 1 As shown, including:

[0107] S1: Get class schedule information data;

[0108] In a specific embodiment, in S1, the obtained course scheduling information data includes:

[0109] Basic student information, including student ID and name;

[0110] Teacher basic information, including teacher number and teacher name;

[0111] Basic classroom information, including classroom number, building number, classroom type, and number of people it can accommodate;

[0112] Teaching task information, including teaching task number, school year, semester, course number, teacher number, teaching class number, school year / semester, start week, end week, total course hours, whether it is an odd or even week, and weekly hours;

[0113] Course selection information, including teaching task number and student number.

[0114] S2: Establish a multi-objective scheduling model based on the average unevenness of students and teachers and the average vacancy rate of the scheduled classrooms;

[0115] In a specific embodiment, in S2, the multi-objective class scheduling model established based on the average unevenness of students and teachers and the average idleness rate of the scheduled classrooms includes a student and teacher average unevenness model and a scheduled classroom average idleness rate model;

[0116] Specifically, the student and teacher average unevenness model is expressed as:

[0117] TUni=α s SUni+α l LUni

[0118] Among them, SUni is the average unevenness model of students, LUni is the average unevenness model of teachers, α s is the student average unevenness weight, α l is the average unevenness weight of teachers;

[0119] The average vacancy rate model of the arranged classrooms is expressed as:

[0120]

[0121] Where R is the set of classrooms, and R = {r1, r2, …, r n ,…,r N}, where n, N∈N *And n <N,cap(r n ) indicates classroom r n The number of people that can be accommodated; In the time period p a , classroom n The number of seats actually used in the teaching week; P is the set of classes in the teaching week;

[0122] The constraints of the multi-objective scheduling model are set as follows:

[0123] The same student can only take one course at the same time, which is expressed as:

[0124]

[0125] The same teacher can only teach one course at the same time, which is expressed as:

[0126]

[0127] Among them, U(r) represents the set of teaching tasks selected by role r, where U(r)∈C and r∈S∪L, S is the set of students, and L is the set of all teachers; r∈S∪L means that role r can be any student or any teacher; when r is a student, U(S p ) represents student S p The selected teaching task set; when r is a teacher, U(l q ) indicates teacher l q The selected set of teaching tasks;

[0128] F(r,c m ,p a ) represents role r, i.e. student s p or teacher q Is it in time period p a Take the course c m ,

[0129]

[0130] Only one course can be taken in the same classroom at the same time, which is expressed as:

[0131]

[0132] Among them, S(r n ,c m ,p a ) indicates classroom r n Is it in time period p a Take the course c m ,and

[0133]

[0134] The number of seats in the classroom must be greater than or equal to the number of students attending classes in that classroom, expressed as:

[0135]

[0136] Among them, std(c m ) represents the number of students selecting teaching task c m ; represents whether teaching task c m is held in classroom r n , and

[0137]

[0138] In a specific embodiment, the student average non-uniformity model is expressed as:

[0139]

[0140] Among them, S is the set of students, and S = {s1, s2,..., s p ,..., s P}, where p, P ∈ N * and p < P, P represents the total number of students; W is the set of teaching weeks, and W = {w1, w2,..., w u ,..., w U}, where u, U ∈ N * and u < U, U represents the total number of teaching weeks; c(s p w u d v ) represents the number of classes attended by student s p in the d u -th week; D is the set of class days per week, and D = {d1, d2,..., d v}, where v, V ∈ N v and v < V, V represents the total number of class days per week; P is the set of class periods in teaching weeks, and P = W × D × T = W × Y = {p1, p2,..., p V}, A = U × B, A represents the total number of class periods in teaching weeks, B represents the total number of class periods per week; T is the set of class periods per day, and T = {t1, t2,..., t *}, where z, Z ∈ N a and z < Z, Z represents the total number of class periods per day, and T A}, A = U × B, A represents the total number of class periods in teaching weeks, B represents the total number of class periods per week; T is the set of class periods per day, and T = {t1, t2,..., t z}, where z, Z ∈ N Z} = T s ∪T x ∪T w , where z, Z ∈ N * and z < Z, Z represents the total number of class periods per day, and T s 、T x 、Tw are the sets of class sessions in the morning, afternoon, and evening respectively; Y is the set of class sessions per week, and Y = D × T = {y1, y2, …, y b , …, y B}, B = V × Z.

[0141] In a specific embodiment, the teacher average non-uniformity model is expressed as:

[0142]

[0143] where L is the set of teachers, and L = {l1, l2, …, l q , …, l Q}, where q, Q ∈ N * and q < Q; Q represents the total number of teachers; c(l q w u d v ) represents the number of classes taught by teacher l q on the d u -th day of the w v -th week.

[0144] Specifically, in this embodiment, an average classroom idle rate model is set to evaluate the idle situation of classrooms. The lower the idle rate of each classroom, the better the utilization rate. Therefore, the lower the average classroom idle rate of the scheduled classrooms, the better. An average non-uniformity of students and teachers is set to evaluate the rationality of the course arrangement for teachers or students, avoiding the situation where the courses of teachers or students are concentrated on a certain day and there are no classes at other times. Therefore, in this embodiment, the lower the average non-uniformity of students and teachers, the better.

[0145] S3: Input the course scheduling information data into the multi-objective course scheduling model, and perform result optimization based on the improved lion swarm optimization algorithm to obtain the optimal solution based on the set optimization objective, which is the final course scheduling result;

[0146] Specifically, the optimization objective is to minimize the average non-uniformity of students and teachers and the average idle rate of the scheduled classrooms.

[0147] In a specific embodiment, in S3, the processed course scheduling information data is input into the multi-objective course scheduling model. As Figure 2 shown, the process of performing result optimization based on the improved lion swarm optimization algorithm and obtaining the optimal solution based on the set optimization objective is as follows:

[0148] S31: Set the total number of lions in the lion swarm to K and the maximum number of iterations to J, where each lion represents a course scheduling method;

[0149] S32: Select KF lions as female lions and KY lions as cubs, where KY=K-KF-1; the proportion of adult lions to the total number of lions is Be;

[0150] Initialize the position of each lion to obtain the initial historical optimal position of each lion, where the initial position of the kth lion, k∈[1,K], is expressed as:

[0151]

[0152] S33: Calculate the fitness value of each lion based on the multi-objective scheduling model, take the lion with the lowest fitness value as the optimal individual, thereby obtaining an initial global optimal position, and take the optimal individual as the lion king;

[0153] S34: updating the position of the k-th lion in sequence, and judging whether the updated position of the k-th lion satisfies the constraint conditions of the multi-objective scheduling model. If so, replacing the position of the k-th lion before the update with the updated position of the k-th lion; otherwise, retaining the position of the k-th lion before the update.

[0154] S35: Update the position of each lion, thereby updating the historical optimal position and the global optimal position;

[0155] S36: Determine whether the maximum number of iterations has been reached. If so, output the global optimal position, i.e., the optimal solution; otherwise, repeat S34-S35.

[0156] In a specific embodiment, in S34 and S35, the process of updating the position of each lion is:

[0157] S351: Determine whether the k-th lion is a lion king, a lioness or a lion cub. If it is a lion king, execute S352; if it is a lioness, execute S353; if it is a lion cub, execute S354;

[0158] S352: From the teaching task set C = {c1, c2, ..., c m ,…,c M}, randomly select K α Teaching tasks, The set of perturbed teaching tasks that constitute the jth iteration of Lion King k is expressed as:

[0159]

[0160] The remaining K β The teaching tasks constitute the unperturbed teaching task set of Lion King k's jth iteration, expressed as:

[0161]

[0162] Among them, α K is the disturbance coefficient of the Lion King teaching task, and αK =γ, γ is a random number generated according to the normal distribution N(0,1), which is limited to the interval [0,1] by truncation; M is the total number of teaching tasks, and K α +K β =M,

[0163] Set the perturbed class schedule information matrix of Lion King k's jth iteration to:

[0164]

[0165] The unperturbed class schedule information matrix of Lion King k's jth iteration is:

[0166]

[0167] in,

[0168] S353: In the teaching task set C = {c1, c2, ..., c m ,…,c M}, randomly select M α Teaching tasks, The set of perturbed teaching tasks that constitute the jth iteration of lioness k is expressed as:

[0169]

[0170] The remaining M β The teaching tasks constitute the unperturbed teaching task set of Lioness k at the jth iteration:

[0171]

[0172] Among them, α M is the disturbance coefficient of the lioness teaching task, and γ is a random number generated from N(0,1) according to the normal distribution, which is limited to the interval [0,1] by truncation; μ represents the step size factor; M α +M β =M,

[0173] Select Lioness K ′ As a collaborative hunting partner, the perturbed schedule information matrix of lioness k in the jth iteration is set to:

[0174]

[0175] The unperturbed schedule information matrix of Lioness k at the jth iteration is:

[0176]

[0177] in,

[0178] S354: In the teaching task set C = {c1, c2, ..., c m ,…,c M}, randomly select Y α Teaching tasks, The set of perturbed teaching tasks that constitute the jth iteration of cub k is expressed as:

[0179]

[0180] The remaining Y β The teaching tasks constitute the unperturbed teaching task set of the kth iteration of the lion cub:

[0181]

[0182] Among them, α Y is the disturbance coefficient of the lion cub teaching task, and γ is a random number generated from a normal distribution N(0,1), which is restricted to the interval [0,1] by truncation; Y α +Y β =M,

[0183] When the lion cub k follows the lion king to hunt, the perturbed schedule information matrix of the lion cub k's jth iteration is set to:

[0184]

[0185] When the lion cub k follows the lioness k′ to hunt, the perturbed schedule information matrix of the lion cub k at the jth iteration is:

[0186]

[0187] When the lion cub k is far away from the lion king's hunting, the perturbed schedule information matrix of the lion cub k's jth iteration is:

[0188]

[0189] The unperturbed class schedule information matrix of the jth iteration of the young lion k is:

[0190]

[0191] Among them, the position of the k-th lion after the j-th iteration is expressed as:

[0192]

[0193] Specifically, the existing lion group optimization algorithm is aimed at solving continuous problems, and since the class scheduling problem is discrete, in this embodiment, the update formulas of the existing lion king, lionesses and lion cubs are improved accordingly to meet the needs of optimizing the discrete problem of class scheduling.

[0194] In a specific embodiment, in S35, the process of updating the historical optimal position and the global optimal position is:

[0195] 1) According to the multi-objective scheduling model, calculate the fitness value of K lions at the current position, that is, the average unevenness of students and teachers TUni k and the average vacancy rate of the classrooms Emp k ;

[0196] 2) Based on the fitness values ​​of the current positions and the historical optimal positions of the K lions, a total matrix is ​​formed, and the Pareto solution set is obtained using the Pareto sorting method. The j-th layer Pareto solution set is Pareto solution The fitness values ​​are and

[0197] 3) Calculate the Pareto solution The congestion degree is calculated as:

[0198]

[0199] In the formula,

[0200]

[0201] Where I is the total number of elements in the Pareto optimal solution set;

[0202] 4) Concentrate the first layer of Pareto solutions, The largest individual is taken as the new global optimal individual, thereby updating the global optimal individual; at the same time, determine whether the number of layers of the Pareto solution set corresponding to the current position of each lion is the same as the number of layers of the Pareto solution set corresponding to the historical optimal position. If they are the same, execute 4), otherwise the position with a smaller number of layers of the Pareto solution set is taken as the new historical optimal position, thereby updating the historical optimal position;

[0203] 5) Determine the crowding degree of each lion’s current position and the crowding degree of the historical optimal position, that is, the corresponding If the congestion degree of the current position is greater, the current position is used as the new historical optimal position, thereby updating the historical optimal position; otherwise, the historical optimal position is not updated.

[0204] Specifically, after Pareto sorting all lions, each lion contains two attributes, one is the layer number and the other is the crowding degree. Suppose there are two lions a and b, lion a is on the 3(j) layer and lion b is on the 5(j) layer. At this time, there is no need to compare the crowding degree, just the layer number. The smaller the layer number, the better. The 3 of lion a is less than the 5 of lion b, so the position of lion a is better. When lion a is on the 3(j) layer and lion b is also on the 3(j) layer, it is necessary to compare the crowding degree. If the crowding degree of a is 200 and the crowding degree of b is 300, it means that the position of lion b with a higher crowding degree is better.

[0205] Specifically, in S33, after initializing the position of each lion, the fitness value of each lion is calculated based on the multi-objective scheduling model. Since in this embodiment, the fitness value obtained is multi-objective, it is impossible to simply determine the lowest fitness value by comparing the sizes. In this embodiment, based on the method proposed in 2), the individual with the largest congestion in the first layer of Pareto solution set is found, that is, the lion individual with the lowest fitness value, as the initial global optimal position.

[0206] Specifically, the historical optimal position of the kth lion after the first j iterations is:

[0207]

[0208] The global optimal position among the K lions at the jth iteration is:

[0209]

[0210] In order to verify the effectiveness of the method proposed in this embodiment, the course information of the first semester of the 2023-2024 academic year of a certain university was obtained, including 2897 students, 332 teachers, 393 classrooms, 385 teaching tasks and 23534 person-times of course selection information. After automatic class scheduling, it took 5.4 hours to obtain a feasible solution. The average unevenness of students and teachers was 19663.1, and the idle rate of the scheduled classrooms was 0.23; the average satisfaction of the actual manual class scheduling was 31230.9, the classroom idle rate was 0.45, and manual class scheduling required 3 people and took about 40 hours.

[0211] Specifically, this embodiment also uses the ITC-2019 class schedule information dataset, compares the method in this embodiment with the existing simulated annealing algorithm, mixed integer linear programming model, and graph-based mixed integer programming model, and uses a penalty value to describe the quality of the algorithm. The penalty value formula is:

[0212] penalty = pen t +pen r +10×(pen d +cons ) (30)

[0213] Among them, penalty is the total penalty of the course scheduling plan, pen t is the time penalty value of the course scheduling plan, pen r is the classroom penalty value of the class scheduling plan, pen d is the penalty value for violating the specified constraints in the course scheduling plan, s is the number of student conflicts in the class scheduling plan. The penalty value results are shown in Table 1. The method proposed in this embodiment can flexibly cope with various constraints and effectively manage resource allocation in the class scheduling problem, reduce the total penalty value of the class scheduling plan, and achieve efficient and stable multi-objective automatic class scheduling.

[0214] Table 1:

[0215]

[0216] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, rather than to limit it. Although the present invention has been described in detail with reference to the aforementioned embodiments, those skilled in the art should understand that they can still modify the technical solutions described in the aforementioned embodiments, or replace some or all of the technical features therein with equivalents. However, these modifications or replacements do not cause the essence of the corresponding technical solutions to deviate from the scope of the technical solutions of the embodiments of the present invention.

Claims

1. A multi-objective intelligent class scheduling method based on an improved lion group optimization algorithm, characterized in that: include: S1: Get class schedule information data; S2: Establish a multi-objective scheduling model based on the average unevenness of students and teachers and the average vacancy rate of the scheduled classrooms; S3: inputting the course scheduling information data into the multi-objective course scheduling model, and optimizing the results based on the improved lion group optimization algorithm, and obtaining the optimal solution based on the set optimization goal, which is the final course scheduling result; The optimization goal is to minimize the average unevenness of students and teachers and the average vacancy rate of the arranged classrooms.

2. The multi-objective intelligent class scheduling method based on the improved lion group optimization algorithm according to claim 1 is characterized in that: In S2, the multi-objective scheduling model established based on the average unevenness of students and teachers and the average idle rate of the scheduled classrooms includes the average unevenness model of students and teachers and the average idle rate model of the scheduled classrooms; The average heterogeneity model of students and teachers is expressed as: TUni=α s SUni+α l Monday Among them, SUni is the average unevenness model of students, LUni is the average unevenness model of teachers, α s is the student average unevenness weight, α l is the average unevenness weight of teachers; The average vacancy rate model of the arranged classrooms is expressed as: Where R is the set of classrooms, and R = {r1, r2, …, r n ,…,r N }, where n, N∈N * And n <N,cap(r n ) indicates classroom r n The number of people that can be accommodated; In the time period p a , classroom n The number of seats actually used in the teaching week; P is the set of classes in the teaching week; The constraints of the multi-objective scheduling model are set as follows: The same student can only take one course at the same time, which is expressed as: The same teacher can only teach one course at the same time, which is expressed as: Among them, U(r) represents the set of teaching tasks selected by role r, where U(r)∈C and r∈S∪L, S is the set of students, and L is the set of all teachers; r∈S∪L means that role r can be any student or any teacher; when r is a student, U(S p ) represents student S p The selected teaching task set; when r is a teacher, U(l q ) indicates teacher l q The selected set of teaching tasks; F(r,c m ,p a ) represents role r, i.e. student s p or teacher q Is it in time period p? a Take the course c m , Only one course can be taken in the same classroom at the same time, which is expressed as: Among them, S(r n ,c m ,p a ) indicates classroom r n Is it in time period p? a Take the course c m ,and The number of seats in a classroom must be greater than or equal to the number of students in the classroom, expressed as: Among them, std(c m ) indicates the selection of teaching task c m Number of students; Represents teaching task c m In the classroom? n Classes, and 3. The multi-objective intelligent class scheduling method based on the improved lion group optimization algorithm according to claim 2 is characterized in that: The student average heterogeneity model is expressed as: Among them, S is the set of students, and S = {s1, s2, …, s p , …, s P}, where p, P ∈ N * and p < P, P represents the total number of students; W is the set of teaching weeks, and W = {w1, w2, …, w u , …, w U}, where u, U ∈ N * and u < U, U represents the total number of teaching weeks; c(s p w u d v ) represents the number of class sessions of student s p in the d u -th day of the w v -th week; D is the set of class days per week, and D = {d1, d2, …, d v , …, d V}, where v, V ∈ N * and v < V, V represents the total number of class days per week; P is the set of class periods in teaching weeks, and P = W × D × T = W × Y = {p1, p2, …, p a , …, p A}, A = U × B, A represents the total number of class periods in teaching weeks, B represents the total number of class periods per week; T is the set of class periods per day, and T = {t1, t2, …, t z , …, t Z} = T s ∪ T x ∪ T w , where z, Z ∈ N * and z < Z, Z represents the total number of class periods per day, and T s , T x , T w are the sets of class periods in the morning, afternoon, and evening respectively; Y is the set of class periods per week, and Y = D × T = {y1, y2, …, y b , …, y B}, B = V × Z.

4. The multi-objective intelligent class scheduling method based on the improved lion group optimization algorithm according to claim 3 is characterized in that: The teacher average unevenness model is expressed as: Among them, \(L\) is the set of teachers, and \(L = \{l_1, l_2, \ldots, l q , \ldots, l Q \}\), where \(q, Q\in N * and \(q < Q\); \(Q\) represents the total number of teachers; \(c(l q w u d v )\) represents the number of classes of teacher \(l q on the \(d u -th day of the \(w v -th week.

5. The multi-objective intelligent class scheduling method based on the improved lion group optimization algorithm according to claim 4 is characterized in that: In S3, the processed course scheduling information data is input into the multi-objective course scheduling model, and the result is optimized based on the improved lion group optimization algorithm. The process of obtaining the optimal solution based on the set optimization goal is as follows: S31: Set the total number of lions in the lion group to K, the maximum number of iterations to J, and each lion represents a class scheduling method; S32: Select KF lions as lionesses and KY lions as cubs, where KY=K-KF-1; the proportion of adult lions to the total number of lions is Be; Initialize the position of each lion to obtain the initial historical optimal position of each lion, where the initial position of the kth lion, k∈[1,K], is expressed as: S33: Calculate the fitness value of each lion based on the multi-objective scheduling model, take the lion with the lowest fitness value as the optimal individual, thereby obtaining an initial global optimal position, and take the optimal individual as the lion king; S34: updating the position of the k-th lion in sequence, and judging whether the updated position of the k-th lion satisfies the constraint conditions of the multi-objective scheduling model. If so, replacing the position of the k-th lion before the update with the updated position of the k-th lion; otherwise, retaining the position of the k-th lion before the update. S35: Update the position of each lion, thereby updating the historical optimal position and the global optimal position; S36: Determine whether the maximum number of iterations has been reached. If so, output the global optimal position, i.e., the optimal solution; otherwise, repeat S34-S35.

6. The multi-objective intelligent class scheduling method based on the improved lion group optimization algorithm according to claim 5 is characterized in that: In S34 and S35, the process of updating the position of each lion is: S351: Determine whether the k-th lion is a lion king, a lioness or a lion cub. If it is a lion king, execute S352; if it is a lioness, execute S353; if it is a lion cub, execute S354; S352: From the teaching task set C = {c1, c2, ..., c m ,…,c M }, randomly select K α Teaching tasks, The set of perturbed teaching tasks that constitute the jth iteration of Lion King k is expressed as: The remaining K β The teaching tasks constitute the unperturbed teaching task set of Lion King k's jth iteration, expressed as: Among them, α K is the disturbance coefficient of the Lion King teaching task, and α K =γ, γ is a random number generated according to the normal distribution N(0,1), which is limited to the interval [0,1] by truncation; M is the total number of teaching tasks, and K α +K β =M, Set the perturbed class schedule information matrix of Lion King k's jth iteration to: The unperturbed class schedule information matrix of Lion King k's jth iteration is: in, S353: In the teaching task set C = {c1, c2, ..., c m ,…,c M }, randomly select M α Teaching tasks, The set of perturbed teaching tasks that constitute the jth iteration of lioness k is expressed as: The remaining M β The teaching tasks constitute the unperturbed teaching task set of Lioness k at the jth iteration: Among them, α M is the disturbance coefficient of the lioness teaching task, and γ is a random number generated from N(0,1) according to the normal distribution, which is limited to the interval [0,1] by truncation; μ represents the step size factor; M α +M β =M, Select lioness k′ as a cooperative hunting partner, and set the perturbed class schedule information matrix of lioness k at the hth iteration to: The unperturbed schedule information matrix of Lioness k at the jth iteration is: in, S354: In the teaching task set C = {c1, c2, ..., c m ,…,c M }, randomly select Y α Teaching tasks, The set of perturbed teaching tasks that constitute the jth iteration of cub k is expressed as: The remaining Y β The teaching tasks constitute the unperturbed teaching task set of the kth iteration of the lion cub: Among them, α Y is the disturbance coefficient of the lion cub teaching task, and γ is a random number generated from a normal distribution N(0,1), which is restricted to the interval [0,1] by truncation; Y α +Y β =M, When the lion cub k follows the lion king to hunt, the perturbed schedule information matrix of the lion cub k's jth iteration is set to: When the lion cub k follows the lioness k′ to hunt, the perturbed schedule information matrix of the lion cub k at the jth iteration is: When the lion cub k is far away from the lion king's hunting, the perturbed schedule information matrix of the lion cub k's jth iteration is: The unperturbed class schedule information matrix of the jth iteration of the young lion k is: Among them, the position of the k-th lion after the j-th iteration is expressed as:

7. The multi-objective intelligent class scheduling method based on the improved lion group optimization algorithm according to claim 6 is characterized in that: In S35, the process of updating the historical optimal position and the global optimal position is: 1) According to the multi-objective scheduling model, calculate the fitness value of K lions at the current position, that is, the average unevenness of students and teachers TUni k and the average vacancy rate of the classrooms Emp k ; 2) Based on the fitness values ​​of the current positions and the historical optimal positions of the K lions, a total matrix is ​​formed, and the Pareto solution set is obtained using the Pareto sorting method. The j-th layer Pareto solution set is Pareto solution The fitness values ​​are and 3) Calculate the Pareto solution The congestion degree is calculated as: In the formula, Where I is the total number of elements in the Pareto optimal solution set; 4) Concentrate the first-level Pareto solutions, The largest individual is taken as the new global optimal individual, thereby updating the global optimal individual; at the same time, determine whether the number of layers of the Pareto solution set corresponding to the current position of each lion is the same as the number of layers of the Pareto solution set corresponding to the historical optimal position. If they are the same, execute 4), otherwise, the lion position with a smaller number of layers of the Pareto solution set is taken as the new historical optimal position, thereby updating the historical optimal position; 5) Determine the crowding degree of each lion’s current position and the crowding degree of the historical optimal position, that is, the corresponding If the congestion degree of the current position is greater, the current position is used as the new historical optimal position, thereby updating the historical optimal position; otherwise, the historical optimal position is not updated.

8. The multi-objective intelligent class scheduling method based on the improved lion group optimization algorithm according to claim 1 is characterized in that: In S1, the obtained course scheduling information data includes: Basic student information, including student ID and name; Teacher basic information, including teacher number and teacher name; Basic classroom information, including classroom number, building number, classroom type, and number of people it can accommodate; Teaching task information, including teaching task number, school year, semester, course number, teacher number, teaching class number, school year / semester, start week, end week, total course hours, whether it is an odd or even week, and weekly hours; Course selection information, including teaching task number and student number.

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