CN111079976B - Lesson arranging method based on improved simulated annealing and hill climbing algorithm mixed search - Google Patents
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Abstract
The invention relates to a course arrangement method based on improved simulated annealing and hill climbing algorithm hybrid search, which comprises the following steps: setting basic data, course arrangement requirements and rules; calculating an evaluation function and algorithm parameters of the class solution; randomly generating an initial class-solution list; generating a local optimal solution by using a hill climbing algorithm and calculating a simulated annealing initial temperature; the method comprises the steps of processing a local optimal solution by using an improved simulated annealing algorithm, firstly, strategically selecting a switching neighborhood of the solution and switching to generate a new neighborhood solution, obtaining the local optimal neighborhood solution by using a hill climbing algorithm on the neighborhood solution, adopting probability to accept the local optimal neighborhood solution, and updating the best local optimal solution and switching neighborhood selection probability; and circularly executing the simulated annealing strategy to select disturbance and a hill climbing algorithm until the algorithm converges and exits, outputting a local optimal class-solution list with the minimum punishment value, and generating a corresponding class-arrangement list. The beneficial effects of the invention are as follows: solves the problem of difficult course arrangement of new college entrance examination, saves teaching resources such as teachers, time of class, classrooms and the like and has better course arrangement result.
Description
Technical Field
The invention belongs to the field of teaching management, and particularly relates to a lesson arranging method based on improved simulated annealing and hill climbing algorithm mixed search.
Background
In 2014, the education department issues "the opinion about the implementation of the level examination of the general high school, announces that comprehensive reform of the high examination will be performed nationally since 2017, that is, examination is performed on 3 subjects among politics, geographies, histories, physics, chemistry, and biology except 3 subjects nationally in the number of words in the high examination.
In 2019, the education department announces that the third college entrance examination comprehensive reform province (Hebei, liaoning, jiangsu, fujian, hubei, hunan, guangdong, chongqing) determines that the examination selection mode is '3+1+2', namely '3' refers to the three subjects outside the number of words which need to be selected, '1' refers to one of history or physics, and '2' refers to the selection of two subjects from biology, chemistry, geography and politics, and the total score is counted according to the grade score.
The problem of course arrangement is NP complete, and algorithms such as genetic algorithm, simulated annealing, ant colony, exhaustion, tabu search and the like are not used for solving the problem in the current industry, and as new college entrance reforms, the combination of selection and department is more, teaching layering makes course arrangement more and more difficult, manual course arrangement is impossible, and the traditional course arrangement method is also difficult to meet the course arrangement requirement.
The prior art has the problems of increasing teaching resources such as teachers, lessons, classrooms and the like and has unsatisfactory lesson arrangement results.
Disclosure of Invention
The invention aims at solving at least one of the technical problems existing in the prior art, provides a course arranging method based on the mixed search of the improved simulated annealing and the climbing algorithm, simultaneously uses the algorithm ideas of the genetic algorithm and the tabu search, integrates the mixed search course arranging method of various algorithm ideas, can save teaching resources and has better course arranging results, solves the course arranging problem in the 3+3 or 3+1+2 mode of the new college entrance examination, meets the requirements of open combination, multi-level teaching, no increase of classroom teacher resources, various hardness and softness teaching of all selected departments of the new college entrance examination, and realizes the personalized requirements of 100% course arranging, zero conflict, zero manual intervention and zero adjustment of the new college entrance examination, one-time table, one-teacher-one-time table and the like.
The technical scheme of the invention comprises a course arrangement method based on improved simulated annealing and hill climbing algorithm mixed search, and is characterized by comprising the following steps: s100, setting a student selection list, a teacher schedule list, a teaching task list and a course arrangement requirement and course arrangement rule; s200, calculating an evaluation function of a class solution violating hard constraint and soft constraint penalty value, calculating parameters required by a class arrangement algorithm, and carrying out optimization calculation on a teaching class according to the setting of S100; s300, randomly generating an initial class-solution list; s400, generating a local optimal solution by using a hill climbing algorithm, calculating a simulated annealing initialization temperature, and taking the solution as a best local optimal solution class table; s500, processing a local optimal solution by using an improved simulated annealing algorithm, firstly, strategically selecting a switching neighborhood of the solution and carrying out switching to generate a new neighborhood solution, obtaining the local optimal neighborhood solution by using a hill climbing algorithm on the neighborhood solution, adopting Metropolis criterion probability to accept the local optimal neighborhood solution, if so, returning to the original local optimal solution and reducing probability coefficients of the selected neighborhood being selected again, and if the new solution is better than the best local optimal solution, taking the new solution as the best local optimal solution class table, and updating the simulated annealing temperature; and S600, the step S500 is circulated until the exit condition is reached, the best local optimal class-solution list result is output, and a corresponding class-arrangement list is generated.
According to the lesson scheduling method based on the hybrid search of the improved simulated annealing and hill climbing algorithm, S100 specifically includes: s110, setting basic data, wherein the basic data comprise students, teachers, courses, classrooms, time of class, administrative classes, teaching classes and teaching levels; s120, setting a student selection list, a teacher arrangement list and a teaching task list; s130, setting course arrangement requirements and course arrangement rules.
According to the lesson scheduling method based on the hybrid search of the improved simulated annealing and hill climbing algorithm, S130 specifically includes: the method is used for correspondingly setting the walking level, teaching requirement, teacher work sharing, no course arrangement, single and double week courses, combined courses, mutual exclusion courses, occupied courses and school individuation requirements.
According to the lesson scheduling method based on the hybrid search of the improved simulated annealing and hill climbing algorithm, S200 specifically includes: s210, calculating an evaluation function of a class solution violating hard constraint and soft constraint penalty values, wherein the violating hard constraint penalty values represent penalty values of student class table conflicts, teacher class table conflicts and course class table conflicts, and the soft constraint penalty values represent penalty values of one or more sub-items of the class table violating class arrangement rules; s220, according to class arrangement requirements and rules, applying and initializing weight parameters violating rigid constraint and soft constraint penalty value evaluation functions, calculating whether an elite retention strategy alpha is used in a selection strategy, wherein the value 0 or 1 can be adopted, a roulette selection strategy or a tournament selection strategy beta can be adopted, the value 0 or 1 can be adopted, the values of alpha and beta are related to a student selection table, the value eta of the tournament coefficient is adopted, the probability drop coefficient gamma of the selected neighborhood being selected again is calculated, and the simulated annealing neighborhood generates disturbance proportion zeta, initial temperature coefficient epsilon, temperature drop coefficient kappa, maximum circulation times delta, continuous non-optimal withdrawal times lambda and the fastest neighborhood coefficient theta; s230, optimizing and calculating all teaching units according to the input student selection list, teacher arrangement list and teaching task list, wherein the teaching units consist of courses, teaching teachers and teaching student triplets, and generating a teaching class with balanced number of students and minimum conflict after optimizing.
According to the lesson scheduling method based on the hybrid search of the improved simulated annealing and hill climbing algorithm, S300 specifically includes: s310, distributing teaching resource units according to the demand number of the lessons for all the teaching units according to one solution of the algorithm, wherein the teaching resource units are Cartesian products of the lessons T and classrooms R; s320, generating a lesson list initial solution randomly, namely randomly distributing teaching resource units for each teaching unit.
According to the lesson scheduling method based on the hybrid search of the improved simulated annealing and hill climbing algorithm, S400 specifically includes: s410, calculating all neighborhoods of the solution; s420, calculating a neighborhood violation course arrangement rule penalty value of the solution, and storing a neighborhood with a penalty value smaller than the original solution penalty value into a better neighborhood set; s430, generating a random number between 0 and 1, randomly selecting a neighborhood from a better neighborhood set as a new solution if the random number is smaller than a maximum neighborhood coefficient theta, otherwise, selecting an optimal neighborhood solution with the minimum penalty value from the better neighborhood set as the new solution; s440, cycling the steps S410-S430 until no more optimal neighborhood exists, namely the solution is a local optimal solution; s450, taking the local optimal solution as a best local optimal solution class table. S460, calculating the simulated annealing initialization temperature as the local optimal solution penalty value.
The lesson ranking method based on the hybrid search of the improved simulated annealing and the hill climbing algorithm, wherein the neighborhood generation of the solution in S410 includes: exchanging two courses, namely, one allocated teaching resource rt1 of the teaching unit tu1 and one allocated teaching resource rt2 of the other teaching unit tu2, wherein tu1 and tu2 cannot be empty at the same time, rt1 and rt2 cannot be empty, tu1 can use rt2, and tu2 can use rt1; two lessons are exchanged, teaching lesson time t1 with t2, i.eWhen rt1 and rt2 can be exchanged, all the exchanged conditions are identical to the exchanged conditions of the two courses.
According to the lesson scheduling method based on the hybrid search of the improved simulated annealing and the hill climbing algorithm, S500 specifically includes processing a locally optimal lesson list by using the improved simulated annealing algorithm, including: s510, calculating punishment values of all teaching units against hard constraints and soft constraints; s520, strategy selection disturbance proportion ζ is equal to TU and is equal to TU; s530, generating a disturbance solution for disturbance executed in the execution of the teaching unit selected from the class list solution, and generating a new local optimal solution by using a hill climbing algorithm; s540, adopting Metropolis criterion to probability of receiving a local optimal neighborhood solution as a new local optimal solution, namely: Δt=new local optimal solution penalty value-original local optimal solution penalty value, Δt <0 accepted, Δt >0 accepted with probability exp (- Δt/T), if accepted, the neighborhood solution is new local optimal solution, if not accepted, the neighborhood solution is backed back to original local optimal solution and the probability coefficient of the selected neighborhood being selected again is reduced, the probability penalty value of the selected teaching unit being selected again is equal to its original value multiplied by probability drop coefficient γ; s550, when the new local optimal solution is better than the best local optimal solution, the new solution is used as the best local optimal solution class table; s560, updating the simulated annealing temperature to be the original temperature multiplied by the temperature drop coefficient kappa.
According to the lesson scheduling method based on the hybrid search of the improved simulated annealing and hill climbing algorithm, the S520 selection strategy comprises: the "elite retention" strategy, when adopted, the teaching unit with the largest penalty value in S510 is selected; the selection strategy of the roulette wheel is adopted, and the probability of the teaching unit selected in S510 is proportional to the penalty value of the teaching unit; when the selection strategy of the tournament is adopted, firstly, randomly selecting eta teaching units of the tournament coefficient during each selection, and then selecting the teaching unit with the largest punishment value from the eta teaching units. All choices are put-back free and repeat free choices, whether to use the "elite retention" strategy is determined by parameter α, and whether to use the "roulette" or "tournament" selection strategy is determined by parameter β.
According to the lesson scheduling method based on the hybrid search of the improved simulated annealing and hill climbing algorithm, S600 specifically includes: s610, executing the step S500 in a circulating way until the circulating times reach the maximum circulating times delta, or when the times of continuously not having better solutions in the step S500 reach the continuously not having optimal solution withdrawal times lambda, or the penalty value of the best local optimal solution is 0, and exiting in a circulating way; and S620, the best local optimal solution is a school timetable arrangement result, and school timetable information such as student school timetables, teacher school timetables, classroom school timetables, class school timetables and the like is output.
The beneficial effects of the invention are as follows: solves the problem of difficult course arrangement of new college entrance examination, saves teaching resources such as teachers, time of class, classrooms and the like and has better course arrangement result.
Drawings
The invention is further described below with reference to the drawings and examples;
FIG. 1 is a general flow diagram according to an embodiment of the present invention;
FIG. 2 is a flowchart of a hill climbing algorithm according to an embodiment of the present invention;
FIG. 3 shows a class-ranking result-student desk according to an embodiment of the present invention;
fig. 4 shows a lesson-ranking results-teacher lesson table according to an embodiment of the present invention.
Detailed Description
Reference will now be made in detail to the present embodiments of the present invention, examples of which are illustrated in the accompanying drawings, wherein the accompanying drawings are used to supplement the description of the written description so that one can intuitively and intuitively understand each technical feature and overall technical scheme of the present invention, but not to limit the scope of the present invention.
In the description of the present invention, a number means one or more, a number means two or more, and greater than, less than, exceeding, etc. are understood to not include the present number, and above, below, within, etc. are understood to include the present number. The description of the first and second is for the purpose of distinguishing between technical features only and should not be construed as indicating or implying relative importance or implicitly indicating the number of technical features indicated or implicitly indicating the precedence of the technical features indicated.
In the description of the present invention, unless explicitly defined otherwise, terms such as arrangement and the like should be construed broadly, and those skilled in the art can reasonably determine the specific meaning of the terms in the present invention in combination with the specific contents of the technical scheme.
Fig. 1 shows a general flow chart according to an embodiment of the invention.
Setting a student selection list, a teacher arrangement list, a teaching task list, a course arrangement requirement and a course arrangement rule; calculating an evaluation function of the class list solution violating the hard constraint and the soft constraint penalty value, calculating parameters required by a class arrangement algorithm, and carrying out optimization calculation on the teaching class according to the setting; randomly generating an initial class-solution list; generating a local optimal solution by using a hill climbing algorithm, calculating a simulated annealing initialization temperature, and taking the solution as a best local optimal solution class table; the method comprises the steps of processing a local optimal solution by using an improved simulated annealing algorithm, firstly, strategically selecting a switching neighborhood of the solution and carrying out switching to generate a new neighborhood solution, obtaining the local optimal neighborhood solution by using a hill climbing algorithm on the neighborhood solution, adopting Metropolis criterion probability to accept the local optimal neighborhood solution, if so, returning to the original local optimal solution and reducing probability coefficients of the selected neighborhood again, and when the new solution is superior to the best local optimal solution, taking the new solution as a best local optimal solution class table, and updating simulated annealing temperature; and outputting the best local optimal class-solution list result to generate a corresponding class-solution list.
According to the technical scheme, the technical scheme of the invention provides a more specific implementation mode, which comprises the following steps:
1. inputting student selection list, teacher arrangement list, teaching task, and setting class arrangement requirement and rule
1.1, a student selection list comprises student IDs, local administrative office IDs, belonging layer IDs and a course ID set;
1.2, a teacher schedule comprises a teacher ID, a teaching course ID, a class number of the teaching course ID, a teaching class ID, a subject group, at most a few classes a day and forbidden arrangement time;
1.3, a teaching task list comprises course ID, course types (basic courses such as language, number of English, etc., selected department courses, learning level examination courses, non-college examination courses, etc.), time demand, priority, number of courses, days of course, subject group, whether to combine duty, ban Ban grades, teachers capable of giving lessons, classrooms capable of giving lessons, and forbidden time;
1.4, setting the course arrangement requirements and rules
a. Setting a shift walking level, carrying out layered teaching on students, and setting a level that the students can walk on shifts without crossing layers;
b. setting the number of class connecting times and interval requirements;
c. setting a single and double-week course;
d. setting class course;
e. teacher who takes lessons continuously
f. Setting the times (optional 1 st and last 1 st in the morning and afternoon) of the teacher work to be shared;
g. setting teachers to avoid course arrangement;
h. setting courses without course arrangement;
i. setting mutual exclusion of teachers;
j. setting course mutual exclusion;
k. setting occupied classes and arranged classes;
setting school individuation requirements;
2. calculating an evaluation function of a class list solution violating hard constraint and soft constraint penalty value, calculating algorithm parameters and calculating a teaching class;
2.1: and calculating an evaluation function of the class solution violating the hard constraint and the soft constraint penalty value.
cost＝∑cost i The algorithm targets at minimizing the cost value, cost i The cost value for each course arrangement rule comprises the following parts:
1) Class level of shifts is the number of people violating the level constraint of each class list, omega 1 To walk byClass-level penalty coefficients;
2) Number of class and interval requirementsc is the number of violating Liangtang, ω 2 For the number of continuous hall times, s is violation of the continuous hall interval constraint, ω 3 Is Lian Tang interval coefficient;
3) Single or double weekc is the number of single and double weeks violating omega 4 Is a single-double coefficient;
4) Class of closing classc is the number of times of violating the office work, omega 5 Is a shift combining coefficient;
5) The teaching plan is levelc is the number of times of uneven teaching plan of a teacher in the same course in different classes, omega 6 Is the flush coefficient of the teaching plan;
6) Course cross teaching with same progress as teacherc is the number of times of not crossing the teacher's course at the same time, omega 7 The teaching coefficients are crossed for courses with the same progress as a teacher;
7) Course distribution balancingc is course unbalance, ω 8 The equilibrium coefficient is distributed for courses;
8) Continuous teaching requirementc is the number of violating continuous lessons, ω 9 The coefficients are required for continuous lessons;
9) Work sharing for teachersc is the number of times that the teacher gets on the first and last sections of the afternoon,for average times of last part of the first part of the morning and afternoon of all teachers, omega 10 The work sharing coefficient is used for teachers;
10 No course arrangementc is the number of times of course violation and omega 11 The course is not arranged with course coefficients;
11 No course arrangement for teachers)c is the number of times of course arrangement against the teacher, omega 12 The teaching coefficients are not arranged for teachers;
12 Mutual exclusion of courses)c is the number of simultaneous lessons of mutually exclusive courses, omega 13 The mutual exclusion coefficient of the course;
13 Mutual exclusion of) and teacherc is the number of simultaneous lessons of mutually exclusive teachers, omega 14 Mutual exclusion coefficients for teachers;
14 Collision of students)c is the total number of collision students in class, omega 15 Is a student conflict factor;
15 Collision of teachers)c is the total number of collision of teachers simultaneously taking lessons, omega 16 The teacher collision coefficient;
16 Curriculum conflict)c is the total number of conflicts, omega, of multiple courses arranged in the same classroom and at the same time 17 Is course conflict coefficient;
17 Number of people walking on duty)c is the total number of people in class, omega 18 The number of people is a factor of the number of people walking on duty;
18 Priority of course and class time)ω c For course priority coefficient, ω t As class time priority coefficient omega 19 The priority coefficient is the lesson time;
19 Custom rule cost = Σcω, c is the number of times the custom rule is violated, ω is the custom rule coefficient;
2.2: algorithm parameters are calculated, and omega is applied and initialized according to the class arrangement requirements and rules set in 2.1 1 ......ω 19 ， ω0 ，ω t Omega; calculating whether an elite retention strategy alpha is used in a selection strategy, using a roulette selection strategy or a tournament selection strategy beta, and using a tournament coefficient eta, suggesting a probability drop coefficient Y of a selected neighborhood being selected again between 2 and 4, wherein the probability drop coefficient Y can be between 0.0 and 1.0, calculating a simulated annealing neighborhood to generate a disturbance proportion zeta, wherein the disturbance proportion zeta is related to the number of input students, the number of teachers and the number of lessons, the larger the lessons, the smaller the zeta should be, the initial temperature coefficient epsilon, the temperature drop coefficient K and the maximum circulation times delta, the proposal is more than 100, the K is related to delta, the continuous non-optimal solution withdrawal times lambda and the maximum neighborhood coefficient theta, and the theta can be set between 0.0 and 1.0.
2.3: and calculating a teaching class, namely calculating all teaching units according to the input student selection list, teacher arrangement list and teaching tasks, wherein one teaching unit TU consists of three groups of courses, teaching teachers and teaching students, and generating the teaching class with balanced number of students and minimum conflict.
3. Randomly generating an initial class-solution list;
3.1: the teaching unit TU consists of a course, a teaching teacher and a teaching student triplet; the teaching resource consists of classroom R and lesson time T, and one solution of the algorithm distributes teaching resource units according to the lesson time requirement to all teaching units, namely
3.2: randomly generating an initial solution of a class chart, namely randomly distributing rt teaching resources for each teaching unit tu;
4. generating a local optimal solution by using a hill climbing algorithm, calculating a simulated annealing initialization temperature, and taking the solution as a best local optimal solution class table;
4.1: all neighbors of the solution are computed, the neighbors of the solution being generated by two means: 1) Exchanging two courses, namely, exchanging one allocated teaching resource rt1 of the teaching unit tu1 with one allocated teaching resource rt2 of the other teaching unit tu2, wherein tu1 and tu2 cannot be empty at the same time, rt1 and rt2 cannot be empty, tu1 can use rt2, and tu2 can use rt1; 2) Exchanging two lessons, i.e. teaching lessons t1 and t2, i.ert1 and rt2 are exchanged all the time, and the exchangeable conditions are the same as in item 1).
4.2: calculating a penalty value cost of a solution neighborhood violation course arrangement rule, and storing a neighborhood with the cost smaller than the original solution cost into a better neighborhood set;
4.3: generating a random number random_float between 0.0 and 1.0, if random_float < theta, and randomly selecting a neighborhood from the better neighborhood set as a new solution; else selects the optimal neighborhood solution with the minimum cost from the optimal neighborhood set as a new solution;
4.4: and 4.1, 4.2 and 4.3 are circulated until no better neighborhood exists, namely the solution is a local optimal solution, namely all neighborhood solution cost values of the solution are larger than cost values of the original solution.
4.5: taking the local optimal solution as a best local optimal class solution table;
4.6: calculating the initial temperature coefficient epsilon of the simulated annealing initialization temperature as the local optimal solution penalty value
5. And (3) processing the local optimal solution by using an improved simulated annealing algorithm, firstly, strategically selecting a switching neighborhood of the solution and carrying out switching to generate a new neighborhood solution, obtaining the local optimal neighborhood solution by using a hill climbing algorithm on the neighborhood solution, adopting Metropolis criterion probability to accept the local optimal neighborhood solution, if so, returning to the original local optimal solution and reducing probability coefficients of the selected neighborhood again, and if the new solution is better than the best local optimal solution, taking the new solution as a best local optimal solution class table, and updating the simulated annealing temperature.
5.1: calculating punishment values of all teaching units violating hard constraints and soft constraints;
5.2: strategy selection disturbance proportion ζ|TU|teaching units;
5.2.1: determining whether a teaching unit with the largest punishment value is necessarily selected according to whether an elite reservation strategy parameter alpha is adopted or not;
5.2.2: determining a selection strategy based on a "use" roulette or "tournament" selection strategy parameter β "; when the 'roulette wheel' is adopted, the probability that the teaching unit is selected is as follows: zeta is the sum of the punishment value of the teaching unit and the punishment value of all teaching units; when the tournament is adopted, eta teaching units are selected from all teaching units at first each time, then the teaching unit with the largest punishment value is selected from the eta teaching units until zeta|TU|teaching unit selection is completed.
5.2.3: the selection is not put back and the selection is not repeated.
5.3: and (3) generating a disturbance solution for the disturbance executed in the execution 4 of the teaching unit selected from the class list solutions, and generating a new local optimal solution by using a hill climbing algorithm.
5.3.1: executing the executed disturbance of 4.1 on all allocation schemes of the teaching units selected in the class list solution to generate a disturbance solution;
5.3.2: and (4) executing the hill climbing algorithm described in the step 4 on the disturbance solution to generate a new local optimal solution.
5.4: adopting Metropolis criterion probability to accept the local optimal neighborhood solution as a new local optimal solution, namely: Δt=new local optimal solution penalty value-original local optimal solution penalty value, Δt <0 accepted, Δt >0 accepted with probability exp (- Δt/T), if accepted, the neighborhood solution is new local optimal solution, if not accepted, the neighborhood solution is backed back to original local optimal solution and the probability coefficient of the selected neighborhood being selected again is reduced, the probability penalty value of the selected teaching unit being selected again is equal to its original value multiplied by probability drop coefficient γ;
5.4.1: calculating a simulated annealing temperature difference of the new solution: Δt=new local optimal solution penalty value-original local optimal solution penalty value;
5.4.2: if delta t <0 accepts the new solution as a locally optimal solution; else if generates a random number rand_float between 0.0 and 1.0, and if rand_float < exp (-delta T/T) accepts the new solution as a local optimal solution; else does not accept the new solution and rolls back to the original locally optimal solution.
5.4.3: if a new solution is not accepted in 5.4.2, all selected tutorial units in 5.2 are updated to choose a penalty value that is multiplied by the probability drop coefficient γ to reduce the probability that they are again chosen.
5.4.4: if a new solution is accepted in 5.4.2, all teaching units select the penalty value to restore to the original penalty value.
5.6: and when the new local optimal solution is better than the best local optimal solution, taking the new solution as the best local optimal solution class table.
5.7: the simulated annealing temperature is updated to the original temperature multiplied by the temperature drop coefficient k.
6. And (5) cycling the step until the exit condition is reached, and outputting a local optimal class-solution list result.
6.1: and (3) circularly executing the step 5 until the circulation times reach the maximum circulation times delta, or when the times of continuously not having the better solutions in the step 5 reach the continuously not-optimal solution exit times epsilon, or preferably, the local optimal solution penalty value is 0, and circularly exiting, namely, the algorithm exit condition.
6.2: and the best local optimal solution is a school timetable result, and various school timetable information required by students, teacher, classrooms, class, grade, course and the like is output.
Fig. 2 is a flowchart illustrating a hill climbing algorithm according to an embodiment of the present invention. In the manner shown in figure 1 embodiment 4.
Fig. 3 shows a class-ranking result-student school timetable according to an embodiment of the present invention. The school timetable is an art school timetable for choosing historical geographic chemistry subjects.
Fig. 4 shows a lesson-ranking results-teacher lesson table according to an embodiment of the present invention. The school timetable is a physical teacher school timetable, wherein 2 study teaching classes are selected, and 2 study teaching classes are selected in the learning level.
The embodiments of the present invention have been described in detail with reference to the accompanying drawings, but the present invention is not limited to the above embodiments, and various changes can be made within the knowledge of one of ordinary skill in the art without departing from the spirit of the present invention.
Claims (3)
1. The course arrangement method based on the improved simulated annealing and hill climbing algorithm hybrid search is characterized by comprising the following steps of:
s100, setting a student selection list, a teacher schedule list, a teaching task list and a course arrangement requirement and course arrangement rule;
s200, calculating an evaluation function of a class solution violating hard constraint and soft constraint penalty value, calculating parameters required by a class-arrangement algorithm, and performing optimization calculation on a teaching class according to the setting of S100, wherein S200 specifically comprises the following steps of;
s210, calculating an evaluation function of a class solution violating hard constraint and soft constraint penalty values, wherein the violating hard constraint penalty values represent penalty values of student class table conflicts, teacher class table conflicts and course class table conflicts, and the soft constraint penalty values represent penalty values of one or more sub-items of the class table violating class arrangement rules;
s220, according to the class arrangement requirements and rules, applying and initializing weight parameters violating rigid constraint and soft constraint penalty value evaluation functions, calculating whether an elite retention strategy alpha is used in a selection strategy, using a roulette selection strategy or a tournament selection strategy beta, a tournament coefficient eta, a probability descent coefficient gamma of a selected neighborhood being selected again, and calculating a simulated annealing neighborhood to generate disturbance proportion zeta, an initial temperature coefficient epsilon, a temperature descent coefficient kappa, a maximum circulation number delta, continuous non-optimal solution withdrawal number lambda and a fastest neighborhood coefficient theta;
s230, optimizing and calculating all teaching units according to the input student selection list, teacher arrangement list and teaching task list, wherein the teaching units consist of course, teaching teacher and teaching student triplets, and generating a teaching class with balanced number of students and minimum conflict after optimizing
S300, randomly generating an initial class-solution list;
the step S300 specifically includes:
s310, distributing teaching resource units according to the demand number of the lessons for all the teaching units according to one solution of the algorithm, wherein the teaching resource units are Cartesian products of the lessons T and classrooms R;
s320, generating a class list initial solution randomly, namely randomly distributing teaching resource units for each teaching unit;
s400, generating a local optimal solution by using a hill climbing algorithm, calculating a simulated annealing initialization temperature, and taking the solution as a best local optimal solution class table, wherein the step S400 specifically comprises the following steps of;
s410, calculating all neighborhoods of the solution;
s420, calculating a neighborhood violation course arrangement rule penalty value of the solution, and storing a neighborhood with a penalty value smaller than the original solution penalty value into a better neighborhood set;
s430, generating a random number between 0 and 1, randomly selecting a neighborhood from a better neighborhood set as a new solution if the random number is smaller than a maximum neighborhood coefficient theta, otherwise, selecting an optimal neighborhood solution with the minimum penalty value from the better neighborhood set as the new solution;
s440, cycling the steps S410-S430 until no more optimal neighborhood exists, namely the solution is a local optimal solution;
s450, taking the local optimal solution as a best local optimal solution class table;
s460, calculating an initial temperature coefficient epsilon of the simulated annealing initialization temperature which is a local optimal solution penalty value;
the generating the neighborhood of the solution in S410 includes:
s441, exchanging two courses, namely, exchanging one allocated teaching resource rt1 of a teaching unit tu1 with one allocated teaching resource rt2 of another teaching unit tu2, wherein tu1 and tu2 cannot be empty at the same time, rt1 and rt2 cannot be empty, and tu1 can use rt2, and tu2 can use rt1;
s442, exchanging two classes, i.e. teaching class time t1 and t2When rt1 and rt2 can be exchanged, all the exchanged conditions are consistent with the exchanged conditions of the two sections of courses;
s500, processing a local optimal solution by using an improved simulated annealing algorithm, firstly, strategically selecting a switching neighborhood of the solution and carrying out switching to generate a new neighborhood solution, obtaining the local optimal neighborhood solution by using a hill climbing algorithm on the neighborhood solution, adopting Metropolis criterion probability to accept the local optimal neighborhood solution, if so, returning to the original local optimal solution and reducing probability coefficients of the selected neighborhood being selected again, and if the new solution is better than the best local optimal solution, taking the new solution as the best local optimal solution class table, and updating the simulated annealing temperature;
s600, the step S500 is circulated until the exit condition is reached, the best local optimal class-solution list result is output, and a corresponding class-arrangement list is generated;
wherein,,
the step S500 specifically includes:
the improved simulated annealing algorithm is used for processing the local optimal class-solution table, which comprises the following steps:
s510, calculating punishment values of all teaching units against hard constraints and soft constraints;
s520, strategy selection disturbance proportion ζ is equal to TU and is equal to TU;
s530, generating a disturbance solution for disturbance executed by a teaching unit selected from the class list solutions, and generating a new local optimal solution by using a hill climbing algorithm;
s540, adopting Metropolis criterion to probability of receiving a local optimal neighborhood solution as a new local optimal solution, namely: Δt=new local optimal solution penalty value-original local optimal solution penalty value, Δt <0 accepted, Δt >0 accepted with probability exp (- Δt/T), if accepted, the neighborhood solution is new local optimal solution, if not accepted, the neighborhood solution is backed back to original local optimal solution and the probability coefficient of the selected neighborhood being selected again is reduced, the probability penalty value of the selected teaching unit being selected again is equal to its original value multiplied by probability drop coefficient γ;
s550, when the new local optimal solution is better than the best local optimal solution, the new solution is used as the best local optimal solution class table;
s560, updating the simulated annealing temperature to be the original temperature multiplied by a temperature drop coefficient kappa;
the S520 selection policy includes:
the "elite retention" strategy, when adopted, the teaching unit with the largest penalty value in S510 is selected;
the selection strategy of the roulette wheel is adopted, and the probability of the teaching unit selected in S510 is proportional to the penalty value of the teaching unit;
when the selection strategy of the tournament is adopted, firstly randomly selecting eta teaching units of the tournament coefficient during each selection, and then selecting the teaching unit with the largest punishment value from the eta teaching units;
all choices are put-back-free and repeat-free choices, whether to use the "elite retention" strategy is determined by parameter α, and whether to use the "roulette" or "tournament" selection strategy is determined by parameter β;
the S600 specifically includes:
s610, executing the step S500 in a circulating way until the circulating times reach the maximum circulating times delta, or when the times of continuously not having better solutions in the step S500 reach the continuously not having optimal solution withdrawal times lambda, or the penalty value of the best local optimal solution is 0, and exiting in a circulating way;
and S620, outputting a student school timetable, a teacher school timetable, a classroom school timetable, a class school timetable, a grade school timetable and a course school timetable, wherein the best local optimal solution is a school timetable arrangement result.
2. The course arrangement method based on the hybrid search of the improved simulated annealing and hill climbing algorithm of claim 1, wherein the S100 specifically comprises:
s110, setting basic data, wherein the basic data comprise students, teachers, courses, classrooms, time of class, administrative classes, teaching classes and teaching levels;
s120, setting a student selection list, a teacher arrangement list and a teaching task list;
s130, setting course arrangement requirements and course arrangement rules.
3. The course arrangement method based on the hybrid search of the improved simulated annealing and hill climbing algorithm of claim 2, wherein S130 specifically comprises: the method is used for correspondingly setting the walking level, teaching requirement, teacher work sharing, no course arrangement, single and double week courses, combined courses, mutual exclusion courses, occupied courses and school individuation requirements.
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