How to implement the optimal arrangement of the schedule of classes in the account. institution?

Question

Algorithms

There is a task - based on data on teachers, groups, subjects, the number of hours per week for each subject, arrange the correct class schedule, preferably optimal (without windows for groups and teachers, preferably without time differences (today the first shift, tomorrow the second), according to opportunities so that it does not happen that the teacher has only 1 pair per day). In which direction to dig? What are the algorithms?

Answer 1

Well, this is a task from scheduling theory - the topic of candidate and doctoral dissertations.
The task of finding optimal pairs is still dangling nearby - they generally gave the Nobel Prize in Economics for it

Answer 2

In general, this is a complex problem, even in the formulation that you have indicated, it will take more than one month to get at least some result.
If you have a purely practical task, just use the programs that do it.
If you want to dig yourself, this is a section of mathematics called Schedule Theory.