10-04-2017, 08:14 PM
Introduction
Making a class schedule is one of those NP hard problems. The problem can be solved using a heuristic search algorithm to find the optimal solution, but it only works for simple cases. For more complex inputs and requirements, finding a considerably good solution can take a while, or it may be impossible. This is where genetic algorithms come in to the game. In this article, I assume that you are familiar with the basic concepts of genetic algorithms, and I won't describe them in detail because it has been done so many times before.
Background
When you make a class schedule, you must take into consideration many requirements (number of professors, students, classes and classrooms, size of classroom, laboratory equipment in classroom, and many others). These requirements can be divided into several groups by their importance. Hard requirements (if you break one of these, then the schedule is infeasible):
A class can be placed only in a spare classroom.
No professor or student group can have more then one class at a time.
A classroom must have enough seats to accommodate all students.
To place a class in a classroom, the classroom must have laboratory equipment (computers, in our case) if the class requires it.
Some soft requirements (can be broken, but the schedule is still feasible):
Preferred time of class by professors.
Preferred classroom by professors.
Distribution (in time or space) of classes for student groups or professors.
Hard and soft requirements, of course, depend on the situation. In this example, only hard requirements are implemented. Let's start by explaining the objects which makes a class schedule.
Objects of Class Schedule
Professor
The Professor class has an ID and the name of the professor. It also contains a list of classes that a professor teaches.
Students Group
The StudentsGroup class has an ID and the name of the student group, as well as the number of students (size of group). It also contains a list of classes that the group attends.
Classroom
The Room class has an ID and the name of the classroom, as well as the number of seats and information about equipment (computers). If the classroom has computers, it is expected that there is a computer for each seat. IDs are generated internally and automatically.
Course
The Course class has an ID and the name of the course.
Class
CourseClass holds a reference to the course to which the class belongs, a reference to the professor who teaches, and a list of student groups that attend the class. It also stores how many seats (sum of student groups' sizes) are needed in the classroom, if the class requires computers in the classroom, and the duration of the class (in hours).
Chromosome
The first thing we should consider when we deal with a genetic algorithm is how to represent our solution in such a way that it is feasible for genetic operations such as crossover and mutation. Also, we should know how to specify how good our solution is. In other words, we should be able to calculate the fitness value of our solution.
Representation
How can we represent the chromosome for a class schedule? Well, we need a slot (time-space slot) for each hour (we assume that time is in one hour granules), for every room, every day. Also, we assume that classes cannot begin before 9am, and should finish before or at 9pm (12 hours total), and working days are from Monday to Friday (5 days total). We can use an std::vector with a size 12*5*number_of_rooms. The slot should be an std::list because during the execution of our algorithm, we allow multiple classes during the same time-space slot. There is an additional hash map which is used to obtain the first time-space slot at which a class begins (its position in vector) from the address of the class' object. Each hour of a class has a separate entry in the vector, but there is only one entry per class in the hash map. For instance, if a class starts at 1pm and lasts for three hours, it has entries in the 1pm, 2pm, and 3pm slots.
Class Schedule Chromosome Representation