A Review of Optimization Algorithms for University Timetable Scheduling

Abstract

The university course timetabling problem looks for the best schedule, to satisfy given criteria as a set of given resources, which may contain lecturers, groups of students, classrooms, or laboratories. Developing a timetable is a fundamental requirement for the healthy functioning of all educational and administrative parts of an academic institution. However, factors such as the availability of hours, the number of subjects, and the allocation of teachers make the timetable problem very complex. This study intends to review several optimization algorithms that could be applied as possible solutions for the university student course timetable problem. The reviewed algorithms take into account the demands of institutional constraints for course timetable management.

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A Review of Optimization Algorithms for University Timetable Scheduling
A Review of Optimization Algorithms for University
Timetable Scheduling
Hayat Alghamdi
College of Computer and Information Systems
Umm Al Qura University
Makkah, Saudi Arabia
s43980248@uqu.edu.sa
Tahani Alsubait
College of Computer and Information Systems
Umm Al Qura University
Makkah, Saudi Arabia
tmsubait@uqu.edu.sa
Hosam Alhakami
College of Computer and Information Systems
Umm Al Qura University
Makkah, Saudi Arabia
hhhakam@uqu.edu.sa
Abdullah Baz
College of Computer and Information Systems
Umm Al Qura University
Makkah, Saudi Arabia
aobaz01@uqu.edu.sa
Abstract—The university course timetabling problem looks for
the best schedule, to satisfy given criteria a s a set of given
resources, which may contain lecturers, groups of students,
classrooms, or laboratories. Developing a timetable is a
fundamental requirement for the healthy functioning of all
educational and administrative parts of a n academic institution.
However, factors such as the availability of h ours, the number of
subjects, and the allocation of teachers make the timetable
problem very complex. This study intends to review several
optimization algorithms that could be applied a s possible
solutions for the university student course timetable problem.
The reviewed a lgorithms take into account the demands of
institutional constraints for course timetable management.
Keywords-timetabling; g enetic algorithms; Particle Swarm
Optimization (PSO)
I. I
NTRODUCTION
Many higher education institutions have teaching staff from
various fields, who work together to meet the educational goals
set. However, creating a timetable with no conflicts, which
these lecturers can use is one of the challenges most
universities face. Generally, a timetable is a table of various
events and their schedule [1]. Therefore, in a university
timetable, the institution assigns the courses taken by students
and delivered by tutors to a defined finite set of resources,
which include time slots and classrooms. This process presents
many challenges. For example, in a typical school, there are
several student groups who may or may not be taking the same
course at the same time [2]. Thus, when scheduling lectures,
one has to ensure that learners, lecturers, and lecture halls do
not conflict. This need makes the timetabling of university
courses to be a complex and time-consuming task to complete.
University timetabling committees cannot perform this
distribution randomly as they must consider several decisive
factors. There are several constraints that guide the process of
making an effective timetable. These constraints, which are
rules, policies, and preferences of universities, lecturers, and
students, can be categorized as hard, soft, or medium. Hard
constraints are those guidelines that should not be violated or
overlapped at all, soft constraints are desires of the involved
stakeholders that can be ignored without any serious
consequences, and medium constraints are preferences that
they are preferred to not be violated [3]. The committee
handling the timetabling must consider all these requirements
to create an optimal outcome. Due to the complexity of this
problem, timetable coordinators spend a considerable amount
of time looking for the best solution. However, even if they
have a lot of experience, the resolution found may not be
optimal due to the large number of possible combinations.
Thus, the distribution of workload among the various lecturers
in an academic institution constitutes a problem of
combinatorial nature. In general, resolving such challenges and
obtaining exact optimal solutions is computationally
intractable. Therefore, the university timetabling problem is an
example of a Non-Polynomial (NP)-hard problem [4]. These
are problems with no particular efficient solutions. In the case
of timetabling where there is no specific algorithm that can be
utilized to schedule classes since each institution has its special
constraints [5, 6]. At the same time, when done manually, the
obtained result depends on both the initial approach and the
experience of the timetabling committee.
Public universities typically take days to manually schedule
all the classes that students should take depending on the
availability of lecturers and classrooms [7]. Thus, the proposal
to automate this process intends to meet real needs, with the
main aim to reduce the time taken to complete it efficiently.
Describing the real problem by mathematical functions, the
study seeks the values of such models with the use of
optimization techniques. This way, it will provide a solution
that maximizes the use of available human resources and
satisfies the needs of all involved parties. This approach
becomes very complex as more restrictions arise, such as the
Corresponding author: Ho sam Alhakami

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A Review of Optimization Algorithms for University Timetable Scheduling
number of courses in the school and the availability of essential
resources like lecturers, students, and classrooms. The
presented solutions behave inefficiently when there is an
expansion of the institution and their accuracy suffers as the
number of courses and classes grow [8]. Thus, a personalized
computational approach to address the issue becomes important
and a priority. Due to the importance of the problem, several
formalizations and solution methods have been proposed. The
approaches based on meta-heuristics are considered to be
particularly relevant. However, these optimization algorithms
are not mutually exclusive. Instead, they combine ideas from
different areas, with the main aim of providing different
solutions to the timetabling issue [9]. One of the most popular
approaches is acquiring solutions based on Genetic Algorithms
(GAs) due to their high degree of computational parallelization
and enhanced computational performance. Overall, university
course timetabling can be treated as organizing a group of
classes to meet the specifications of particular institutions.
Over the years, various researchers have created various
algorithms to find an optimal solution to this issue. For
instance, authors in [9] created graph coloring schemes for
timetable scheduling in 1967. Their work formed the
foundation upon which more sophisticated techniques have
been based. One of these models is linear programming, which
was used to solve a labor scheduling problem in [10].
Moreover, a GA presents one of the best possible methods
to address NP-complete problems. At its core, a GA is a
parameter optimization strategy that iterates over a population,
seeking the best fit for a problem until it obtains an optimal
solution [11]. Several works have been completed with this
algorithm for the treatment of timesheets. The GA borrows
heavily from the field of natural sciences on the way it works.
In particular, it allows observing events from the lens of natural
phenomena, such as mutations and natural selection [12].
Hence, it helps developing computational mechanisms, which
resemble these processes. Therefore, GAs use and specify
biological terminologies, such as crossing-over and mutation,
in a precise and specialized way [13]. In particular, through the
process of cross-over, the fittest generations pass on their
attributes to their offspring. In turn, mutation helps to prevent
stagnation within a population and is essential for the proper
functioning of the algorithm. Along this line, this study will use
surveys to understand the general foundations for the problem
of university lesson planning. This activity will assist in
formulating the optimization model and describing the manner
in which the algorithm can be adapted to make it applicable to
the problem under investigation.
II. R
ELATED WORDK
Because university course timetabling is an NP-hard
problem, there are several methods that have been explored in
attempts to find optimal solutions. The manual approach
requires several days of work and often results in inefficient
outcomes [4, 14]. However, there are several other procedures
that can be used to schedule academic activities and in which
restrictions related to the type of problem considered must be
respected. Nonetheless, the objective often involves
distributing teachers and students in a particular course
depending on time and resource availability, while also
respecting their desires. Educational timetables are of three
types: school, course, and exam timetables [1]. Scheduling the
course timetable presents the most difficulties among the three
as it is utilized frequently through a typical university semester
and it covers only particular days within a week. University
timetabling is not simple due to various constraints that would
be applied to produce effective course timetabling [15-17].
Eventually, the timetabling constraints can be classified as hard
and soft; the hard constraints are considered as mandatory
while the soft constrains are optional [18-20]. Table I
summarizes the most important soft and hard constraints of
course timetabling.
TABLE I.
SOFT AND HARD CONSTRAINTS
Hard constraints Soft constraints Ref.
- Courses having common students
cannot
be allotted at the same time slot on the
same day.
- The t
otal number of available periods of
the daily timetable is 8 hours (maximum)
Honours and g
eneral courses
need to be scheduled in non-
overlapping time-slots.
[15]
- A room cannot be
assigned to more than
one lecture in a given period.
-
Courses belonging to a curriculum must
be assigned to different periods.
-
Courses taught by a lecturer must be
assigned to different p eriods.
-
The number of students taking a
course must fit into the
assigned
room.
-
Each additional student over the
capacity of the room counts as a
violation.
-
Lectures for a given curriculum
must be consecutive.
[16]
The timetable should be scheduled based
on the university calendar
To open the course, a minimum
number of students should be
registered
[17]
- Considers the workl oad of the lecturers.
- Takes into
account the free time (i.e.
office hours and resets) of the lecturers.
[18]
-
Every course should be assigned to a
venue at a particular ti meslot.
- The
scheduled courses must not exceed
the venue capacity.
[19]
-
Lecture rooms must not be booked twice
at the same time.
-
All lecture venues and rooms must be
scheduled once not twic e.
-
Break periods must be allocated
before other courses.
-
Faculty general courses must be
allocated to
slots before
departmental courses.
[20]
-
No student group has two events at the
same time.
-
No lecturer has two e vents at the same
time.
-
No event is in a room wit h less capacity
than the number of students at the event.
[21]
Hard and soft constrains are related to many factors such as
courses, lecturers, students, classrooms, and operational dates
and hours [16, 18, 19, 21]. Thus, it is important to apply
optimization algorithms for effective scheduling of the course
timetable. The use of optimization techniques in problem-
solving dates back several decades. Nonetheless, it has recently
been boosted by the advent of computers and the increase in
their processing capacity, which has led to a rise of the number
of scheduling approaches. However, the application of these
methods to solve practical problems has not been verified at the
same proportion as the rate of their development. One of the
reasons is the complexities of the real behavior and the model
generated, which are described by non-linear behavior
functions and whose solution space may be non-convex [14].
Heuristic methods have played an important role in resolving

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A Review of Optimization Algorithms for University Timetable Scheduling
these types of problems. Primarily, they involve values of the
functions in the process, regardless of whether there is
unimodality of the function or continuity in their derivatives.
On the other hand, they demand a large number of calculations
as stated b y authors in [22], who argue that instead of
performing many additional computations to determine a
gradient with mathematical programming techniques, it may be
more beneficial to use this time and resources to explore the
search space more intensively. Among the heuristic
optimization techniques, there are metaheuristic methods,
which promise accurate and optimal solutions to the timetable
scheduling issue. Notable approaches of this nature include
Greedy Randomized Adaptive Search (GRASP), simulated
annealing, tabu search, GAs, microchanonic annealing, and
microchanonic optimization [23]. Scheduling problems are
usually addressed by heuristic techniques due to their structure
and complexity [22]. For instance, authors in [23] state that the
simulated annealing scheme provides an efficient solution
when applied to scenarios that require some form of
programming. Several authors present comparisons and
evaluations of the performance of different metaheuristics in
solving scheduling problems [24]. Some of the common
metaheuristic strategies include evolutionary algorithms, ant
colony, local search, simulated annealing, and tabu search, but
none of them can be singled out as the best. Table II shows a
summary of some of these algorithms, including their
advantages, disadvantages, and tools that can be applied to
develop them. Using this Table, it is possible to identify the
methodologies that can be applied to develop a solution to the
university timetabling problem effectively. The problem of
scheduling can be found in many areas, e.g. in the assignment
of drivers to vehicles in a public transport company or in the
development of school timetables. However, conflicts are
common due to competing interests among the stakeholders
involved and the existence of constraints that should be
satisfied. In order to find the best possible solution to such
issues, a swarm-intelligent algorithm, named Particle Swarm
Optimization (PSO), can be used. This meta-heuristic was
developed to find and optimize solutions for continuous
problems. Nonetheless, it turned out to be a very suitable
method for achieving quick and good solutions within these
applications. At this point, however, the process must be
adapted to the given circumstances for this discrete problem.
TABLE II.
COMPARISON OF DIFFERENT SCHEDULING AND OPTIMIZATION ALGORITHMS
Reference
Year
Technique Tools Advantages Disadvantages
[25] 2015
PSO
Programming languages, such
as Python. Supported by
Gaussian 09 program package.
Simple to implement. Does not converge fast.
[26] 2017
Integer programming Various solver package s for
global optimization. Few parameters that need to be adjusted.
Difficult to define the initial design
parameters.
[27] 2016
Multi-objective
optimization
Can be implemented using
various programming
languages.
Able to run parallel computation. Can converge prematurely.
[28] 2016
Hyper-heuristics Python or R programming
languages. Can be robust. Complex to implement for
inexperienced programmers.
[29] 2017
Integer programming Solver packages, such as
BARON.
Have higher probability and efficiency in
finding the highest optimization
Cannot work out problems of
scattering.
[20] 2015
Metaheuristic
techniques
Python or R programming
languages. Can converge fast Dos not have short comput ational time.
[32] 2018
Fix-and-optimize
metaheuristic
Python or R programming
languages. Does not overlap and mutate Not efficient in working pr oblems
linked with scattering.
[32] 2015
Great deluge algorithm Matlab Has short computational time. Complex to implement for
inexperienced programmers.
[33] 2016
Linear integer model Solver packages, such as
GAMS library.
Efficient in solving problems that do not
have accurate mathematical models.
Complex to implement for
inexperienced programmers.
[34] 2017
Artificial bee colony
algorithm Matl ab It is easy to use and can interface with
other algorithms efficiently.
Converges prematurely, resulting in no
solutions in some instances.
[35] 2017
Stochastic gradient
descent
Stochastic simulation toolkit
(StochKit)
Simple to implement and works fast
when applied to small datasets.
Hyperparameters need to be tuned
manually. Hence, people not familiar
with it find it challenging to use.
[36] 2018
Broyden-Fletcher-
Goldfarb-Shanno
(BFGS) algorithm
The libLBFGS library writte n in
the C++.
Has better convergence than most
algorithms
Performs poorly in the context of non-
smooth optimization.
[37] 2020
Simulated annealing
algorithm.
Software tools, such as
KDSimStudio and Simulat ed
Conversation Development t ool.
Gradually converges to a global optimal
solution and, thereby, escapes from a
local solution.
Requires enhancements to function
effectively.
[38] 2020
Tabu search algorithm
Available frameworks, such as
the Tabu Search Framework
written in C++.
Together with a memor y concept, it can
be utilized to explore iteration problems
more precisely than other algorithms.
It performs poorly in large dimension
problems.
[39] 2020
Tabu search algorithm Frameworks, such as the Tabu
Search Framework.
Ignores recently explored nei ghborhoods
to avoid settling on a local optimum
solution.
As it does not have memor y, it requires
other algorithms or additional
components to function effectively.
[40] 2020
Elite immune ant
colony optimization
algorithm
Matlab
Combines the strengths of both the ant
colony and immune theor y to ensure its
efficiency.
Complex to implement.

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A Review of Optimization Algorithms for University Timetable Scheduling
A. Genetic Algorithms
The main task of scheduling algorithms in solving the
university course timetabling problem is to find a solution that
satisfies a set of restrictions. These limitations are either
essential or nonessential. Essential restrictions are those that
generate an unworkable timetable if they are not satisfied. On
the other hand, the nonessential ones improve the quality of the
framework. GAs are a strategy class that can be employed to
resolve these conditions efficiently. They are based on the
principles of genetics and natural selection, with the central
idea being the selection of the fittest individuals in a
population, who then recombine with others or mutate into new
forms to generate new groups [41]. GAs are particularly
applied to complex optimization problems, which are
challenges that have different parameters or characteristics that
need to be combined in search of the best solution and, at the
same time, cannot be represented mathematically [42, 43].
Figure 1 illustrates the flowchart of the GA algorithm, from the
initial population to when a suitable result is obtained.
Fig. 1. GA flowchart [4 1].
Over the years, several researchers have applied GAs to
solve such problems. For instance, authors in [44] dealt applied
the GA to address the issue of scheduling class timetables. The
differential feature in this work is the use of crossover
operators only between rows and, later, columns. Many authors
also utilize several methods to treat infective solutions, which
are those that do not meet the essential restrictions. In [45], the
algorithm was applied to resolve the problem in two phases.
First, a GA was applied to generate solutions that only meet the
essential restrictions, and, in the second stage, based on the
initial population generated in the initial step, GAs were
employed to satisfy the non-essential conditions. In [46], a
greedy approach was proposed to generate a robust initial
population. Subsequently, the authors applied the GA to
optimize this solution further. Other works, such as [47],
propose the application of a repair function, which is
introduced after crossover and mutation operations, to deal
with infactible solutions. In [48], it is proposed to use local
search methods to improve the solution, which, consequently,
reduces the number of violations of non-essential restrictions.
These methods are usually applied after the generation of each
population in the evolution process. Often, GAs are
implemented in the Delphi 5.0 programming environment and
the problem input data are imported from the Saber Software
Database.
The problem of timetabling consists of scheduling a
sequence of classes between teachers and students in a limited
period of time, while satisfying a set of restrictions. This
problem exists in any educational institution, but it becomes
increasingly complex as the size of the establishments grows.
Primarily, this phenomenon arises because the timetabling of
courses belongs to the NP-hard class, for which polynomial-
time algorithms have been unable to obtain optimal solutions
[49]. The timetabling problem has been studied for several
years, with pioneering solutions forming the foundation for
more effective techniques. The literature reveals several types
of solutions, such as graph-based techniques and other
approaches that find a maximal sequence of pairings in the
bipartite graph composed of teachers and classes. Authors in
[50] used programming by applying a Lagrangian relaxation
technique, while authors in [23] formulated and solved the
problem as an allocation challenge. Authors in [51] used flow
resolution techniques in networks. As mentioned above, many
authors divided the restrictions between hard and soft, where
the hard restrictions define the feasible solutions, and the soft
restrictions are included in the objective function. While
satisfying the hard conditions means that the solution addresses
the problem successfully, its quality is dependent on the
procedure to blocks of different durations. Another popular
approach is the employment of a multiobjective GA, which
combines two points of view: student-oriented and teacher-
oriented. Moreover, one can use a two-stage GRASP
algorithm. Others formulated another model for the problem,
also using soft constraints in the objective function. One can
explore a hyperheuristics framework based on graphs,
researching local search algorithms based on low-level coloring
algorithms. Other approaches can also apply a tabu search,
using domain-independent neighborhood structures to penalize
neighborhoods unable to generate better solutions. A
combination of the bee colony meta-heuristic with an
assimilation policy to guide the search process has also been
proposed. Therefore, there are several approaches that can be
followed to solve the university course timetabling issue,
although they all have their advantages and disadvantages.
B. Particle Swarm Optimization
PSO was originally developed in 1995 to solve continuous
problems [52]. The idea of simulating a swarm of bees has
evolved into a meta-heuristic and presented an optimization
procedure with some basic extensions. Based on this premise,
the PSO procedure can be further modified to solve
combinatorial problems [53, 54]. The boids (bird-like objects)
model has been introduced, whereby each boid represents an
individual who obeys three implemented rules in order to
simulate swarm behavior for computer graphics and films,
since it was found that the choreography of flocks of birds was
aesthetic. The alignment ensures that individuals move in the
same direction as their neighbors. Merging several boids
enables cohesion, in which a single boid moves in the middle
of a defined group, whereas separation causes boids to diverge
in a small space. Depending on a given rule, a marked boid is
aligned with the other boids. Later on, rest areas were added to

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A Review of Optimization Algorithms for University Timetable Scheduling
the boids model [55]. The individuals also have a need to
remain within the swarm. The more a boid approaches a resting
place, the greater the desire to move towards it, pulling more
boids in this direction. Later, Kennedy and Eberhart developed
the Swarm Optimization [55]. Theoretically, individuals can
benefit from the discoveries and past experiences of their
colleagues when searching for food [56]. This advantage can
become critical and outweigh the disadvantages of food
competition if the resource is unpredictably patched [57].
Kennedy and Eberhart followed this hypothesis that
information exchange between group members offers an
evolutionary advantage in the further development of the PSO
by implementing social behavior in the birds and, hence,
making them mass- and collision-free particles. They also
extended the model by not only having them look for a rest
area but also using a “cornfield vector” on which the best
feeding place exists. These particles now have a memory of
their best position in relation to such a feeding place and a
knowledge of the best position so far within the entire swarm
[57]. Based on these considerations, the classic PSO for
continuous problems was developed. Figure 2 shows the
flowchart of the PSO algorithm.
Fig. 2. Flowchart of the PSO algorit hm.
To optimize the solution, the PSO developed for continuous
problems was modified in such a way that it was suitable for
solving combinatorial problems. Various compositions of
parameters were examined for their performance and it was
observed that the attempt to modify the PSO in such a way that
it was able to solve a combinatorial problem without the
characteristics of swarm-intelligence [59]. The PSO
significantly improved the quality of the solution of the
manually created timetable with reasonable computing effort.
In particular, the influence of an individual event can be
emphasized in combination with swapping a random time
window of the current solution. This exercise suggests a good
current solution [60]. This exercise suggests a good balance
between exploration and exploration of the solution space.
Since the method presented primarily deals with continuous
problems, further research is needed to determine its suitability
in addressing the university timetable problem.
While formulating a time table, it is important to consider
the context of the problem within the educational institution in
question. The problem may vary according to the institution
and its business model, as, for example, in public and private
educational establishments. Public schools usually have an
open timetable model, in which subjects are offered and
courses are built around them [60]. Thus, students are free to
choose the subjects and they want to take and at what times. As
the subjects are free, there is no requirement for rooms where it
should be taught, and this allocation is also part of the process
as a whole [59, 61]. Thus, it is possible for a course to be
taught in several different classrooms throughout the week. In
contrast, most private institutions follow a closed model. In this
case, a course coordinator allocates the subjects that a student
will take. Eventually, the learner has to approve the given set of
units according to the level of study. In addition, the subjects
are linked to courses they are being offered, and they are
completely free as in the case of public institutions. As a result,
subjects should not be allocated to classrooms, as they have a
fixed location. That is, the classroom to which they are
assigned. Thus, lecturers can switch rooms but not the student
since teachers in private institutions can teach several subjects,
although there is no requirement that a subject should always
be taught by the same instructor. However, in public
institutions, it is common for a teacher to be hired for one or
more specific subjects.
III. D
ISCUSSION
Lesson planning deals with the scheduling of classes at a
specific time in a given location, with particular participants
that have to attend. In the best case, the solution of the problem
results in plans that enable all students to take part in the
meetings of interest at a certain location and time. There are,
however, restrictions to the allocation of resources, which
include time, space, and the availability of both teaching staff
and the students. No other class should happen at the same time
and venue with an ongoing one, and neither should two lessons
demand the presence of the same group of students
concurrently. Double occupancy of rooms has the same
potential for conflict. As mentioned above, creating an efficient
timetable is a typical NP-hard problem, which does not have a
specific methodology of finding an optimal solution [62, 63].
Moreover, course timetables do not consider the preferences of
students, as is generally the case in appointment requests.
In the case of university lesson planning, this phenomenon
means that lecturers play the role of active agents and students
that of passive agents. At the same time, a lecture hall has to be
of appropriate size, should possess the required equipment, and
be available at an acceptable time for all participants without
causing violations of both essential and nonessential constraints
[63]. Therefore, the dates of a resulting timetable correspond to

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A Review of Optimization Algorithms for University Timetable Scheduling
assignments of a previously defined matrix of possible time
windows.
The conditions, which a timetable should satisfy can be
divided into hard and soft constraints. Violations of hard
constraints are not permitted because they could lead to the
unavailability of lecturers, e.g. they might be scheduled to
attend two concurrent classes. On the other hand, soft
constraints can be left unsatisfied since such a case does not
affect the admissibility of the timetable. The punishment for
non-compliance with soft constraints is included in the
assessment of the timetable [14]. Soft constraints occur, for
example, when deadline requests for events cannot be met. In
this case, these incidents can be shifted from their original
desired dates to another time window without affecting the
effectiveness of the timetable.
The lesson planning activity in schools is further made
difficult by the options that students have while selecting the
classes to attend. For instance, one does not have to stick to
given subject combinations, but can largely plan study
programs independently. The attendance of individual courses
does not have to take place in a particular semester, but can
usually be integrated into the study period at will. The aim of
university timetable scheduling is to use the resulting multitude
of subject combinations to create a program, which is as free of
overlaps as possible for all [64, 65]. Although the problems of
school and course timetabling may appear similar at a first
glance, they present significantly different problem sets, with
the latter’s being more complex than those of the former.
While formulating a timetable, it is important to consider
the context of the problem faced by the educational institution
in question. The issue may vary depending on the
establishment and its business model. For example, while they
are both institutions of higher learning, public and private
universities have different funding models, which affect how
they offer their classes and the types of services their students
enjoy. Public schools usually have an open structure, in which
subjects are offered and courses are built around them, while
students are free to choose which subjects they want to take
and at what time. As the subjects are free, there is no
requirement for rooms where they should be taught, and this
allocation is also part of the process as a whole [66]. Thus, it is
possible for a course to be taught in several different
classrooms throughout the week. On the other hand, most
private institutions follow a closed model. In this case, a course
coordinator allocates the subjects that a student will take.
Eventually, the student has to approve the given set of units
according to the level of study. In addition, the subjects are
linked to courses in which they are being offered, and they are
not completely free as in the case of public institutions. As a
result, subjects should not be allocated to classrooms, as they
have a fixed location. That is, the classroom to which they are
assigned. Thus, lecturers can switch rooms but not the student
since teachers in private institutions can teach several subjects,
although there is no requirement that a subject should always
be taught by the same instructor. However, in public
institutions, it is common for a teacher to be hired for one or
more specific subjects.
University course timetabling solves the problem of
creating assignments given specific time slots, classrooms,
teachers, and subjects. The goal is to prevent a room from
being occupied by two subjects simultaneously, or two teachers
teaching the same class, or a teacher to have to teach two
classes at the same time. The quality indicator of a solution
varies, with some researchers using the sum of the preferences
of a given discipline, such as a teacher allocation, to measure
the effectiveness of a timetable [66, 67]. Others adopt soft
restrictions and utilize them to assess the quality of the
solution, while there are instances where student preferences or
the spacing between classes has been employed to achieve the
same goal. Authors in [4] consider a matrix of conflicts
between learners taking two courses i and j simultaneously.
The objective function considers the minimization of the
number of cases where i and j are scheduled at the same time.
Therefore, just as there are several methods of creating an
optimal solution to the course timetabling problem, the quality
of the resulting solutions can be evaluated in various ways.
IV. C
ONCLUSION
The problem of planning school hours is described as
having to schedule a series of meetings between teachers and
students over a set period of time and meet a number of
different types of constraints. Since the types of restrictions
generally change from one institution to another, different
solutions to this problem have been proposed. The problem of
school hours, it is a problem of combinatorial optimization with
a vast search space and with a generally large number of
restrictions. It is considered as an NP-hard problem. For
problems like these, there is still no algorithm that tests all the
possibilities to find the optimum solution in a timely manner.
Therefore, this problem has been approached through heuristic
techniques, and more recently by meta-heuristics.
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