Visualization Methods for Educational Timetabling Problems:

A Systematic Review of Literature

Wanderley de Souza Alencar, Hugo Alexandre Dantas do Nascimento,

Fabrizzio Alphonsus A. de M. Nunes Soares and Humberto J. Longo

Instituto de Inform

atica, Universidade Federal de Goi

as, Alameda Palmeiras, Campus Samambaia, Goi

ania-GO, Brazil

Keywords:

Timetabling, Visualization, Educational, Systematic Review of the Literature, Scheduling, Interactive,

NP-hard problem.

Abstract:

This paper investigates, through a Systematic Review of the Literature (SRL), the application of advanced

Information Visualization (IV) methods to the Educational Timetabling Problem (Ed-TTP). The aim is to

show how IV can facilitate the human perception of the several elements embedded in a school or university

timetable scheduling. We also investigates how interactive IVs have been proposed to help creating/improving

timetabling solutions, particularly when time conﬂict is a major challenging to be solved. In this SRL we

considered publications from the last twenty years (1998–2018) indexed by seven solid scientiﬁc databases.

The review clearly identiﬁed that there is a small amount of studies devoted to the intersection between IV and

Ed-TTP in that period. Ideas for future research in this intersection ﬁeld are discussed.

1 INTRODUCTION

In educational institutions (schools, colleges, univer-

sities, etc.), regardless of the level at which they act,

one of the most recurrent and important problems

is the preparation of class-teacher schedules. The

scientiﬁc literature dedicated to this problem gene-

rally calls it Educational Timetabling Problem (Ed-

TTP), being a subcategory of the so-called Scheduling

Optimization Problems, as exempliﬁed by Fernandes

et al. (2016) and Saviniec et al. (2018).

Solving an instance of an Ed-TTP is, typically, to

ﬁnd a way to associate a set of events to a set of avai-

lable timeslots, and, in some cases, also to deﬁne the

locations where these events will occur. An event is

often called a class or a didactic session, and brings

together a group of teachers and students who will

carry it out using a room (a typical classroom, a la-

boratory, a theater, a studio, etc.). In real scenarios,

another common fact is the need for an eligible solu-

tion that satisﬁes hard and soft constraints relating ex-

pected events and all the necessary resources, such as

teachers or lectures, auxiliary equipment (blackboard,

data projector, computer, etc.), speciﬁc rooms (labo-

ratory, theater, a studio, etc.) and technical support

teams. The hard constraints are of compulsory atten-

dance, while soft constraint are optional, but conve-

nient in favor of improving the quality of the obtained

solution.

As a result of more than six decades of research,

the scientiﬁc community devoted to timetabling de-

monstrates that most of its variations belong to the

class of N P -Hard problems, as shown by Werra et al.

(2002) and Elloumi et al. (2014), among others. There

are currently a large number of computational met-

hods available for its satisfactory resolution, dealing

with different problem speciﬁcations and sizes of in-

stances. Many of these methods are synthesized in

(Schaerf, 1999; Lewis, 2008; Pillay, 2014; Babaei

et al., 2015; Oude Vrielink et al., 2017).

In general, the identiﬁed solution for an instance

of a timetabling problem is visually presented in the

form of a 2D table or a set of them, showing the days

of the week and the times of the scheduled activi-

ties and even the place where each activity will occur.

User interaction with the table can be supported in or-

der to provide extra textual information or to allow

manipulation of the time scheduling. Such a conﬁgu-

ration, very common in many timetabling systems, is

referred here as a traditional 2D-table format/system.

Understanding all types of information using a ta-

ble representation may be a challenging task. The

Information Visualization (IV) area highlights that

some other visual techniques can emphasize proper-

ties of an abstract object, thus allowing a better under-

standing of it and raising cognition, as argue Gershon

Alencar, W., Dantas do Nascimento, H., Soares, F. and Longo, H.

Visualization Methods for Educational Timetabling Problems: A Systematic Review of Literature.

DOI: 10.5220/0007375802750281

In Proceedings of the 14th International Joint Conference on Computer Vision, Imaging and Computer Graphics Theory and Applications (VISIGRAPP 2019), pages 275-281

ISBN: 978-989-758-354-4

275

and Eick (1997) and Card et al. (1999).

In this context, the current paper presents the

“state of art” of IV methods applied to Ed-TTPs by an

analysis of the scientiﬁc publications registered in the

last twenty years (1998–2018) in seven solid scientiﬁc

databases. In addition, we present some possibilities

for future work that researchers, dedicating themsel-

ves to the intersection of the areas of timetabling and

information visualization, may pursue.

The remainder of this work is organized as fol-

lows: Section 2 describes the methodology adopted

for the literature review; Section 3 explains the steps

conducted in the review and their quantitative results;

Section 4 presents the contributions of the main pa-

pers found in the SRL, with focus to the proposed

IV techniques and their forms of interaction; and

Section 5 draws our conclusions about the relations-

hip between IV and Ed-TTP.

2 RESEARCH METHODOLOGY

For the study, we performed a Systematic Review of

the Literature (SRL), since it is a process that provi-

des well-deﬁned, solidly backed bases for the iden-

tiﬁcation, evaluation, synthesis and interpretation of

the relevant evidences to a particular research ques-

tion. Following the SRL guideline deﬁned in (Kit-

chenham and Charters, 2007), three main stages were

taken: (I) deﬁning a review protocol; (II) conducting

the review of the studies; and (III) reporting the re-

view.

The ﬁrst stage involved, in turn, the deﬁnition of:

(I.1) research questions; (I.2) keywords, synonyms

and search strategy; (I.3) inclusion and exclusion cri-

teria for the selection of studies; and (I.4) a checklist

for study quality assessment.

Each of these elements is detailed next. To carry

out the SRL in a collaborative way between the aut-

hors of current paper, two software platforms were

used: Parsifal (https://parsif.al/) and SESRA

(http://sesra.net/).

2.1 Research Questions

The main objective of the SRL was to answer the fol-

lowing question: “What is the state of the art in the

application of IV methods to the presentation or/and

the manipulation of solutions for Ed-TTP?”.

Some more speciﬁc questions that unfolded the

previous one were formulated: (RQ.1) What are the

IV methods currently available for presenting and/or

manipulating solutions for Ed-TTP? (RQ.2) Do the

visualizations help to identify different aspects of a

timetabling solution such as: unassigned classes and

teachers/lectures, the distribution of the classes over

the week, time scheduling conﬂicts, the matching be-

tween the teachers’ preferences and what was effecti-

vely scheduled for them, etc.? (RQ.3) Has the effecti-

veness of the new visualizations been compared to

the traditional 2D-table format? (RQ.4) If the answer

for Question RQ.3 is “yes”, then what measurements

were adopted for evaluating effectiveness? (RQ.5) Do

the visualizations show a single solution or the “so-

lution space” for the timetabling problem being sol-

ved? (RQ.6) Do the visualizations support human in-

teraction? (RQ.7) If the answer for Question RQ.6

is “yes”, then what types of interaction (for example:

applying data ﬁlters, drag-and-dropping elements of

the visualization, selecting areas of interest for focu-

sed optimization, etc.) are supported? (RQ.8) If the

answer for Question RQ.6 is “yes”, which are the aims

of the interactive features designed for the visualiza-

tions (helping understand the timetabling; helping de-

ﬁne the timetabling problem in a more precise way;

or helping ﬁnd a better solution for the timetabling

problem)?

It is important to emphasize that the above que-

stions RQ.6–RQ.8 are directly related to the use of

interactive techniques, mediated by a visual user in-

terface, as an approach to solve scheduling problems,

in this case, a timetabling problem.

2.2 Keywords, Synonyms and Search

Strategy

The following keywords, usually with a high in-

cidence in the scientiﬁc literature dedicated to the

topic, and their associated synonyms, were cho-

sen for driving the SRL: (K.1) timetabling (timeta-

ble, time table, time-table); and (K.2) visualization

(GUI, interface, presentation, view, visual, visualisa-

tion); (K.3) educational (classroom, college, educa-

tion, school, university).

The general logic search string was deﬁned

as [[timetabling] ∧ [visualization ∧ educational]], with

each pair of brackets a disjuntion of synonyms.

This string was adjusted for every electronic da-

tabase in order to meet its search syntax. We se-

arched on seven databases: (1) ACM Digital Li-

brary; (2) DOAJ – Directory of Open Access Jour-

nals; (3) IEEE Digital Library; (4) Science Direct;

(5) Scielo; (6) Scopus; and (7) Springer Link, since

they gather most of the publications on the area of ti-

metabling and IV.

In order to concentrate the search on the most rele-

vant papers (and not potentially in thousands of unre-

lated publications), the search string was applied only

IVAPP 2019 - 10th International Conference on Information Visualization Theory and Applications

276

on the ﬁelds paper titles, keywords, and abstracts of

the databases, usually referenced as TAK, except for

the DOAJ and the Springer Link, in which the se-

arch was made throughout the full text of the papers.

For the Scopus database, only the K.1 part of the se-

arch string was applied on TAK, while the remain-

der of it (K.2 and K.3) was veriﬁed on the full text.

This broadened the search, but still kept the amount

of results manageable. Another special case was the

ACM Digital Library, where the search was done in

the “The ACM Guide to Computing Literature” col-

lection, since this contains the complete set of articles

in the area of Computing and related ﬁelds.

In addition, we restricted the search in all databa-

ses to the period from 1998 to 2018 (until Oct/2018).

Through an extensive search before the realization of

the SRL, in the aforementioned databases and using

the same search string, publications prior to the year

1998 were identiﬁed but disregarded, since they no-

tably use traditional 2D-table to present solutions for

the Ed-TTP. Furthermore, when some kind of inte-

ractivity was reported, it was performed by simple

drag-and-drop or copy-and-paste operations and se-

lect/deselect of elements, such as cells and regions.

Consequently, only works published in the the last

twenty years were considered relevant.

2.3 Inclusion/Exclusion Criteria

Inclusion and exclusion criteria were deﬁned for gui-

ding the selection of primary studies relevant to the

SRL. A study was included if it was: (1) available

in full-text; (2) published in a journal or in the an-

nals of a conference; (3) a technical report, including

surveys; or (4) a master dissertation or a doctoral the-

sis. On the other hand, it was excluded if it: (1) was

not written in English; (2) did not present, or dis-

cuss, techniques of the IV area; or (3) did not propose

and/or discuss an IV technique for the Ed-TTP; (4) fo-

cused only on traditional 2D-table visualizations with

ordinary user interactions.

A set of Yes/No quality assessment questions was

also deﬁned based on a reﬁnement of the main rese-

arch questions (RQs). For instance, they asked if the

visualization method in use could be changed in the

graphical interface or if a particular type of interaction

for some speciﬁc goal was supported.

3 CONDUCTING THE REVIEW

The proper search strings, with the corrected search

conditions, were applied to the databases. Next, as

a Study Selection step, the bibliographic references

were evaluated according to the inclusion and the ex-

clusion criteria (with the help of the SRL software

platforms). When necessary, the full text of the stu-

dies was consulted.

Table 1 summarizes the number of papers recove-

red when searching in each database, and the amount

of accepted (selected) and reject studies during the

Selection step. In Total, when removing duplicates,

only 10 studies were accepted, with 8 of them being

academic productions of a same research group.

Table 1: Number of Studies (1998–2018) in the SRL.

Database Total Accepted Rejected

ACM DL 346 4 342

DOAJ 11 0 11

IEEE DL 54 5 49

Scielo 1,734 0 1,734

ScienceDir 64 0 64

Scopus 1,362 7 1,355

Springer 2,314 2 2,312

Some limitations faced during the search process and

the strategies adopted in order to overcome them are

worth mentioning. The Scielo database did not al-

low a search with the complete search string. There-

fore, three search activities had to be performed, each

using a distinct pair of the components of the search

string: timetabling (K.1), visualization (K.2) and edu-

cational (K.3). The employed strings were: (K.1 ∧

K.3), that returned six studies; (K.2 ∧ K.3), that re-

sulted in 1,734 studies; and (K.1 ∧ K.2), that returned

only one study. The union of these results had exactly

1,734 papers. After reading and analyzing titles and

abstracts, only twelve papers had to be read comple-

tely and none of them were accepted.

Another particular, and more complex case was

that of Springer Link database. The search in it can

not be limited to Title-Abstract-Keywords (TAK) and

had to be performed throughout the full text. As a

consequence, 16,542 studies were returned: 2,545 pu-

blished in conferences and 13,997 in journals. The

results were then ﬁltered to show only the ones in

the ﬁelds of “Computer Science”, “Engineering” and

“Mathematics”, what reduced the search to 2,314 pa-

pers.

Given the limited number of accepted papers, the

quality criteria were not evaluated and, therefore, the

Quality Assessment step was not performed.

Finally, all accepted papers were fully read and

all relevant data for answering the search questions

was extracted. Table 2 synthesizes the major aspects

of identiﬁed studies in this SRL. The table columns

contain the following information:

Visualization Methods for Educational Timetabling Problems: A Systematic Review of Literature

277

1. Bibliographic reference of the study;

2. IV method(s) that was applied;

3. Data elements displayed by the IV method;

4. Types of Interaction supported by the IV, conside-

ring ﬁve possibilities — [OF] allow to change the

objective function of the underlying optimization

timetabling problem; [Constr.] allow to change

constraints of the optimization problem; [Techn.]

allow to choose and run one of many optimization

methods; [Manual Sol.] a timetabling solution

can be manually changed using the visualization;

and [Sel. Area] allow to select a region for de-

leting, including or changing data in group;

5. Available application that implements the work;

and

6. Optimization technique(s) being used for the reso-

lution of the underlying problem.

It is important to note that one of the difﬁculties

encountered during the SRL is that some of the stu-

dies do not clearly present information that allows us

to answer certain research questions in a safe way. In

this scenario, some level of interpretation was neces-

sary, but always with the largest effort to provide the

right answer. In the worst case, the evaluation could

not be performed in that context or the response was

inconclusive, which is signaled by a dash (–) in Ta-

ble 2.

Next, we describe the main concepts in some of

the studied selected by the SRL.

4 VISUALIZATION METHODS

FOR Ed-TTP

In one of the ﬁrst studies published in the investiga-

ted period (Piechowiak and Kolski, 2004), the aut-

hors propose an interactive decision support system

for the analysis of educational timetabling problems

and the elaboration of solutions for them. The sy-

stem has a visualization module that shows an inter-

face customized to the user proﬁle (designers, analy-

zers and consultors) and that employs both 2D-tables

and a time chart (resources × time) for user interacti-

ons. A timetabling solution is built manually, but with

a constraint-based reasoning engine to assist the user

in obtaining a solution to the target problem, inclu-

ding hard and soft constraint violation detection in a

semi-automatic way.

Another paper, by Thomas et al. (2008) focuses on

solving Examination Timetabling Problems (Exam-

TTP), a type of Ed-TTP. The authors propose a visual

framework that operates on three interrelated phases:

pre-processing (visualizing raw data inputted from

the user), processing (solving the optimization pro-

blem and visualizing the generated timetabling solu-

tion) and post-processing (improving the timetabling

solution) of a timetabling solution. A visual model

is used by the authors as an instrument to clarify the

problem complexity – a NP-hard problem – and to

provide an integrated visualization of the phases that

can contribute to its understanding and satisfactory re-

solution. The article details the use of IV techniques

for the pre-processing phase, in which, for example,

directed graph drawings indicate the relationship bet-

ween enrolled candidates (students) with the courses

for a particular semester. In another example, courses

are represented by nodes and constraints are modelled

by edges, as shown in Figure 1a. The node color in-

dicates the period of the day when a course is taught.

Nodes with the same color are being offered concur-

rently in the same academic period.

In an extension of the previous work, and by me-

ans of a pair of strongly related studies (Thomas et al.,

2009b,a), more visualization techniques are proposed

for the pre-processing phase. The new visualizations

include: a tree view (aggregating many types of data),

a directed graph drawing, a histogram combined with

a circular graph layout (courses × enrolled students);

and some standard histograms (rooms × subjects and

rooms × timeslots). It is possible for the user to in-

teract with the visualizations but for the aim of better

understanding the data.

Still researching on Exam-TTP, further studies of

the same group of authors (Thomas et al., 2010b,c)

propose a tool, called VizSolution, for the processing

phase of the visual framework they conceived. An in-

teractive visualization approach is adopted, in which

a user and a machine (a scheduler implemented as a

constraint satisfaction program) operate in a symbio-

tic way for solving a timetabling problem, including

the allocation of classrooms. The tool allows to de-

ﬁne the problem by means of an element called Fil-

ter, which employs graph drawing to represent con-

straints, as shown in Figure 1b. Graph drawings (in

2D and projected 3D) are also used to indicate con-

ﬂicts and/or preferences.

With the goal of helping the user to more ea-

sily identify and to solve time conﬂicts in teachers

and courses’ schedules, some researchers (Fui et al.,

2010) have proposes a system, named CORECTS,

that models a timetabling solution as a graph. A

modiﬁed version of a standard graph drawing algo-

rithm is employed for visually presenting the solution

and to highlight conﬂicts. Via “simple strokes gestu-

res” made by user on the visualization (using a touch

screen monitor), it is possible to do operations that

IVAPP 2019 - 10th International Conference on Information Visualization Theory and Applications

278

affect the conﬂicts.

Back to the Exam-TTP (Thomas et al., 2011), pa-

rallel coordinates were used for answering the ques-

tion: “How hard is this problem to solve?”. The aut-

hors conceived the ParExaViz tool, which facilitates

the exploration of raw data of an Exam-TTP instance

and to highlight conﬂicts.

Addressing the problem of university timetabling,

some other authors (Abdelraouf et al., 2011) intro-

duce a visual graphic communication tool that lets the

users to specify their problem in an abstract manner,

involving human resources (people), events (lectures)

and meta-events (courses). These elements are repre-

sented by nodes in a graph, while edges indicate their

relationships. The edges have different interpretations

according to the type of the elements involved. A vi-

sual interface integrates textual and graphical compo-

nents (many tabs). The timetabling problem is solved

by a module that implements a constraint satisfaction

algorithm.

Finally, a system called ExamViz (Thomas et al.,

2012) is conceived with an integrated problem sol-

ving environment (PSE) to the Exam-TTP. It works as

a computational steering mechanism with automated

steering interactions and/or with a user-driven pro-

cess. Through the user interface, it is possible to per-

form conﬂict analysis in the timetable and to apply

a reconciliation process based on evolutionary algo-

rithms. The analysis can be done visually using pa-

rallel coordinates as well as 2D-tables and graph dra-

wings.

5 CONCLUSIONS

Based on a SRL, we found that, in the last twenty

years, only few studies have investigated the use of

advanced information visualization methods for hel-

ping understand and/or solve educational timetabling

problems. This contrasts to the majority of scienti-

ﬁc papers in the timetabling area, which main con-

cern is to provide a method capable of solving the

problem close to optimality, with little or no atten-

tion to the visualization aspect. Some examples of

such works are Nouri and Driss (2016), Babaei et al.

(2018) and Lindahl et al. (2018). Nevertheless, in the

latter article (Lindahl et al., 2018), the authors high-

light that the work could be complemented by having

a graphics user interface. Another recent work (Oude

Vrielink et al., 2017) emphasizes that, while the aca-

demia tends to develop intelligent and profound met-

hods to solve timetabling problems, the industry ap-

pears to develop and to design an easy to use inte-

ractive tool that aims at meeting the needs of the edu-

(a)

(b)

Figure 1: Examples of timetable visualizations: (a) repro-

duced from Thomas et al. (2008); (b) VizSolution, reprodu-

ced from Thomas et al. (2010b).

cational institutions.

Some ideas for future work were identiﬁed during

this SRL. They include:

1. Developing new visualization approaches for hel-

ping to identify and understand the main factors

responsible for infeasibility in large-scale timeta-

bling problem instances;

2. Proposing new visualizations for supporting in-

teractive optimization of educational timetabling

problems and investigating their effectiveness and

usability;

3. Extending the SRL for including the study of com-

mercial and non-commercial software systems for

Ed-TTP, focusing on the visualizations and on the

interaction features; and

4. Adjusting visualization methods proposed to time-

tabling in other areas, such as for organizing hos-

pitals’ agendas and transportation (bus, train and

airplane) schedules, to the Ed-TTP scenario.

Visualization Methods for Educational Timetabling Problems: A Systematic Review of Literature

279

Table 2: Analysis of the Accepted Publications. Some features are marked as [Y]es, [N]o or [–] for inconclusive.

Study Identiﬁcation and Characterization Interaction types by IV Technique(s) Application and Solution Techn. Appl.

Reference IV Method Displayed Data Elements Optimiz. Manual Select Applic. Method(s) Used to

Identiﬁcation Applied by IV Method OF Constr. Techn. Solution Area Solve the Ed-TTP

Piechowiak and Kolski (2004) 2D-table and time chart. timetable, resources x time. N Y N Y N Y Manual with constraint-based rea-

soning.

Thomas et al. (2008) Oriented cluster graph

drawing.

classes and students enrolled. – Y N Y N N Manual or by any automatic sche-

duler.

Thomas et al. (2009b) Directed graph drawing,

histogram, daisy chart,

tree view

pre-processing data (raw input

data).

N N N N Y Y There is no attempt to solve the pro-

blem, just processing/visualizing

raw input data.

Thomas et al. (2009a) 2D-table, oriented clus-

ter graph drawing, histo-

gram and tree represen-

tation

timetable (complete) and pre-

processing data (raw input data).

N Y N N Y Y Constraint Satisfaction Program.

Thomas et al. (2010b) 2D-table, graph drawing

(2D, 3D).

timetable (complete), constraints

and conﬂicts.

– Y N Y Y Y Constraint Satisfaction Program (in

a constraints network, with back-

tracking) with user collaboration.

Thomas et al. (2010c) 2D-table, graph drawing

(2D, 3D).

timetable (complete), constraints

and conﬂicts.

– Y N Y Y Y Constraint Satisfaction Program (in

a constraints network) with user

collaboration.

Thomas et al. (2010a) 2D-table, graph drawing,

tree representation

timetable (complete), constraints,

conﬂicts.

N Y N Y Y Y Visual analysis heuristics and evo-

lutionary algorithms.

Abdelraouf et al. (2011) Undirected graph dra-

wing (representing peop-

les, courses, ...)

timetable with day/time, graphs and

text

N Y N Y N Y Constraint satisfaction problem sol-

ving.

Thomas et al. (2011) Parallel coordinates (for

uni/multi dimensional

variables).

timetable (complete). N N N N Y Y There is no resolution of the pro-

blem, just processing raw data.

Thomas et al. (2012) 2D-table, graph drawing

(2D, 3D), parallel coor-

dinates.

timetable (complete), constraints

and conﬂicts.

– Y – Y – Y Manual and user-driven problem

solving environment, with clashes

reconciliation (AI Techniques).

IVAPP 2019 - 10th International Conference on Information Visualization Theory and Applications

280

ACKNOWLEDGEMENTS

This work was ﬁnancially supported by the

Coordenac¸

ao de Aperfeic¸oamento de Pessoal de

ıvel Superior (CAPES) and the Fundac¸

ao de

Amparo

a Pesquisa do Estado de Goi

as (FAPEG).

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