Multiobjective Memetic Algorithms applied to University Timetabling

Problems

Nuno Leite

1,2

, Fernando Mel

ıcio

1,2

and Agostinho Rosa

2,3

ISEL - Lisbon Polytechnic Institute, R. Conselheiro Em

ıdio Navarro, 1, 1959-007 Lisboa, Portugal

LaSEEB-System and Robotics Institute, Av. Rovisco Pais 1, TN 6.21, 1049-001 Lisboa, Portugal

Department of Bioengineering/IST, TU-Lisbon, Av. Rovisco Pais, 1, 1049-001 Lisboa, Portugal

1 STAGE OF THE RESEARCH

1.1 Introduction

The present document describes the Ph.D. thesis pro-

posal of Nuno Leite, doctoral candidate in Electrical

and Computer Engineering at the Technical Univer-

sity of Lisbon (IST/TU-Lisbon). The thesis is titled

“Multiobjective Memetic Algorithms applied to Uni-

versity Timetabling Problems” and is supervised by

Drs. Agostinho Rosa (IST/TU-Lisbon) and Fernando

Mel

ıcio (ISEL/Polytechnic Institute of Lisbon). The

research work is developed in the LaSEEB (Evolu-

tionary Systems and Biomedical Engineering Lab) at

the IST/TU-Lisbon. The ﬁve year doctoral program

enrolled by Nuno Leite started in December 2010 and

ends in December 2015. The curricular part of the

doctoral program include the realization of four Ph.D.

courses.

1.2 Scope of Research

Nuno’s thesis concerns the study and implementation

of population based metaheuristics for solving uni-

versity timetabling problems, e.g. the examination

timetabling and post-enrolment course timetabling

problems. The study will be focused in approaching

these problems as single and multiobjective problems

using memetic algorithms.

1.3 Developed Work

Nuno has now completed three of the four Ph.D.

courses. These courses are: Nonlinear Optimization

(completed), Intelligent Optimization (completed),

Multiobjective Optimization with Evolutionary Al-

gorithms (completed), and Statistical Learning (not

completed yet). Related to the thesis work, Nuno has

published one conference paper (Leite et al., 2012).

This paper was further selected so that a revised and

extended version of this paper will be published by

Springer-Verlag in a SCI Series book (Leite et al.,

2013b). In May 2013, the authors submitted a po-

sition paper to the IJCCI/ECTA 2013 (Leite et al.,

2013a), which was accepted for publication as a short

paper. In the paper (Leite et al., 2012), the authors

present a bi-objective memetic algorithm for solv-

ing a real instance of the uncapacitated examination

timetabling problem from the ISEL/Polytechnic Insti-

tute of Lisbon. The automatic algorithm implemented

was able to produce feasible timetables with lower

number of conﬂicts in students’s exams compared

with the manual solution, and in a shorter time. In

the paper (Leite et al., 2013b), the previous work was

further extended to solve the capacitated case. Also,

rooms are allocated automatically by the algorithm.

In the novel work (Leite et al., 2013a), the applica-

tion of a recently proposed single-objective memetic

algorithm (known as SFLA – Shufﬂed Frog-Leaping

Algorithm) to the examination timetabling problem is

studied. The proposed adaptation was evaluated on

the standard Toronto benchmark datasets with com-

parable results to the state-of-the-art algorithms. We

now intend to study forms of improving the proposed

algorithm which include: (i) implement a diversity

management procedure in order to control the popu-

lation diversity, (ii) study the problem landscape char-

acteristics and propose efﬁcient neighbourhood oper-

ators to be incorporated in the local search step of

the algorithm, and (iii) propose an extension of the

algorithm by managing multiple objectives and ex-

periment with the Toronto and the 2nd International

Timetabling Competition (ITC2007) benchmark data.

Leite N., Melício F. and Rosa A. (2013).

Multiobjective Memetic Algorithms applied to University Timetabling Problems.

In Doctoral Consortium, pages 29-37

 SCITEPRESS

2 OUTLINE OF OBJECTIVES

2.1 General Objectives

The research work undertaken has the following ob-

jectives:

1. Solve hard multiobjective combinatorial opti-

mization problems by approaching them with

Multiobjective Memetic Algorithms. The study

will focus on University Timetabling Problems

such as the Examination timetabling problem or

the Post-enrolment course timetabling problem.

2. Propose a novel multiobjective problem for-

mulation and benchmark data for examination

timetabling problem instances found in Por-

tuguese universities.

3. Implement the proposed algorithms in a parallel

way using existing frameworks and libraries.

4. Implement an application with a graphical user

interface that helps the timetable planner in

the multiobjective (many-objective) optimization

process.

2.2 Description

The following items describe in more detail the ob-

jectives of the research work.

1. Study university timetabling problems in its dif-

ferent dimensions: as scalar (single-objective) and

as multiobjective optimization problems. Typi-

cally, multiobjective approaches solve intermedi-

ate scalar versions of the problem at hands (e.g.

multiobjective evolutionary algorithms that use

decomposition, MOEA/D (Zhang and Li, 2007)).

In particular, in examination timetabling, we will

consider the following problems:

- single-objective problems of Toronto

and

ITC2007

benchmark datasets;

- bi-objective problems of Toronto benchmark

datasets;

- many-objective problems of ITC2007 bench-

mark datasets.

2. Propose scalar and multiobjective memetic algo-

rithms that can efﬁciently solve the studied prob-

lems. Compare the proposed algorithms with cur-

rent state-of-the-art algorithms.

University of Toronto benchmark data proposed

in (Carter et al., 1996).

2nd International Timetabling Competition benchmark

data (McCollum et al., 2012).

3. Propose a model and benchmark data for a new

multiobjective examination timetabling problem

found typically in Portuguese universities. This

model extends the ITC2007 model and cover a

more realistic model comprising:

- different interrelated examination sessions that

include intermediate evaluation tests (usually

two or three tests or a global test in some cases)

during the academic semester or year. These

are followed by a ﬁnal examination period,

which is formed, normally, by two examination

sessions;

- consider more hard and soft constraints. Some

characteristics of the problem are the follow-

ing. The intermediate evaluation tests during

the semester should take place in the days of

one of the classes. In this scenario the classes’s

timetables have to be considered in order to

know the days of each class for schedule the

evaluation tests. For examinations with few

students (e.g. less than 100), the examina-

tions should take place in the rooms of one of

the classes. Otherwise, if the examination has

a large number of students, then it should be

scheduled into examination special rooms. The

date of the last intermediary examination test

must be far apart from the corresponding ﬁrst

ﬁnal examination date. Also, all examinations

should be spread out for each student, number

of used periods minimized, among other con-

straints.

This new problem will be also solved by the pro-

posed multiobjective algorithm.

4. Study and design a multiobjective memetic algo-

rithm parallel implementation.

5. Study forms of interacting with the decision

maker in many-objective optimization. Design an

interactive multiobjective memetic algorithm and

an application with a graphical user interface that

expose the algorithm functionality.

In the following section, we describe the research

problem in detail.

3 RESEARCH PROBLEM

In this thesis we address the class of university

timetabling problems, which include problems such

as course scheduling and examination timetabling.

The problem will be approached in a generic way but

we intend to conduct practical experiments on spe-

ciﬁc problems such as the examination timetabling

IJCCI2013-DoctoralConsortium

problem (ETTP) found in universities. The univer-

sity timetabling problems belong to the general class

of NP-complete Combinatorial optimization prob-

lems (Lewis, 2008). This implies that deterministic

exact algorithms, which guarantee ﬁnding of optimal

solutions, can only be applied to small sized prob-

lem instances. Due to this, there’s a growing inter-

est in using metaheuristics (Glover and Kochenberger,

2003), (Gendreau and Potvin, 2010) to solve real in-

stances of these hard combinatorial problems.

The university timetabling is a subset of the gen-

eral family of timetabling and scheduling problems.

The aim of these problems is to assign a set of en-

tities (e.g. tasks, events, people, vehicles) to limited

number of resources over time, respecting a set of pre-

deﬁned schedule requirements (Lewis, 2008). In this

sense, the university timetabling problem is generi-

cally deﬁned as the task of assigning a number of

events, such as lectures, exams, or meetings, to a lim-

ited set of timeslots and rooms, satisfying a set of con-

straints. A categorization of typical constraints can

be found in (Lewis, 2008). The constraints are fur-

ther classiﬁed in hard and soft constraints. The ﬁrst

ones are related to the feasibility of the timetable (e.g.

a teacher cannot be scheduled to give two different

lectures at the same timeslot in course timetabling, or

a student cannot take two different exams at the the

same timeslot, in examination timetabling), and can-

not be violated. The soft constraints should be satis-

ﬁed, if possible, as they contribute to the improvement

of the timetable quality for the different stakehold-

ers (students, institution, professors/invigilators, etc.),

but they could be violated. An example of a soft con-

straint is the Period spread (McCollum et al., 2012)

in examination timetabling, with the aim of spreading

the exams for all students as much as possible.

Real instances of university timetabling problems

encountered in practice, such as the ETTP, have sev-

eral hard and soft constraints. As in many other prob-

lems in scheduling and other areas, these constraints

can be seen as multiple objectives, conﬂicting or not,

which means that university timetabling problems are

multiobjective optimization problems (MOPs) in na-

ture. Due to the associated extra complexity, in prac-

tice these problems have been approached mainly as

single-objective problems and very few studies con-

sider multiobjective approaches.

The approaches found in literature to solve the

ETTP were ﬁrst categorised by Carter (Carter, 1986)

into four types: sequential methods, cluster methods,

constraint-based methods and generalised search.

Later, Petrovic and Burke (Petrovic and Burke,

2004) added more categories: hybrid evolutionary al-

gorithms, metaheuristics, multi-criteria approaches,

case based reasoning techniques, hyperheuristics and

adaptive approaches.

Evolutionary approaches are well suited to tackle

multiobjective problems because a population of so-

lutions is already maintained, therefore a set of non-

dominated solutions (trade-off solutions) could be

determined at the end of one generation of the al-

gorithm. The Multiobjective Evolutionary Algo-

rithms (MOEAs) have been extensively studied in

the last 20 years (Van Veldhuizen and Lamont,

2000) (Zhou et al., 2011). It is well known that

combining a local search procedure into an evolution-

ary algorithm greatly improves the algorithm’s perfor-

mance. These algorithms were named Memetic Algo-

rithms (MAs) (Moscato and Norman, 1992) (Neri and

Cotta, 2012). Recently, researchers began combin-

ing the ideas of MOEAs with memetic evolution, and

propose several Multiobjective Memetic Algorithms

(MOMAs). These were used recently for solving hard

Combinatorial optimization problems with good suc-

cess (Jaszkiewicz et al., 2012). Hybridizations of evo-

lutionary algorithms with other techniques other than

local search metaheuristics, for instance with exact

algorithms, seem also to be very promising (Raidl,

2006). In (Ehrgott and Gandibleux, 2008) the au-

thors survey Multiobjective (meta)heuristics for solv-

ing multiobjective combinatorial optimization prob-

lems, focusing on recent approaches, where meta-

heuristics are hybridized with exact methods.

In Multiobjective Optimization (MOO), the prob-

lems are usually classiﬁed in two categories. If the

number of objectives is below three or four, the op-

timization problem is termed simply as MOP; other-

wise, if for a number of objectives greater than three

or four, the problem is termed Many-objective opti-

mization problem (Zhou et al., 2011).

The early algorithms proposed for Evolutionary

Multiobjective Optimization (EMO), such as NSGA-

II (Deb et al., 2002), don’t work well for the many-

objective case (Ishibuchi et al., 2008) (Zhou et al.,

2011). As such, many-objective problems pose new

challenges for algorithm design, visualisation and im-

plementation.

Multiobjective optimization involves three

phases (Coello et al., 2006), (Branke et al., 2008):

model building, optimization, and decision making.

So, converting a MOP into a single-objective problem

puts the decision making task before optimization,

and before the existing alternatives are known.

The task of a multiobjective algorithm, as shown

in Figure 1, is to ﬁnd a good approximation of

the true Pareto front to the decision maker (DM).

Three aspects of the solution set quality are usually

considered:

MultiobjectiveMemeticAlgorithmsappliedtoUniversityTimetablingProblems

Figure 1: Requirements of a MOEA. (Illustration from

Prof. Peter J. Fleming site, http://www.shef.ac.uk/acse/

staff/peter ﬂeming/manyoo).

1. Proximity, the produced set should contain solu-

tions close to the true Pareto set.

2. Diversity, the solutions in the approximated set

should be well distributed.

3. Pertinency, the produced set should contain solu-

tions in the DM’s region of interest (ROI). The

deﬁnition of a ROI is especially relevant as the

number of objectives increase, because the num-

ber of solutions of the approximated set also in-

creases, thus increasing the difﬁculty of the DM

to analyse all the alternatives.

4 STATE OF THE ART

4.1 Single-objective Approaches to the

ETTP

The development of systems to automate the con-

struction of university examination timetables has

begun in the 1960 decade. The paper (Qu et al.,

2009) constitute a survey of the recent (from 1995

to 2008) techniques and algorithmic approaches used

to solve this problem. Lewis (Lewis, 2008) sur-

veys metaheuristic-based techniques applied to Uni-

versity Timetabling problems. These two surveys

describe techniques applied to Toronto, Nottingham

and Melbourne benchmarks. M

uller (M

uller, 2009)

and Gogos (Gogos et al., 2012) propose two efﬁcient

scalar optimization techniques to the ITC2007 bench-

mark data (these authors were the winner and second

classiﬁed in the ITC2007 competition, respectively).

uller’s algorithm is based on a general Constraint

solver developed by the author which was adapted to

the ETTP. Gogos apply a multi-stage algorithm com-

prising several metaheuristics and also a step where a

Branch & Bound based method was applied.

Researchers recognized that next to the algorithm

used to optimize this problem, the way the neighbour-

hoods are constructed and sampled is important (De-

meester et al., 2012) (Abdullah et al., 2010). The

Kempe chains, introduced by Morgenstern (Morgen-

stern, 1989) for solving graph colouring problems,

is one of the most successful neighbourhoods. The

Kempe chain-based neighbourhood was ﬁrst applied

on the ETTP by Thompson and Dowsland (Thomp-

son and Dowsland, 1998), which used the Simulated

Annealing metaheuristic. The Kempe chain heuris-

tic maintains feasibility by swapping infeasible exams

between time slots. The simple neighbourhood intro-

duced in Burke and Bykov (Burke and Bykov, 2008)

is also frequently used. This heuristic swaps all exams

of two randomly chosen time slots, and so it maintains

feasibility.

4.2 Multiobjective Approaches to the

ETTP

More recently, the ETTP has been approached like a

Multiobjective/Multi-criteria Optimization problem,

recognizing the true dimensions of real world prob-

lems, that typically have many facets to consider

(proximity costs between student exams, timetable

lengths, room assignment, invigilator availability,

etc.). Silva et al. (Silva et al., 2004) present

an overview on multiobjective timetabling meta-

heuristics. Multi-criteria techniques were proposed

in (Burke et al., 2001) and (Petrovic and Bykov,

2003). Pais and Amaral (Pais and Amaral, 2009)

also approach ETTP (Toronto benchmark) as a mul-

tiobjective problem, and consider the four objec-

tives studied in (Petrovic and Bykov, 2003). Other

recent works (C

e et al., 2004), (Wong et al.,

2004), (Cheong et al., 2009) and (Mumford, 2010),

applied MOEAs to solve the ETTP. The current au-

thors propose in (Leite et al., 2012) a MOEA based

on NSGA-II and applied it to a real problem instance

of a Portuguese university. The crossover and muta-

tion operators were adapted from the ones in (Cheong

et al., 2009). A computational analysis involving

MOEAs for the ETTP is given in (Paquete and Fon-

seca, 2001). Burke et al. (Burke et al., 2008) and

later (McCollum et al., 2012) present the ITC2007

problem as an MOP. They consider four objectives,

each representing a compromise between the various

interested parties or stakeholders. These parties are:

(1) student interests for a good individual timetable,

(2) interests of exam invigilators (and students), (3)

IJCCI2013-DoctoralConsortium

the front load (representing the desire of the exam

markers to receive the largest exams as soon as pos-

sible so as to have more time for marking), and (4)

the estate management interests in avoiding the use

of some rooms and periods. Due to the complexity

of this four objective problem, in Burke et al. (Burke

et al., 2008) work the objectives are further grouped

in two objectives concerning the students interests and

the administration interests. The authors then apply a

solver (CPLEX solver) to solve smaller versions of

the real datasets. It is mentioned that due to the unop-

timized formulation used, the full instances could not

be solved.

4.3 Parallel Metaheuristics

Alba et al. (Alba et al., 2013) present recent ad-

vances and new trends on Parallel metaheuristics.

Talbi (Talbi and Hasle, 2013) present an editorial re-

view of the application of metaheuristics on GPUs.

Coello et al. (Coello et al., 2006) also dedicate a chap-

ter to MOEA parallelization. In (Nebro and Durillo,

2010), a MOEA/D parallel implementation was pro-

posed.

4.4 Many-objective Optimization

Algorithms

In addition to the previous referred research on

multi and many-objective optimization, we include

some recent developments on the NSGA-II and the

MOEA/D algorithms. In (Deb and Jain, 2012), the

authors propose a many-objective NSGA-II (MO-

NSGA-II). Recently (Jain and Deb, 2013), the same

authors present an improved MO-NSGA-II. In (yan

Tan et al., 2013), it is proposed an improved MOEA/D

for many-objective optimization.

5 METHODOLOGY

I’m developing a portable library containing single-

objective and multi-objective algorithms. The lan-

guage used is the C++ programming language. In or-

der to reuse some code and to implement the parallel

MOEA we are using the ParadisEO library (Cahon

et al., 2004).

5.1 Neighbourhood and Variation

Operators

I intend to implement some efﬁcient neighbourhoods

such as Kempe chains and time slot swaping, men-

tioned in Subsection 4.1. We will extend the re-

cently developed Shufﬂed Frog-Leaping Algorithm to

include these neighbourhoods. We will analyse and

implement other neighbourhoods and variation oper-

ators such as the ones proposed in (Abdullah et al.,

2010) and (Cheong et al., 2009). The performance

of these operators will be studied ﬁrst on the smaller

dataset (Leite et al., 2012), in order to visualize its op-

eration on the timetables produced, and later we will

test with the bigger datasets of Toronto and ITC2007

benchmarks.

5.2 Hybrid EMO Methodology

As mentioned in the objectives outline, we in-

tend to tackle the university timetabling prob-

lems using EMO algorithms combined with other

(meta)heuristics, forming the so called memetic algo-

rithms.

We intend to extend the recently proposed SFLA

algorithm and implement a multiobjective SFLA.

Some efforts have been done in this path (Rahimi-

Vahed and Mirzaei, 2007).

For the local search we intend to explore several of

the most successful techniques in the literature such

as Hill Climbing, Simulated Annealing, Tabu Search,

among others. The acceptance criteria implemented is

very important as shown, for example, by the method

implemented by (Burke and Bykov, 2008), which

achieves the best results on some Toronto datasets.

Other idea will be explored in the ﬁnal project of

the fourth and last doctoral course, yet to be com-

pleted. In this project I intend to implement a learning

algorithm, called STAGE (Boyan and Moore, 2001),

and use it to solve the ETTP. The STAGE algorithm

works by learning an evaluation function that pre-

dicts the outcome of a local search algorithm, such

as hillclimbing, from features of states visited dur-

ing search. The learned evaluation function is then

used to bias future search trajectories toward better

optima on the same problem. In (Boyan and Moore,

2001) the authors use the STAGE algorithm to solve

several known large-scale optimization domains, such

as bin-packing, channel routing, cartogram design or

Boolean satisﬁability problem.

We intend to study the application of the STAGE

algorithm on the ETTP and test it with the bench-

marks available. We also want to study other re-

gression strategies such as SVM (Support Vector Ma-

chines) regression.

MultiobjectiveMemeticAlgorithmsappliedtoUniversityTimetablingProblems

5.3 Variable Timetable Length

Solutions

One of the typical objectives of timetabling opti-

mization is to ﬁnd solutions with the lower num-

ber of time slots. This was explored in some

single-objective (Carter et al., 1996) (Caramia et al.,

2008) and multiobjective methods (C

e et al.,

2004) (Cheong et al., 2009) for the Toronto bench-

mark. Manipulating variable timetable length solu-

tions, by creating new time slots needed to accommo-

date infeasible exams generated by the variation oper-

ators, and then trying to repair those solutions, seems

another tool for conveniently exploring the search

space. Associated to this are the methods proposed

in the graph colouring literature, speciﬁcally for solv-

ing the Minimum Vertex Colouring problem. As anal-

ysed in the timetabling literature, the ETTP consider-

ing just the student clash hard constraint with k time

slots is equal to the k−vertex colouring problem. So,

graph colouring heuristics are also of interest to our

analysis. One example of an effective memetic algo-

rithm for tackling the graph colouring problem is the

work (L

u and Hao, 2010).

So, we intend to create operators that vary the

time slots as needed in order to rearrange the exams.

Repairing schemes and speciﬁc constraint-handling

techniques to handle infeasible solutions will be de-

vised.

5.4 Algorithm Comparison and

Performance Measures

For a fair algorithm comparison of the proposed al-

gorithms on benchmark data for the Toronto dataset,

we intend to use similar computers to those tested in

the literature. For the ITC2007 data, the organizers of

the competition provided an application for estimat-

ing the CPU time available for running the optimiza-

tion algorithm (for single-objective/non-parallel algo-

rithm comparison purposes). This application only

applies to single CPU machines.

Desirable characteristics of a MOEA include gen-

eration of nondominated set close as much as possi-

ble to the true Pareto front, and, secondly, that solu-

tions in the obtained nondominated set should be dis-

tributed in a diverse and uniform manner. For eval-

uating these two aspects we will consider the use of

performance metrics suggested in the literature (Zit-

zler et al., 2003) and that are used by researchers in

this ﬁeld to compare the several MOEAs.

5.5 Activity Plan until December 2015

In the next months, I intend to explore thoroughly

the concepts mentioned earlier about many-objective

optimization. At the same time, we will improve

(by exploring the described points mentioned in the

earlier sections) and extend the single-objective pro-

posed in (Leite et al., 2013a) to the ITC2007. Next,

we will study forms of extending it to a multiobjec-

tive framework and implement also a parallel version

of the algorithm. The last objective mentioned of cre-

ating a graphical interface for the MOEA is optional

in this phase of the work.

5.5.1 Goals for Publication

We intend to prepare in the mean time commu-

nications and articles to submit to related confer-

ences and journals. We are considering the follow-

ing international conferences: Evolutionary Compu-

tation, Theory and Applications (IJCCI-ECTA), Prac-

tice and Theory of Automated Timetabling (PATAT),

Multidisciplinary International Scheduling Confer-

ence (MISTA). For the journals we are considering

the following ones: Elsevier’s European Journal of

Operational Research (EJOR), Springer’s Journal of

Scheduling (JSched), Springer’s Annals of Opera-

tions Research (AOR) and IEEE Transactions on Evo-

lutionary Computation (TEVC).

6 EXPECTED OUTCOME

With the realization of this Ph.D. thesis I expect to

give novel contributions to the study of the University

Timetabling ﬁeld. The expected outcome of the thesis

is:

• Extend the study of university timetabling prob-

lems, exploring them as multiobjective problems,

which they are in nature. The majority of the ex-

isting studies consider single-objective problems

and very few consider two-objective problems.

We will extend this framework by considering for-

mulations with three and more objectives.

• Contribute to the understanding of the search

space of the analysed timetabling problems.

• Provide efﬁcient neighbourhood operators for the

selected problems.

• Provide efﬁcient multiobjective memetic algo-

rithms that improve upon the results of the state-

of-the-art algorithms for the multiobjective and

single-objective problem instances of the anal-

ysed problems.

IJCCI2013-DoctoralConsortium

• The proposed algorithms should be optimized in

terms of time performance due to the their parallel

implementation. This provides for efﬁcient usage

of the multicore machines available in nowadays

mainstream market, and, more importantly, pro-

vide for new modiﬁcations to a given timetable

to be done in a much short period of time. The

parallelism is also important because multiobjec-

tive optimization algorithms are more complex

and manipulate more data compared to single-

objective optimization algorithms.

• New multiobjective examination timetabling

problem formulation and benchmark data from

practical problem found in Portuguese universi-

ties.

• Publish research results in related refereed confer-

ences and journals.

• User application providing a graphical user inter-

face that helps the decision maker to search inter-

actively given a selected set of objectives, guiding

the search process towards a preferred Pareto sub-

set.

ACKNOWLEDGEMENTS

Nuno Leite’s work is partially supported by the FCT

SFRH/PROTEC/67953/2010 grant. The authors work

is also supported by the PEst-OE/EEI/LA0009/2011

grant.

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