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International Journal of Engineering & Computer Science IJECS-IJENS Vol:13 No:02 8

134902-8181-IJECS-IJENS © April 2013 IJENS I J E N S

An Automated Approach Based On Bee Swarm in

Tackling University Examination Timetabling

Problem

Fong Cheng Weng, Hishammuddin bin Asmuni*

Software Engineering Research Group, Software Engineering Department, Universiti Teknologi Malaysia, 81310 UTM Skudai,

Johor, Malaysia *

Corresponding author.

E-mail address: [email protected] (CW. Fong), [email protected] (H. Asmuni)

Abstract-- A recently invented foraging behavior optimization

algorithm which is the Artificial Bee Colony (ABC) algorithm

has been widely implemented in addressing various types of optimization problems such as job shop scheduling, constraint

optimization problems, complex numerical optimization

problems, and mathematical function problems. However, the

high exploration ability of conventional ABC has caused a

slowdown in its convergence speed. Inspired from the Particle Swarm Optimization (PSO) method, an automated approach has

been proposed in this study and is named as the Global Best

Concept - Artificial Bee Colony (GBABC) algorithm. The

algorithm is formulated using the global best concept, which is

then implemented into the employed bee phase to incorporate the global best solution information into solutions. This is for the

sake of leading the search process towards exploring other

potential search regions to locate the best global solution. In

addition, to improve its exploitation ability, a local search

method has been incorporated into the onlooker bee phase. With the use of the global best concept and local search method, the

convergence speed, exploration and exploitation abilities of the

basic ABC have been significantly enhanced. Experiments are

carried out on standard university examination benchmark

problems (Carter’s un-capacitated dataset). Results obtained demonstrate that, generally, the GBABC had outperformed the

basic ABC algorithm in almost all instances and its performance

is also comparable to other published literature. Index Term-- University examination timetabling, Artificial bee

colony algorithm, Hill climbing.

1. INTRODUCTION

Various type of timetabling problems have been

addressed by using optimization methods such as job shop

scheduling [1-4], flow shop scheduling [5-7], software project

scheduling [8], open shop scheduling [9], machine scheduling

[10-14], and transportation scheduling [15]. In this paper, the

timetabling of un iversity examination is the focus of the study

and an overview of related studies can be seen at [16-18].

University examination t imetabling is a process of

assigning a number o f exams into a set of permitted time slots

without sacrificing its feasibility; a feasib le timetable is one

that is clash free. Generally, two distinct types of constraints

are encountered in generating a t imetable – the hard

constraints and soft constraints. Hard constraints must be

satisfied under any circumstance in order to preserve the

feasibility of the timetable while fulfillment of soft constraints

is optional, but its vio lation should be minimized. Th is is

because a timetable generated is assessed based on its ability

to fulfill both hard and soft constraints.

Approaches in rectify ing university examination

timetabling problems vary over a wide rage. From the survey

papers [16-18], heuristic approaches that have been applied in

solving timetabling problems are mostly based on graph

coloring heuristics [16, 19-20]. In recent years, application of

meta-heuristic and hybridization approaches have become the

main focus and examples of such approaches include the Tabu

search [21-25], Simulated Annealing [26-28], Honey Bee

Mating optimizat ion [29], Genetic algorithm [30-31], and

Great Deluge algorithm [32-36]. Related publications on

university timetabling problems can be found in [16-18, 37-

39]. Th is study, on the other hand, addressed this problem

using the Artificial Bee Colony (ABC) algorithm.

It is well known that population-based methods like

the ABC algorithm must possess adequate exploration and

exploitation ab ilit ies [40]. The exp loration ability allows the

bee colony to search and identify possible unknown regions in

the search space, whereas the explo itation ability permits the

formulat ion of better solutions based on the information of

previous solutions. Ironically, instead of complementing each

other, these two abilities are actually in contradiction.

Therefore, this study has been conducted to balance these two

abilities.

The proposed Global Best Concept - Art ificial Bee

Colony (GBABC) algorithm in th is study had been anticipated

to improve the convergence speed by enhancing both

exploration and exp loitation ab ilities simultaneously with the

implementation of the global best concept, which were

inspired from the Particle Swarm Optimization (PSO) method

and Local Search method. The effect iveness of the proposed

algorithm was tested against a set of benchmark datasets - the

Carter incapacitated benchmark datasets. Comparison was

then made with current state-of-the-art algorithm. In a nutshell,

experimental results illustrated that GBABC can generate high

quality solutions as compared to basic ABC and the results are

also comparable with best reported results.

The rest of the paper is organized as follows. Firstly,

description on examination timetabling problem is presented

mailto:[email protected]



in Sect ion 2. Section 3 gives an overview on the basic ABC

algorithm. The proposed method and experimental results are

presented in Sect ion 4 and Sect ion 5 respectively. Lastly, a

brief conclusion regarding this study is presented in Section 6.

2. PROBLEM DESCRIPTION

2.1 Examination timetabling problem

In this research work, Carter’s un-capacitated

examination benchmark datasets (introduced by Carter et al.

[19]) is used to examine the performance of the proposed

approach. This benchmark datasets have been widely used in

last decade (see [19, 24, 32-33, 36, 41-48]). Most examination

timetabling prob lems are associated to three attributes [32], i.e:

a number of exams;

a number of predefined time slots; and

a set of student exam enrollments that clearly

describe the conflicting exams.

[18-19, 49] stated that examination timetabling can

be defined as the action of assigning a number of exams into

given set of permitted time slots and the timetable itself must

be able to satisfy a number of constraints (hard and soft) at the

same time. From the survey papers [49], the constraints are

vary widely across different institutions. In addition, the

degree of variation of constraints has also increased due to the

raise of the number of students and the degree of

modularization of courses in university [49].

Regardless of the quality o f the timetable, a feasible

timetable must satisfy all hard constraints given. A common

hard constraint is to make sure that no student has to attend

two or more exams at the same t ime, i.e. , there are no clashes.

Another example of hard constraint is to ensure the

sufficiency of resources (rooms and seats capacity) at any

timeslot. On the other hand, soft constraint refers to a set of

extra demands on a timetable. For instance, having a large

time gap between two exams will give the students ample time

to do revision. Furthermore, it is also desirable to have an

exam with large number of participants scheduled at a time

earlier than other examinations to allow sufficient time for

marking the answer sheets. It should be emphasized here that

it is not possible to satisfy all soft constraints, but its violation

should be kept as low as possible [50].

For Carter’s un-capacitated examination benchmark

datasets, the room capacity constraint is not considered during

the timetable construction and only one hard constraint is

considered which is to produce a clash free timetable. The

level of hard constraint satisfaction can be evaluated based on

Eq. (1) and the required inputs for examination t imetabling are

as shown below (refer to [18-19]):

N, number of exams;

M, number of students;

P, a predefined timeslots;

Conflict matrix, c=(cij) N×N where each element in the

symmetrical matrix is the number of students that

will sit for both exams i and j, where i, j 1,…,N}.

ti is the timeslots within a set of predefine timeslots

(1 ≤ ti ≤ P) and contains the scheduled exam i (j

1,…,N}

(1)

The soft constraint considered in Carter’s un-

capacitated examination benchmark datasets is to spread the

conflicting exams as evenly as possible so that the students

have much time for rev ision process. The quality of a

timetable is assessed based on the degree of satisfaction of soft

constraints. In order to measure the quality of a timetable, a

fitness function or proximity cost function (Eq. 2) (see [16,

18]) is indispensable. Eq. (2) is used to calculate penalty for

two consecutive exams enro lled by a student. The penalty

value assigned is based on the time gap(s) between two

conflicting exams, where prox(ti, tj)=16, 8, 4, 2, 1 if the time

gaps are 0, 1, 2, 3, and 4 respectively.

(2)

Thus, the objective of university examination

timetabling (Carter’s un-capacitated datasets) is to satisfy the

hard constraint and min imize the violation of soft constraints ,

which is tantamount to minimizing the value of (Eq. 2).

2.2 Scope and limitation of the research work

In this paper focuses on examination

timetabling problem (Carter’s un-capacitated examination

benchmark dataset [19]) is take into account. University

timetabling problem can be divided into two types: university

course and examination t imetabling. Both of these timetabling

problems are similar in some way, but there are significant



differences between them. In course timetabling problem, the

course can only scheduled into one room at one time slot. In

contrast, mult iple exams can be allocated into same room at

one time slot as long as there is enough accommodation and

no conflict exists between the exams [51]. In Carter’s

benchmark dataset, there is only one hard and soft constraint

is considered. Hard constraint refers to generate a clash free

timetable, while soft constraint refers to spread the exams

evenly so that students can have more time for revision

process. Note that the room capacity constraint is overlook in

this dataset.

3. OVERVIEW OF ARTIFICIAL BEE COLONY (ABC)

ALGORITHM

The ABC algorithm was introduced by Karaboga [52]

and mimics the foraging behavior of real honey bees. Due to

its excellent ability, large number of researches has done

studies on its application in addressing optimizat ion problems

in recent years. A survey paper on application of bee swarm

optimization (ABC algorithm, Bee Colony algorithm, Bee

Swarm Optimizat ion, and Honey Bee Mating Optimization)

can be seen in [53] and the authors also reported that 54% of

currently published publications are related to the ABC

algorithm.

In a swarm based algorithm, there are a number of

agents that work co llaboratively in solving the problems. Each

of the bees (employed bee, onlooker and scout) in ABC

algorithm represents an agent which communicates and

cooperates among themselves to find a food source (solution)

with good quality of nectar (cost or fitness value for a problem

in hand). Fig. 1 (graphical illustration as presented in Fig. 2)

is an example of a general framework of the ABC algorithm

(adopted from Karaboga [52]). The figure shows that, during

the first stage, a number of food sources are initialized with

respect to the number of employed bee. At the employed bee

phase, the employed bees will t ry to exp lore new food sources

based on their memories and old food sources will be replaced

by new explored food sources only if the new food sources

have equal or better quality nectars. Communication between

the employed and onlooker bees occur when they are trying to

advertise promising food sources region to onlooker bees in

the hive. Cooperation occurs when a number of onlooker bees

in the onlooker bee phase explore regions of food sources

advertised by the employed bees.

If the quality of a food source cannot be improved in

a predefined iterations (defined in a parameter called limit),

the employed bee will turn into a scout bee in order to exp lore

new food source. The newly d iscovered food source will then

be memorized and the old food source is abandoned. Thus,

artificial bees in ABC algorithm are able to globally exp lore

the problem search reg ion (done by scout bees) and locally

explore the search region (done by employed and onlooker

bees) so that the exploration and explo itation abilities are

maintained. It should be noted that both employed and

onlooker bees generate new food sources by performing

neighborhood search and accept new food sources using the

greedy selection scheme where they accept only food sources

with better nectar. In addition, all solutions are improved

during the employed bee phase while only selected food

sources are improved during the onlooker bee phase (based on

probability selection scheme – the Roulette Wheel Selection).

The attractive strengths of ABC algorithm have

sparked the interest of many researchers to study and apply it

to solve real optimization problems. These include problems

in flow shop scheduling [5] and university examination

timetabling [54-55]. Nevertheless, certain aspects of this ABC

are still insufficient to execute strong explorat ion during the

scout bee phase. Its explo itation ability during the employed

and onlooker bee phases are also considerably weak and thus

have led to slow convergence power. The weaknesses of the

basic ABC algorithm together with their reasons and induced

outcomes are as explained in Table I.



Fig. 1. General framework of the ABC algorithm

1. Initialization:

2. Set the population size;

3. //population size = Number of EmployedBee = Number of OnlookerBee;

4. Initialize the population;

5. Calculate fitness value for each solution, f(sol);

6. Identify global best solution, solBS;

7. Set number of iterations, NumIteration;

8. Set value for parameter limit, limit;

9. Set itrCounter, limitCounter for each solution (sol) ← 0;

10.

11. Improvement:

12. While (itrCounter ≤ NumIteration) 13. //Employed bee phase

14. For i = 1 to EmployedBee do

15. Select solution soli and generate new solution soli’ by performing

16. neighborhood search;

17. If f(soli’) ≤ f(soli)

18. soli ← soli’;

19. End if

20. End for i

21.

22. //Onlooker bee phase

23. For j = 1 to OnlookerBee do

24. Calculate selection probability P, for each solution (pj to pOnlookerBee)

25. using Roulette Wheel Selection scheme;

26. sol* ← select solution based on the probability P;

27. Generate new solution sol*’ from sol* by performing neighborhood

28. search;

29. If f(sol*’) ≤ f(sol*)

30. sol* ← sol*’;

31. else

32. limitCounter++;

33. End if

34.

35. If f(solBS) ≤ f(sol*’) //update global best solution

36. solBS ← sol*’;

37. End if

38. End for j

39. 40. //Scout bee phase

41. For s = 1 to EmployedBee do

42. If (limitCounter for sols ≥ limit)

43. sols is abandoned and new solution solnew, is generated randomly;

44. Set limit counter for new solution solnew to 0, limitCounter ← 0;

45. sols ← solnew;

46. End for s

47.

45. itrCounter++;

46. End While



Fig. 2. Graphical illustration on basic ABC algorithm

The GBABC algorithm proposed in this study was

developed to compensate the weaknesses of the basic ABC

algorithm by enhancing the explorat ion and exploitation

abilities as well as the convergence speed of the search

process. Details of the proposed GBABC are demonstrated in

Section 4.

4. PROPOSED ARTIFICIAL BEE COLONY ALGORITHM

4.1 Hill climbing and particle swarm optimization techniques

The hill climbing algorithm is the simplest local

search method. It iterat ively evaluates the quality of

neighboring solutions and accepts tentative solution

based on the greedy selection scheme, which means

that only the best solution is accepted. However, this also

causes the performance of the algorithm to become poor as it

may prematurely converge and/or trap in the local optima.

This problem has been addressed by hybridizing the hill

climbing algorithm with other methods. For instance, the

hybridizat ion between constraint programming, simulated

annealing, and hill climbing method proposed by Merlot et al.

[43] has demonstrated its effectiveness in addressing

university examination timetabling problem.

Terminate and return best

solution found

Repeat

Population

Best solution in

population is updated

Population

Each of the solution S is updated

once using neighborhood search

Employed bee phase

Repeat for

next

solution S S

Population

Initialize solutions S and

identify best solution

Initialization phase

S

S –Solution

NS – New solution

Population

Abandoned solution is

identified

New

New solution,

NS, is generated

randomly

New

Scout bee phase

NS

1

2

S

Onlooker bee phase

Population Repeat for next

solution S

S

S

Repeat

for next

solution S

2 Select solution S for update process

based on probability selection

(Roulette Wheel Selection) using

neighborhood search

Calculate selection

probability for each

solution S

1



T ABLE I WEAKNESSES OF BASIC ABC ALGORITHM

Phase Weakness Reasons Consequences

Employed

bee

Weak

exploitation

The processes of the employed and

onlooker bee phases are the same, which

is to perform neighborhood search in

order to locate the solutions. Each of the

solution then performs only one

neighborhood search.

Weak exploitation on solutions causes the

convergence speed to be slow.

Onlooker

bee

Imbalance

exploitation

ability

The phase explo its the solutions using the

roulette wheel selection mechanis m. This

may lead to a search process which is

highly concentrated in exploit ing solution

with higher fitness.

Solutions with poor fitness are less likely to

be exploited. Thus, the process may

overlook promising solutions that can be

reached via those solutions.

Scout bee High exp loration

ability

New solution is generated randomly when

the old solution cannot be improved.

Randomly generated solutions may cause the

search process to search the region blindly;

this is difficult for the search process to

locate promising search regions. Hence, it

causes the search process to converge at a

slower speed.

In PSO, the search process is guided by the use of

local and global information [56]. Local information refers to

the best current solution discovered by a particle, whereas

global informat ion is the best current global solution in the

population. Therefore, all the new tentative solutions

generated are based on the combination of local and g lobal

knowledge. Th is can drive the search towards promising

regions rather than blindly exploring the entire search region.

4.2 Global Best Concept - Artificial Bee Colony (GBABC)

algorithm

This GBABC algorithm is a hybrid ization of the

global best concept and hill climbing optimizat ion technique.

The framework of the proposed algorithm is as shown in Fig.

4 and its graphical illustration is as shown in Fig. 5.

The proposed method consists of two phases - the

initialization phase and the improvement phase. The

improvement phase can be further d ivided into three sub bee

phases, which are comprised of the employed, onlooker, and

scout bees respectively. The next section shall give some

descriptions on the phases.

4.2.1 Initialization phase

In this phase, the individual bee inside the population

gives a feasible solution using a combination of sequential

heuristics (largest degree + saturation degree + largest

enrollment), which is similar to that generated by Asmuni [57].

This phase neglects the soft constraints, but emphasizes on the

fulfillment of hard constraints.



Fig. 4. Framework of GBABC algorithm

4.2.2 Improvement phase

In the improvement phase, the processes of exp loring

and exploit ing the search region are controlled by the

employed, onlooker and scout bees.

4.2.2.1 Employed bee phase

From Fig. 4 (line 5-6) and Fig. 5, it can be seen that

the employed bee no longer explo its solutions by using

neighborhood search, but uses the global best concept

borrowed from the concept of PSO. Th is substitution of

method is done because the best solution usually contains

valuable information. Therefore, it is important that its

informat ion is added to read ily available solutions in the

population to lead the search process to promising areas.

1. Initialization:

2. Set the population size;

3. //population size = Number of EmployedBee = Number of OnlookerBee;

4. Initialize the population;

5. Calculate fitness value for each solution, f(sol);

6. Identify global best solution, solBS;

7. Set number of iterations, NumIteration;

8. Set number of iterations for hill climbing, HCIteration;

9. Set itrCounter, hcCounter ← 0;

10.

11. Improvement:

12. While (itrCounter ≤ NumIteration)

13. //Employed bee phase

14. For i = 1 to EmployedBee do

15. Incorporate information of best solution, solBS into soli based on

16. global best concept from PSO;

17. End for i

18.

19. //Onlooker bee phase

20. For j = 1 to OnlookerBee do

21. While (hcCounter ≤ HCIteration)

22. Select solution soli and generate solj’ by performing

23. neighborhood search;

24. If f(solj’) ≤ f(solj)

25. Solj ← solj’;

26. End if

27. hcCounter++;

28. End While;

29. If f(solBS) ≤ f(solj) //update best solution

30. solBS ← solj;

31. End if

32. End for j

33. 34. //Scout bee phase

35. All the solutions (sol) in the population are abandoned and new solutions

36. (solnew) are generated randomly, sol ← solnew;

37. Calculate fitness value for each new solutions, f(sol);

38. itrCounter++;

39. End While



Fig. 5. Graphical illustration on proposed method, GBABC

In this study, the incorporation of the aforementioned

informat ion is done by using haploid crossover [58-59]. Fig. 6

demonstrates the crossover process to generate new solution

S1’ from S1 with the integration of the global best solution

(BS). Firstly, two random t ime slots are generated, which are

t1 and t4. Then, all the exams (i.e., e5, e13, e15 and e16) in

time slot t4 are moved from BS to timeslot t1 in S1. Any

exam that clashes with other exams or has already been there

(i.e ., e15) in the new time slot are not moved. After that, a

repair process is generated to maintain the feasibility of the

solution to eliminate duplicating exams in the new solution

(i.e., e5 in time slot t3 and e13 and e16 in time slot t4).

4.2.2.2 Onlooker bee phase

In the onlooker bee phase, the hill climbing (Fig. 4.

line 21-28) approach is used to refine the search region with

the selection mechanis m used in basic ABC being eliminated.

Neighborhood structures used in generating new tentative

solution include:

Nb 1: randomly selects and moves an exam into a feasible

time slot.

Nb 2: randomly selects two exams and swap their time slots.

Feasibility is preserved concurrently.

The hill climbing algorithm is incorporated to explo it

the entire solutions in the population locally; to eliminate

reliability on the selection scheme (roulette wheel selection) in

BS – Global best solution

S – Solution in population

NS – New solution

NGS – New solution

with BS information

Terminate and return best

solution found

Repeat

Population

Initialize solutions, best

solution is stored

Initialized phase

S

Population

Solution is abandoned

New

New solution NS

is generated

randomly

New

Scout bee phase

Repeat

All solutions, S, are abandoned. New

solutions NS are generated randomly

NS

Population

Information from global best

solution is incorporated into

solutions in population

Employed bee phase

BS S

NGS

Global best concept

Repeat

for next

solution

S

Onlooker bee phase

Population

All solutions, S, are improved using

Hill Climbing local search method.

Best solution is stored.

Hill Climbing

S

BS

Repeat for

next

solution S

Update best

solution fond



basic ABC to focus more on exp loit ing fittest solution; and to

improve the convergence speed of the search process.

4.2.2.3 Scout bee phase

In this last phase, all the enhanced solutions are

abandoned and new set of solutions are randomly generated

for the next iteration (line 35-37 in Fig. 4). The purpose of re -

generating a new set of solutions is to lead the search away

from local optima (local search within the onlooker bee phase).

Since the new solutions are placed on individual iterations,

therefore we eliminated the use of the parameter, limit, in the

basic ABC algorithm. Execution of the algorithm is repeated

until the stopping criteria is met, that is when it reaches the

3000th

iteration.

Even though ABC has been applied in addressing

university timetabling problem by Alzaqebah and Abdullah

[54-55], its results remain misleading in some cases due to the

inefficiency of the algorithm itself, as reported in [55]. Two

problems induced from the selection mechanism used in ABC

algorithm reported in [54] are: “(i) A “super-individual” being

too often selected the whole population tends to converge

towards his position. The diversity of the population is then to

reduce to allow the algorithm to progress; (ii) with the

progression of algorithm, the differences between fitness are

reduced. The best one then get quite the same selection

probability as the others and the algorithm stops progressing.”

These two problems are then further investigated in this study

in order to verify the existence of them in ABC algorithm (see

Section 5.1).

As compared with previous studies that applied ABC

algorithm in related domain [54-55], our p roposed approach

differs greatly in terms of explorat ion and exploitation

processes. The differences between previous application of

ABC and the GBABC proposed in this study are as listed in

Table II.

Fig. 6. Incorporation of global best concept using haploid crossover

T ABLE II COMPARISON BETWEEN SA-ABC AND GBABC

Features SA-ABC [54] GBABC (the

proposed method)

Initial population Saturation degree Largest degree +

Saturation degree

+ Largest enrollment

Local search method Simulated Annealing Hill Climbing

Scout bee solution

generation

Random generation Random

generation

Replacement of solutions in scout

bee phase

Unknown, since the authors did not report

on the value of

parameter limit used

Yes, carried out for the entire

population

Incorporate global

best solution information into

solution

No Yes, based on

global best concept inspired

from PSO

Improvement on

every solutions in

each iteration

No, selection

mechanism is used to

select solutions to be improved

Yes, all solutions

are improved

Selection mechanism Disruptive selection None

4.2.3 Goal of the proposed algorithm (GBABC)

As discussed earlier, the main purpose of this

GBABC is to strike a balance between the exploration and

exploitation ab ilities of a basic ABC, since the performance of

any meta-heuristic approaches is determined based on these

abilities. This balance is crucial as the algorithm’s

convergence speed is highly dependent on it [60]. W ith strong

exploration ability, the algorithm is powerfu l in exp loring

multip le search regions simultaneously, but it cannot locate

promising reg ions that may have the optimal g lobal solut ion.

The can be enhanced by allowing the algorithm to have certain

degree of exp loitation ability. However, as stated before, with

higher exp loration ability, the algorithm will take a longer

time to converge. Compromising on the algorithm’s

exploitation ability is not the best solution as well because the

algorithm may trap in the local optima when the search

process on search region is not wide enough.

In the basic ABC algorithm, its exploration ability is

higher than exploitation ab ility. Obviously, it means that the

basic ABC algorithm can exp lore many search regions at the

same t ime, but it takes a considerably longer time to converge

and may not locate the best global optimal solution. This is

the reason that the hill climbing optimization approach is

incorporated into the proposed GBABC algorithm to enhance

the exp loitation ability of ABC. This approach is preferred



because it is a local search m approach that has satisfying

exploitation ability and does not possess any exploration

ability [61]. The global best concept inspired from the PSO,

on the other hand, is inserted into the employed bee phase so

that the algorithm will continuously explore promising regions .

This can reduce the effect o f randomization [62] in the scout

bee phase.

5. COMPUTATIONAL EXPERIMENT This section presents an extensive discussion on the

computational experiments conducted. Generally,

experiments conducted to identify the effects of selected

mechanis m used in basic ABC (Sect ion 5.1) and GBABC

(Section 5.2) were tested based on Carter’s examination

benchmark dataset; the dataset consists of 11 types of

instances. All the experiments were conducted on a 2.2 GHz

laptop and the algorithms were coded using dev C++. Details

of Carter’s benchmark datasets can be seen in Table III.

T ABLE III

CARTER’S BENCHMARK DATASETS

Datasets

Number

of time

slots

Number

of exams

Number

of

students

Conflict

density

car-f-92 32 543 18,419 0.14

car-s-91 35 682 16,925 0.13

ear-f-83 24 190 1125 0.27

hec-s-92 18 81 2823 0.42

kfu-s-93 20 461 5349 0.06

lse-f-91 18 381 2726 0.06

sta-f-83 13 139 611 0.14

tre-s-92 23 261 4360 0.18

uta-s-92 35 622 21,267 0.13

ute-s-92 10 184 2750 0.08

yor-f-83 21 181 941 0.29

5.1 Experiment on effects of selected mechanism on the ABC

algorithm

As aforementioned (Section 4.2.2.3), authors in [54-

55] have reported two problems in the selection process .

Attempts to rectify these problems were done by conducting

experiments on two versions of ABC, hereafter referred to as

ABC1 and ABC2.

ABC1 refers to an ABC algorithm that has the

roulette wheel selection whereas in ABC2, this selection

method was eliminated. The latter was done to investigate its

influence on the solutions generated later on. The parameters

used in both algorithms (shown in Table IV) are the same as

those reported in Alzaqebah and Abdullah [54-55]. The

population size was 50 and the number of iterat ion was 500.

Since the authors used one scout bee instead of the parameter,

limit, it was thus postulated that only one food source was

abandoned by the scout bee in all iterat ions and the limit

placed was 30. Both algorithms were run 10 times and the

experimental results are as shown in Table V.

Fig. 7 shows the convergence graphs of ABC1 and

ABC2 for the uta-s-92 and car-f-92 instances. It can be

observed that the convergence graphs for both algorithms are

nearly the same and this implies that the performances for

both algorithms are roughly comparable.

Fig. 8 demonstrates the distribution of penalty cost

value for in itial and improved population. It can be seen that

the distribution of improved population for ABC with (ABC1)

and without selection mechanism (ABC2) are almost the same.

Simply to say, the population diversity and differences

between the fitness did not reduce, and the population did not

converge towards the fittest individual as reported in

Alzaqebah and Abdullah [55]. The fo llowing conclusions can

be drawn from the experimental results:

“super-individual” was frequently selected to be

improved using the roulette wheel selection.

Since there were no solutions involved in the mate

and survive process (e.g. crossover in genetic

algorithm), the population did not converge towards

the “super-individual” position and diversity of the

population was not reduced.

Termination criterion for the ABC algorithm was not

influenced by the existence of a selection mechanism.

T ABLE IV

PARAMETER SETTING FOR ABC1 AND ABC2

Parameter ABC1 ABC2

Population size 50 50

Number of iteration 500 500

Scout bee 1 1

limit 30 30

T ABLE V

RESULT COMPARISON FOR ABC1 AND ABC2

Datasets ABC1 ABC2

Best Best

car-f-92 4.89 4.97

car-s-91 5.69 5.81

ear-f-83 37.51 38.31

hec-s-92 11.78 11.79

kfu-s-93 15.91 15.88

lse-f-91 12.64 12.52

sta-f-83 158.38 158.36

tre-s-92 8.80 8.92

uta-s-92 3.85 3.86

ute-s-92 27.77 28.18

yor-f-83 40.22 40.43



3.8

3.9

4

4.1

4.2

4.3

4.4

0 100 200 300 400 500

Co

st P

en

alty

Iteration

ABC-with selection scheme

ABC-without selection scheme

4.8

5

5.2

5.4

5.6

5.8

0 100 200 300 400 500

Co

st P

en

alty

Iteration

ABC-with selection scheme

ABC-without selection scheme

(a)

(b)

Fig. 7. Convergence graphs for (a) uta-s-92 and (b) car-f-92

(a)

(b)

Fig. 8. Cost penalty value for initial and improved population for instance of car-f-92 (a) with selection mechanism (b) without selection mechanism

5.2 Experiment on proposed algorithm

Table VI illustrates the parameter setting for both

GBABC and ABC; the parameters have been selected based

on some preliminary experiments. From the preliminary

experimental results, it seems that the most crucial parameter

is the number of timeslot for the haploid crossover process

(incorporation of g lobal best solution information). The

higher the number of time slot selected for haploid crossover,

the more the focus is placed on leading the search towards the

global best solution area, and the lower the diversity of the

population. On the contrary, if the number o f t ime slot

selected for crossover process is too small, the search process

will possess random exploration characteristic.

Table VII demonstrates a comparison of the results of

basic ABC, proposed approach (GBABC), and bee family

methods that have been applied on this domain. The bee

family methods are divided into:

B1 - Alzaqebah and Abdullah [54]: Hybrid ization of ABC

with simulated annealing

B2 - Sabar et al. [29]: Honey bee mating optimization

B3 - Alzaqebah and Abdullah [63]: Bees Algorithm

T ABLE VI

PARAMETER SETTING FOR GBABC AND ABC

Parameter GBABC ABC

Population size 50 50

Number of iteration 3000 3000

Local search (hill climbing) iteration 1000 -

Crossover (haploid) points 8 -

limit - 30



T ABLE VII RESULT COMPARISON BETWEEN BEE FAMILY APPROACHES

Datasets ABC GBABC B1 B2 B3

Best Avg. Best Avg. Best Avg. Best Avg. Best Avg.

car-f-92 4.80 4.82 4.42 4.71 4.36 - 3.90 4.30 4.76 -

car-s-91 5.60 5.66 5.10 5.22 5.19 - 4.79 4.86 5.79 -

ear-f-83 37.47 38.47 34.56 35.14 32.26 - 34.69 36.43 38.93 -

hec-s-92 11.58 11.87 10.62 10.72 10.89 - 10.66 10.84 11.64 -

kfu-s-93 15.25 15.65 14.12 14.27 13.73 - 13.00 13.41 15.70 -

lse-f-91 12.48 12.57 11.15 11.26 11.15 - 10.00 10.56 12.66 -

sta-f-83 158.27 158.33 157.25 157.95 157.23 - 157.04 159.67 158.05 -

tre-s-92 8.85 8.90 8.36 8.46 9.22 - 7.87 8.00 9.05 -

uta-s-92 3.75 3.81 3.50 3.55 3.83 - 3.10 3.28 3.92 -

ute-s-92 27.65 28.00 25.80 26.23 26.73 - 25.94 26.98 28.05 -

yor-f-83 40.21 40.65 36.68 37.46 40.63 - 36.15 36.77 40.01 -

The proposed approach was run 30 times for

each instance (each taking 2 to 8 hours, depending on the size

of instances) using different random seeds. As reported by

Burke et al. [50], the university examination timetabling

process usually starts weeks before the actual use of it.

Therefore, it is acceptable for the proposed method to be run

many times. The best and best average results are highlighted

in bold. From Table VII, it can be observed that GBABC

gives competitive results and it has given the best results in

two instances, which are hec-s-92 and ute-s-92.

The proposed approach also gave better results for

the entire dataset as compared to the basic ABC algorithm.

This is because the method had globally exp lored (exp loration)

new set of solutions by using the global best solution

informat ion in the employed bee phase. For all iterat ions, the

method had also locally exp lored (exp loitation) all the

identified search regions using hill climbing local search in the

onlooker bee phase.

The proposed approach was also compared with

other population-based approaches proposed in the literature,

notably:

P1 – Turabieh and Abdullah [32]: Great deluge with

electromagnetic-like mechanism

P2 – Cote and Sabourin [64]: Bi-objective algorithm with

local search

P3 – Burke et al. [50]: Variable neighborhood genetic

algorithm

P4 – Eley [65]: Ant algorithm with hill climbing

P5 – Pillay and Banzhaf [30]: Informed genetic algorithm

As illustrated in Table VIII below, the results of

GBABC are more competitive than other population-based

approaches in literature. Even though no any best result has

been generated by the GBABC, it is still considered as a stable

approach because the differences between best and average

results are small across all instances (except for yor-f-83).

Several results obtained from single solution based

approaches in published works have been compared with the

GBABC. The comparison is as shown in Tab le IX and the

selected approaches are:

S1 – Di Gaspero and Schaerf [66]: Tabu search algorithm

S2 – Merlot et al. [43]: Hybridizat ion of constraint

programming, simulated annealing an hill climbing

S3 – Burke and Newall [33]: Great deluge algorithm

S4 – Abdullah et al. [46]: A large neighborhood search

with local search

S5 – Yang and Petrovic [67]: A novel similarity measure

for heuristic selection in examination timetabling

S6 – Caramia et al. [68]: Iterated algorithm with novel

improvement factors



T ABLE VIII RESULT COMPARISON BETWEEN GBABC AND OTHER POPULATION-BASED APPROACHES IN THE LITERATURE

Datasets GBABC P1 P2 P3 P4 P5

Best Avg. Best Avg. Best Avg. Best Best Best

car-f-92 4.42 4.71 4.10 4.89 4.20 4.40 3.90 - 4.20

car-s-91 5.10 5.22 4.28 4.80 5.20 5.50 4.60 - 4.90

ear-f-83 34.56 35.14 34.92 35.93 34.20 35.60 32.80 - 35.90

hec-s-92 10.62 10.72 10.73 10.82 10.20 16.50 10.00 11.70 11.50

kfu-s-93 14.12 14.27 13.00 13.53 14.20 14.40 13.00 15.80 14.40

lse-f-91 11.15 11.26 10.01 10.21 11.20 11.50 10.00 13.30 10.90

sta-f-83 157.25 157.95 158.26 159.69 157.20 157.60 156.90 157.90 157.80

tre-s-92 8.36 8.46 7.88 7.97 8.20 8.80 7.90 - 8.40

uta-s-92 3.50 3.55 3.20 3.27 3.20 3.60 3.20 - 3.40

ute-s-92 25.80 26.23 26.11 27.00 25.20 25.50 24.80 26.70 27.20

yor-f-83 36.68 37.46 36.22 36.27 36.20 37.50 34.90 40.70 39.30

T ABLE IX

RESULT COMPARISON BETWEEN GABC AND OTHER SINGLE SOLUTION BASED APPROACHES IN THE LITERATURE

Datasets GBABC S1 S2 S3 S4 S5 S6

Best Avg. Best Avg. Best Avg. Best Best Best Best

car-f-92 4.42 4.71 5.20 5.60 4.30 4.40 4.10 4.40 3.93 6.00

car-s-91 5.10 5.22 6.20 6.50 5.10 5.20 4.65 5.20 4.50 6.60

ear-f-83 34.56 35.14 45.70 46.70 35.10 35.40 37.05 34.90 33.70 29.30

hec-s-92 10.62 10.72 12.40 12.60 10.60 10.70 11.54 10.30 10.83 9.20

kfu-s-93 14.12 14.27 18.00 19.50 13.50 14.00 13.90 13.50 13.82 13.80

lse-f-91 11.15 11.26 15.50 15.90 10.50 11.00 10.82 10.20 10.35 9.60

sta-f-83 157.25 157. 95 160.80 166.80 157.30 157.40 168.73 159.20 158.30 158.20

tre-s-92 8.36 8.46 10.00 10.50 8.40 8.60 8.35 8.40 7.92 9.40

uta-s-92 3.50 3.55 4.20 4.50 3.50 3.60 3.20 3.60 3.14 3.50

ute-s-92 25.80 26.23 29.00 31.30 25.10 25.20 25.83 26.00 25.39 24.40

yor-f-83 36.68 37.46 41.00 42.10 37.40 37.90 37.28 36.20 36.35 36.20

Table IX reveals that although GBABC is capable of

generating only one best result (sta-f-83), it still manages to

produce competitive results as compared with the state-of-the-

art approaches. On average, the GBABC has produced good

quality results for 4 instances, which are ear-s-91, tre-s-92,

uta-s-92 and yor-f-83.

Fig. 9 illustrates the convergence graph for ute-s-92

instance. The x-axis represents the iteration number while the

y-axis represents the best cost penalty value found along the

search. As refer to Fig. 9, there is a relatively steep slope at the

early of the search process indicates that there is a large

improvement in term of the penalty cost value. This probably

due to the exp loration process of the search is guided by using

the valuable information from g lobal best solution (global best

concept) which leads the search towards promising search

region. In addition, it is also believed that the used of strong

exploitation hill climbing local search capable to fine-tuning

the promising search region in searching local optimal

solutions. However, the improvement of the solutions quality

is decreases gradually as the number of iterat ion increases and

the search converges at end of the search process.

Fig. 10 illustrates the boxplots of the distribution of

penalty cost for all instances in the Carter dataset. It can be

seen that the differences between the best, median, and worse

penalty cost value are s mall. This shows that the hill climbing

optimization method and global best concept had enhanced the

exploitation ab ility of basic ABC and could lead the search

process explore towards promising search regions.

Fig. 9. Convergence graph for ute-s-92 instance

6. CONCLUSION

In this study, an automated approach, Global Best

Concept - Artificial Bee Colony (GBABC) algorithm has been

presented and applied in addressing university examination

timetabling problem. This method is different from

conventional ABC algorithm in three ways. Firstly, with the

use of the PSO global best concept in the employed bee phase,



all the solutions generated in the scout bee phase had been

successfully incorporated with the global best information.

Thus, the search process was guided to exp lore pro mising

search regions. Secondly, the local search process was applied

to locally exp lore promising solutions in the onlooker bee

phase. Lastly, the abandon of all solutions in the scout bee

phase for all iterations was done to allow the search to escape

from local optima. In short, both modified employed and

onlooker bee phases had improved the convergence speed of

ABC.

Fig. 10. Boxplots of the penalty cost for each instances in Carter dataset

To assess the performance of GBABC, both ABC

and GBABC were tested on their ability to rectify

examination timetabling benchmark problem. Experimental

results demonstrated that solutions generated by GBABC

outperformed ABC in all instances. In addition, this study

has also demonstrates that the important of exploration and

exploitation abilities in searching solutions in the search

region. Other than that, an experiment was carried out to

verify the performance of selection mechanis m, similar to

that reported by Alzaqebah and Abdullah [54-55]. In short,

this GBABC can be implemented on other timetabling

process easily, for instance, the university course timetable

(similar to examination timetabling problem to some extent

but there are significant differences between them) in order

to demonstrate the generality of GBABC. Besides that, the

performance (exp loitation power) o f GBABC can be further

improved using more sophisticated local search methods

such as great deluge algorithm or simulated annealing. In

addition, the explorat ion power of GBABC can also improve

by using more advanced exp loration mechanis m and this is

subjected to future works.

To conclude, this study has contributed in the

following ways:

This study has demonstrated that the application of

PSO g lobal best concept in basic ABC algorithm can

lead the search process towards exp loring promising

search regions.

It has also been illustrated that the exploration and

exploitation of new candidate solutions for all

iterations can be done by exploring and exp loit ing a

wider solution search region. This had allowed the

proposed GBABC algorithm to escape from local

optima to give good solutions and the improved the

convergence speed.

The informat ion presented in this paper are less

misleading than those reported in Alzaqebah and

Abdullah [54-55].

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