=Paper=
{{Paper
|id=Vol-1830/Paper81
|storemode=property
|title=Concurrent Student Seminar Scheduling Using Genetic Algorithm
|pdfUrl=https://ceur-ws.org/Vol-1830/Paper81.pdf
|volume=Vol-1830
|authors=Ojoajogu Ajanya,Hamza O. Salami
}}
==Concurrent Student Seminar Scheduling Using Genetic Algorithm==
https://ceur-ws.org/Vol-1830/Paper81.pdf
International Conference on Information and Communication Technology and Its Applications
(ICTA 2016)
Federal University of Technology, Minna, Nigeria
November 28 – 30, 2016
Concurrent Student Seminar Scheduling Using Genetic Algorithm
Ojoajogu Ajanya and Hamza O. Salami
Department of Computer Science, Federal University of Technology, Minna, Nigeria
ogajanya@yahoo.com, ho.salami@futminna.edu.ng
Abstract—Scheduling involves assigning variables to specific teachers and the students. Timetable problem is a real-life
domains according to resources and wishes. Usually, many combinational problem concerned with scheduling of a
students are ready to present seminars at the same time. In certain number of events within a specific time frame.
order to maximize time, student seminars can hold Therefore, seminar scheduling is an example of the
concurrently in multiple venues. Manual scheduling of student timetabling problem.
seminars is tedious since it must be painstakingly planned to Seminar scheduling entails arranging time slots for
minimize clashing of panelists, who must be present when seminar sessions while considering some constraints like
students present. This paper presents a genetic algorithm (GA) number of participants, capacity of the venue, number of
for automatically scheduling parallel student seminars to
presentations by facilitators, and so on. Seminar scheduling
minimize clashes and inconvenience to panelists. Experimental
results show that GA-based seminar scheduling is promising.
problem is a problem related to assigning variables to
specific domains according to resources and wishes. As
Keywords-genetic algorithm; seminar scheduling; parallel population of participants gets larger and larger while
seminars resources like venues and supervisors remain constant or
diminish, manually performing scheduling under these
constraints becomes an incredibly hard problem. Also, each
I. INTRODUCTION defined constraint restricts the area and the problem becomes
Order is a critical factor that guarantees proper harder, thus it takes a long time to get a solution by human-
organization of events; where there is disorderliness, there is based techniques.
bound to be confusion and ultimately, loss of productivity. In The main contribution of this paper is in the use of
the academic community seminars are examples of events Genetic Algorithm (GA) to plan concurrent student seminars
which must be properly ordered. Student seminars are oral in order to avoid/minimize conflicts in the seminar
presentations which are part of the requirements for students’ schedules. GA is a search and optimization technique based
academic programmes. Seminars are usually coordinated by on natural genetics and natural selection [2]. The rest of this
a designated member of staff who takes into consideration paper is organized as follows: A review of related works is
the schedules of the panelists who should be physically presented in Section II. The seminar scheduling problem is
present at the seminars. A student’s panelists comprise explained in Section III. In Section IV, a detailed description
his/her project supervisors, co-supervisors and of a GA for automatic seminar scheduling is presented.
examiners/assessors. Experimental results appear in Section V, while the paper is
In cases where many students are ready to present concluded in Section VI.
seminars around the same period, two approaches can be
adopted. On one hand, students can present seminars one-at-
a-time. Even though this approach eliminates the clashing of II. RELATED WORKS
panelists, it creates the problem of having all panelists
available throughout the seminar presentations. On the other Although little has been written about seminar
hand, seminars can be scheduled to run concurrently. The scheduling, it is closely related to other problems that have
latter approach minimizes the overall seminar presentation received significant research attention like the timetabling
time, but requires that students are carefully scheduled such problem and examination scheduling [3].
that the panelists who should be on ground during the A genetic algorithm-based intelligent system was
presentations are not required to be in more that one seminar proposed in [4] for course scheduling in higher education.
location at any given time. The GA helped to optimize the preparation of class
A timetable is “a table of events arranged according to schedules. The test result obtained 99 conflicting classes
the time when they take place” [1]. Timetables are very from 635 existing classes. The average non-conflict
important for the university administration; they give scheduling accuracy of the system is 84.4%.
students and teachers a schedule indicating the right time and In [5], GA was used to develop an optimization-based
the right place to be, the availability of the rooms, the time to prototype for nurse assignment that makes daily decisions on
be spent by the teachers for the period, the availability of the assigning nurses to patients. A prototype for assigning nurses
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International Conference on Information and Communication Technology and Its Applications (ICTA 2016)
to patients with the purpose of minimizing excess workload present during a student’s seminar because they ask
on the nurses was developed. questions and based on the student’s response, determine if
According to [6], scheduling classes is a time consuming the student can proceed to the next stage of study or not. It is
job for administrators. Many constraints are defined for important for supervisors to be present during their
classrooms, faculty members, and courses, whereby, a course supervisees’ seminars because they might be required to
may require a classroom with some minimum number of clarify issues related to their supervisees’ research.
seats and with some audiovisual equipment. Also, a faculty Let S = {s1, s2, s3 … sNS} be a set of NS students and let L
member may prefer not to teach two or more courses in a = { l1, l2, l3 … lNL} be a set of NL lecturers. The panelist
row, or may prefer teaching before certain time. In view of matrix P is a NS x NL matrix. The entry Pij in the matrix is 1
these, the researcher employed GA for finding a “good” if the jth lecturer lj is a panelist for the ith student si.
schedule that results in an efficient use of each classroom, in Otherwise, the entry is zero. A sample of the panelist matrix
relation to time, space, and constraints. is shown in Fig. 1. From the first row of the matrix, l2 and l3
Analytical Hierarchy Process (AHP) and GA have been are panelists for s1. Furthermore, from column one of the
combined to create a time table schedule that matches most matrix, l1 is a panelist for only s3. Let the number of periods
of the teachers’ preferences [7]. The approach consists of the (i.e., time slots) and venues be denoted by NP and NV,
integration of a satisfaction function to the genetic algorithm. respectively. Assume that the NS students are to be
The parameters of the satisfaction function are the teachers’ scheduled concurrently in NV venues within NP periods. Let
loads and a set of scores calculated using the analytical a session be defined as a combination of a venue and a
hierarchy process. The key point of AHP in calculating the period. Fig. 2 shows how sessions are numbered from
scores is the pairwise comparison of a set of teachers’ periods and venues. Note that the number of sessions, NSS =
criteria. The new approach was consequently a combination NV * NP.
of AHP and GA, and it gives rise to a new methodology to SSP involves assigning students to different sessions
solve the time table problem that is called AHP/GA. such that certain hard and soft constraints are satisfied. Hard
Researchers in [8] presented an experimental constraints are constraints that need to be satisfied for a
investigation into solving the Assignment model using GA solution to be feasible. Soft constraints are constraints that
and Simulated Annealing. Various parameters affecting the must not necessarily be fulfilled, that is, they are allowed to
algorithms are studied and their influence on convergence to be violated.
the final optimum solution was shown. While solving this The hard constraints for the SSP are:
problem through GA, a unique encoding scheme was used Each student shall present exactly one seminar.
together with Partially Matched Crossover (PMX). Only one student can present a seminar in a given
In their work, [9] combined the attributes of fuzzy logic session.
and Genetic Algorithm to create a Fuzzy Genetic Heuristic All the panelists for a student must be present during
(FGH) Algorithm which they used to solve the university the student’s seminar.
course timetable problem. They posit that fuzzy logic models No panelist can be in more than one venue at a time.
are easy to comprehend because they use linguistic terms and The only soft constraint considered seeks to minimize
structured rules but do not come with search algorithms. inconvenience resulting from lecturers moving from one
Unlike GA, fuzzy models adopt techniques from other areas venue to another at different time periods:
such as statistics and linear system identification. Thus they Each panelist should remain in one venue throughout the
harnessed GA’s search ability by merging both paradigms entire seminar presentations.
and created FGH algorithm, which describes Fuzzy Set Fig. 3 shows two ways of scheduling student seminars
model using GA search attribute. FGH uses an indirect within two venues and two periods. Panelists (obtained from
representation featuring event allocation priorities and Fig. 1) are shown alongside each student. Panelists causing
invokes a timetable builder routine for constructing complete hard constraint violations are shown in red, while those
timetable. causing soft constraint violations are shown in green. There
The work reported in [3] focused on the preference-based are two hard constraint violations from the seminar schedule
conference scheduling (PBCS) problem, in which of Fig. 3(a) since l2 and l5 are required to be in multiple
preferences of conference attendees are taken into venues at the same period; l2 is required to be in venue 1 and
consideration. PBCS was formulated as an integer venue 2 in period 1, whereas l5 is required to be in both
programming problem. Since the formulation is NP venues in period 2. Furthermore, there are two soft constraint
complete, simulated annealing was used to obtain good violations from Fig. 3(a); l3 moves from venue 1 to venue 2,
solutions to a PBCS for a real life conference that involved while l4 moves from venue 2 to venue 1. There are no hard
scheduling 213 sessions over 10 time-blocks for 520 constraint violations on Fig. 3(b). The only soft constraint
attendees who had preferences. violations are as a result of l2 and l5 changing venues.
III. SEMINAR SCHEDULING PROBLEM IV. GENETIC ALGORITHM
The seminar scheduling problem (SSP) is concerned with Genetic Algorithm (GA) is a search algorithm which
arranging concurrent student seminars in such a way that no mimics the survival of the fittest strategy that occurs in the
panelists are required to be in more than one seminar at the natural world [7]. It is an iterative search technique
same time, and the movement of panelists to different venues developed based on evolutionary genetics which seeks the
is minimized. A student’s panelists are his/her research best of a set of solutions [10]. GA follows five phases
supervisors and examiners/assessors. Examiners must be namely: generating an initial population, evaluating the
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International Conference on Information and Communication Technology and Its Applications (ICTA 2016)
fitness of the chromosome, selection, crossover and which is an encoded version of potential solution parameters
mutation. The process of selection, crossover and mutation rather than optimizing the parameters themselves [12].
are iterated until the optimal solution is obtained [11]. This Thirdly, GA uses fitness values obtained from objective
algorithm explores the search space and makes use of the functions without other artificial over engineered black box
generated knowledge to find a better population. A flowchart mathematics [7]. The user typically chooses the best
of the standard GA is presented in Fig. 4. The performance structure of the last population as the final solution. The
of GA is usually evaluated in terms of convergence rate and algorithm is complete when one of the following occurs: a
the number of generations to reach the optimal solution. specified tolerance threshold is achieved; a specified number
of generations has passed; a specified amount of
Lecturers computational time has passed; or the solution fitness has
plateaued [13].
The inputs to the GA for solving the SSP are the number
l1 l2 l3 l4 l5
of venues NV, the number of periods NP, and the panelist
s1 0 1 1 0 0 matrix P. The output of the GA is the seminar schedule
Students
similar to those shown in Fig. 3.
s2 0 1 0 1 0
s3 1 0 1 0 1
A. Chromosome Representation
Each chromosome is a row vector having NS genes. The
s4 0 0 0 1 1 value in each gene determines the session in which a student
presents his/her seminar. For example, the value of the first
Figure 1. A Panelist Matrix with Four Students and Five Lecturers gene states the session during which s1 presents, the value of
the second gene specifies the session during which s2
presents, and so on. Because each student must present in a
unique session, the values in the chromosome are distinct
Period 1 Period 2
integers ranging from 1 to NSS. It is noteworthy that this
chromosome representation ensures that the first two hard
Venue 1 Session 1 Session 4 constraints are always satisfied. Fig. 5 shows how the
seminar schedules shown in Fig. 3 are encoded as
Venue 2 Session 2 Session 5 chromosomes. The chromosome in Fig. 5(a) indicates that
s1, s2, s3 and s4 present in the first, second, fourth and third
Venue 3 Session 3 Session 6
sessions respectively, while Fig. 5(b) shows that s1, s2, s3
(a) and s4 present in the first, fourth, third and second sessions,
respectively.
Period 1 Period 2 Period 3
Session 1 Session 3 Session 5
B. Fitness Function
Venue 1
As mentioned in Section IV(A), the first two hard
Venue 2 Session 2 Session 4 Session 4 constraints have been taken care of from the chromosome
(b) representation. The third hard constraint is assumed to hold
all the time. Thus once a student appears in a session, all the
Figure 2. Sessions (a) three venues and two periods (b) two venues and student’s panelists are assumed to be present. The fitness
three periods function therefore handles the last hard constraint and the
only soft constraint. The last hard constraint states that
panelists can only be in one place at a time. A clash occurs
Period 1 Period 2 when a panelist is required to be in different venues at the
Venue 1 s1 (l2, l3) s4 (l4, l5)
same period. Similarly, the soft constraint seeks to eliminate
the inconvenience of panelists moving from one venue to the
Venue 2 s2 (l2, l4) s3 (l1, l3, l5) other. The fitness function F for the GA can be described
(a)
mathematically using (1).
Period 1 Period 2
NL
s1 (l2, l3) s3 (l1, l3, l5) F (C ) (100 * Clashes (C , i) Movements(C , i))
Venue 1 i 1
Venue 2 s4 (l4, l5) s2 (l2, l4)
Where, NL is the number of lecturers; C is the
(b) chromosome; and Clashes(C, i) is a function that computes
Figure 3. Constraint violations (a) Hard and soft constraints violations (b)
the number of times li is required to be in multiple venues at
Soft constraints violations the same period, when chromosome C is used to generate the
seminar schedule. Movements(C, i) is a function that
A notable characteristic of GA is that it is a parallel computes the number of times li is required to move from
population-based search with stochastic selection, crossover one venue to another, when chromosome C is used to
and mutation [12]. Secondly, GA works on the chromosome generate the seminar schedule.
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International Conference on Information and Communication Technology and Its Applications (ICTA 2016)
E. Mutation
Start Mutation is the infrequent introduction of new features
into the solution strings of the population pool to maintain
Initialization diversity in the population. Mutation was achieved by
swapping two randomly selected genes of a chromosome
based on the probability of mutation. The mutation operator
Evaluation stops the algorithm from getting stuck in local minima. Fig. 6
shows how mutation swaps a pair of genes (sessions)
between two students. The first and third genes, which are
Selection shaded were swapped during mutation.
F. Stopping Criteria
Crossover Selection, crossover and mutation were repeated after
generation of the initial population until one of the following
conditions is satisfied: (i) the best fitness value of zero is
Mutation obtained, signifying that no constraint is violated, (ii) the
No maximum number of generations is reached, (iii) or the
fitness value does not improve within a preset number of
Meet stopping criteria generations.
Yes V. EXPERIMENTAL RESULTS
End This section discusses experimental results used to
validate the proposed GA. The GA was implemented using
Figure 4. Flowchart of the Genetic algorithm process [14] the MATLAB® simulation tool.
Because hard constraints are more severe than soft A. Evaluation Criteria
constraints, the former are penalized 100 times more than the The fitness values and running times were used to
latter. The GA searches for the chromosome with the evaluate the performance of the developed GA-based
minimum fitness value (minimum total number of clashes seminar scheduler.
and movements). The fitness values of the seminar schedule
presented in Fig. 3(a) is 202 since there are two clashes and B. Experimental Dataset
two movements of panelists. On the other hand, the schedule
Eleven datasets were used to evaluate the GA-based
in Fig. 3(b) has a fitness value of 2 since all hard constraints
student seminar scheduler. Table I shows the characteristics
were satisfied but panelists changed venues twice.
of each dataset. The first dataset comprises real data obtained
C. Selection from the Department of Computer Science, Federal
University of Technology, Minna when Masters students of
This process is used in the GA to determine which the Department presented their final thesis seminars in April
solutions are to be preserved and allowed to reproduce and 2016. The panelist matrix for that dataset is shown in Table
which ones are to be discarded based on their fitness values. II. For the other ten datasets, the number of venues, number
The primary objective of the selection operator is to retain of periods, and the panelist matrices were randomly
the good solutions and eliminate the bad ones in a population generated such that each student had between two and four
and still keep the population size constant. The type of randomly selected panelists. Note that the second, third,
selection operator to be used is the rank selection, chosen for fourth and fifth datasets have the same panelist matrix and
its ability to allow fittest individual to be selected. The number of sessions, but different combinations of number of
fitness values of the chromosomes were used to sort them in venues and periods.
ascending order. This prevents bias towards individuals that
are highly fit, thereby reducing speedy convergence.
C. Experimental Setup
D. Crossover MATLAB R2010a was used to implement the GA. The
The crossover operator is used to create new solutions experiments were carried out on a computer system having a
from the existing solutions available in the mating pool after processor speed of 2.4GHz as well as main memory capacity
applying rank selection operator. Crossover exchanges the of 4GB, and running the 64-bit windows 7 operating system.
gene information between the solutions in the mating pool. The parameters used to run the GA experiments are as
Partially-mapped crossover was used in this work because it follows: the GA was halted after 1,000 generations or if the
prevents duplication of genes. Crossover operators like best fitness value obtained did not improve within 50
single point crossovers and double point crossovers often generations. The probability of mutating each gene in the
result in duplication of genes indicating that a student population is 0.02 while the probability of crossover is 0.9.
presents in multiple sessions, violating the hard constraint All the experiments were run 30 times since GA is
that requires each student to present his/her seminar once. stochastic.
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International Conference on Information and Communication Technology and Its Applications (ICTA 2016)
D. Results and Discussion 1 2 3 4 1 2 3 4
Fig. 7 shows a seminar schedule generated by GA. The 1 2 4 3 1 4 3 2
fitness value obtained from this schedule is four, since there (a) (b)
are no panelist clashes but panelists had to change venue four
Figure 5. Chromosome representation for seminar schedule (a)
times, as indicated by the green-colored panelists. Chromosome for Fig. 3(a); (b) Chromosome for Fig. 3(b)
The second, third, fourth and fifth datasets all have 12
sessions as well as the same panelist matrix. They only differ
in the number of venues and periods. Fig. 8 shows the
relationship between the average fitness value and number of
venues for a fixed number of sessions using the four datasets.
It can be seen that as the number of venues increases, the
1 2 3 4 1 2 3 4
number of constraint violations also increases. In the extreme
case of excessive parallelism, there is only one period and 2 4 1 3 1 4 2 3
(a) (b)
multiple venues, so all seminars take place at once, resulting
in significant constraint violations. On the other hand, when Figure 6. Mutation (a) Before mutation (b) After mutation
there is only one venue, there are no constraint violations
because is no parallelism at all and each student presents in a
distinct period.
Table III shows the fitness values and execution time of
GA for all the datasets. There are no results for Dataset 9, TABLE I. SUMMARY OF THE DATASETS
because the GA is programmed to compare the number of
Dataset Number Number of Number of Number of
students with the number of sessions before actual execution of venues periods students Panelists
starts. If the former is greater than the later, the GA displays 1 2 7 11 13
an error message and terminates because hard constraint(s) 2 6 2 6 10
are guaranteed to be violated when the number of students 3 4 3 6 10
exceeds the number of sessions. Otherwise, the GA proceeds 4 3 4 6 10
5 2 6 6 10
normally. The number of venues and periods for Dataset 9 6 3 6 15 15
are two and twelve respectively, resulting in twenty four 7 3 8 20 18
sessions, while the number of students is twenty seven. 8 3 10 25 18
Fitness values for majority of the datasets shown in Table III 9 2 12 27 20
are less than 100, indicating that only soft constraints were 10 3 15 30 20
11 2 20 40 20
violated. This shows that the GA is highly successful in
finding good seminar schedules.
VI. CONCLUSION
TABLE II. PANELIST MATRIX FOR FIRST DATASET
In this research work, a Genetic Algorithm was formulated
Lecturers
for scheduling seminars. The GA seeks to minimize clashes 1 2 3 4 5 6 7 8 9 10 11 12 13
among panelists and inconvenience due to panelists’ change 1 1 0 0 1 0 0 0 0 0 1 0 0 0
of venues. Experimental results show that soft constraint 2 0 1 1 0 1 0 0 0 0 0 0 0 0
violations regarding movement of panelists can hardly be 3 0 1 1 0 0 0 0 0 0 0 0 0 1
Students
4 1 0 1 0 0 0 0 0 0 0 1 0 0
avoided, whereas hard constraint violations can be avoided
5 0 0 1 0 0 0 0 1 1 0 0 0 0
depending on the inputs to the GA. In future, we plan to 6 1 0 0 0 0 1 0 0 0 0 0 1 0
incorporate panelists’ preferences for period(s) in the GA. 7 1 1 0 0 1 0 0 0 0 0 0 0 0
Furthermore, the GA can be improved so that empty 8 0 1 0 0 0 0 1 0 0 0 0 0 0
sessions when no students are presenting do not appear 9 1 1 0 0 0 0 0 0 0 0 0 0 0
between sessions when students are presenting. For 10 1 1 0 0 1 0 0 0 0 0 0 0 0
11 1 0 0 0 0 0 1 0 0 0 0 0 0
example, sessions 3, 5 and 11 on Fig. 7 are empty, so they
should appear at later periods, so that students and lecturers
can finish with the seminar as soon as possible.
Period 1 Period 2 Period 3 Period 4 Period 5 Period 6 Period 7
Venue 1 s1 s11 s9 s8
(l1, l4, l10) (l1, l7) (l1, l2) (l2, l7)
Venue 2 s3 s10 s7 s2 s5 s4 s6
(l2, l3, l13) (l1, l2, l5) (l1, l2, l5) (l2, l3, l5) (l3, l8, l9) (l1, l3, l11) (l1, l6, l12)
Figure 7. Generated schedule for first dataset
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International Conference on Information and Communication Technology and Its Applications (ICTA 2016)
Figure 8. Relationship between average fitness value and number of venues
TABLE III. FITNESS VALUES AND EXECUTION TIMES FOR GA
Fitness Value Execution Time (seconds)
Dataset
Mean Min Max Mean Min Max
1 4.20 3.00 6.00 0.90 0.56 1.64
2 501.00 501.00 501.00 0.53 0.39 0.69
3 201.27 201.00 202.00 0.51 0.37 0.74
4 102.00 102.00 102.00 0.40 0.28 0.48
5 0.00 0.00 0.00 0.01 0.00 0.02
6 112.47 109.00 115.00 1.27 0.57 3.52
7 16.83 14.00 20.00 2.21 0.96 3.71
8 24.10 20.00 29.00 2.88 1.30 4.94
9 - - - - - -
10 23.50 20.00 28.00 2.17 1.27 6.54
11 18.17 13.00 26.00 3.94 2.17 7.09
[8] A. Sahu, and R. Tapadar, “ Solving the assignment problem using
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