ArticlePDF Available

Intelligence Classification of the Timetable Problem: A Memetic Approach

January 2017
International Journal on Data Science and Technology 3(2):24

DOI:10.11648/j.ijdst.20170302.12

Authors:

Andrew Eboka

Federal College of Education (Technical), Asaba, Nigeria, Delta

. 1st and 2 nd Generation of population from Parents.

…

Figures - uploaded by Andrew Eboka

Content may be subject to copyright.

Content uploaded by Andrew Eboka

Content may be subject to copyright.

International Journal on Data Science and Technology

2017; 3(2): 24-33

http://www.sciencepublishinggroup.com/j/ijdst

doi: 10.11648/j.ijdst.20170302.12

ISSN: 2472-2200 (Print); ISSN: 2472-2235 (Online)

Intelligence Classification of the Timetable Problem: A

Memetic Approach

Eboka Andrew Okonji, Yerokun Mary Oluwatoyin, Okoba Ifeoma Patricia

Department of Computer Education, Federal College of Education Technical, Asaba, Nigeria

Email address:

ebokaandrew@gmail.com (E. A. Okonji), agapenexus@hotmail.co.uk (Y. M. Oluwatoyin), okobah.ify@gmail.com (O. I. Patricia)

To cite this article:

Eboka Andrew Okonji, Yerokun Mary Oluwatoyin, Okoba Ifeoma Patricia. Intelligence Classification of the Timetable Problem: A Memetic

Approach. International Journal on Data Science and Technology. Vol. 3, No. 2, 2017, pp. 24-33. doi: 10.11648/j.ijdst.20170302.12

Received: April 5, 2017; Accepted: May 15, 2017; Published: July 27, 2017

Abstract: Scheduling tasks persist in our daily functioning and as academia, abounds more in University circle as hard-NP

constraint satisfaction tasks. Many studies exist with the objective of resolving the many conflicted constraints that exists in a

timetable schedule using various algorithms. Many of such algorithms simply search the domain space for a goal state that

satisfies the problem constraints. Our study yields an outcome assignment that provides a complete, feasible and optimal

academic schedule that satisfies medium cum hard constraints for the Federal University of Petroleum Resource Effurun in

Delta State of Nigeria using memetic algorithm. Results showed that model converges after 4minutes and 29seconds; while its

convergence time depends on use of belief space to ensure agents do not violate model bounds, encoding scheme used amongst

others. The schedule considers both instructors and students’ preference as medium constraints of high priority.

Keywords: Fitness, Constraints, Cross-Over, Mutation, Timetable, Memetic Algorithm, Intelligent, Schedule

1. Introduction

University timetable is a continuously evolving study that

is often plagued by conflict resolution whose careful

management and planning is of the essence – in order to

yield a feasible schedule that is friendly to both instructors

and students. The field of problem solving aims at resolving

such issues that continue to bedevil the management of

timetable in the Nigerian University (case in point). The case

often – is that reports have shown, Government has no

prerequisite funding to provide adequate infrastructure and

the needed laboratories that will help to improve the quality

of education. These and other constraints, continues to

hamper effective management and planning of timetable (as

well as examination, as the crux of the education system and

certifies that awardees have been found worthy in character

and learning as bestowed with the responsibility deserving of

the certificate an awardee possess (NEEDs Report, 2015).

Survey inspections via the Committee for Budget Monitoring

setup on the Federal Government of Nigeria / Academic Staff

Union of Universities (FGN/ASUU) 2009 memoranda of

understanding, posits that this problem is far from being

resolved in nearest time possible as government perceives

education as a money-gulping (rather than money-yielding

sector of the nation). This, Government insists on their terms

has necessitated the downward review of monetary allocation

as clearly seen from the Federal Government’s 2016

Budgetary Allocation – for which 8-percent of the total

allocation goes to fund the educational sector (2016 Budget).

This makes the examination timetable planning purely, a

constraint satisfaction task (ASUU, 2015).

Constraint satisfaction problem (CSP) consists of 3-parts:

(a) variables, (b) values satisfying each variable, and (c) set

of constraints that makes possible assignment of a value to

each variable. Thus, the task aims at a domain that seeks

solution to a set of problem via a search algorithm or model

that assigns values to each variable with the aim of satisfying

each variable as well as adhering to all possible constraints

(Zhang and Lau, 2005; Ozcan, 2005; Ojugo et al, 2016).

Every assignment is a state in a search space. An assignment

of values to all variable is termed complete; partial if some

variables are not satisfied with values, and an assignment is

consistent if it violates not constraints that help assign an

optimal value to its variable (Coddington, 2012; Ojugo et al,

2015, 2016).

The timetable scheduling problem has remained a classical

NP-hard CSP for being a multi-objective and multi-constraint

optimization task as its searches a domain space to yield an

25 Eboka Andrew Okonji et al.: Intelligence Classification of the Timetable Problem: A Memetic Approach

approximate-feasible, optimal and complete solution: given a

set of instructors, assigned a corresponding set of lectures

classes (courses) for timeslots within certain days of the

week, such that with a corresponding set of enrolled students,

the task results in a tuple scheduled event for Ni instructor-

class pair within Nt timeslots to yield a schedule where no

instructor or student is in more than one lecture class at a

time, and no room is expected to accommodate more than its

capacity and more than a lecture at a time (Abrahamson et al,

1996; Anh et al, 2006; Miners et al, 1995; Saleh Elmohamed

et al, 1998; Kumal and Dowd, 2005; Michaelwicz, 1998;

Ojugo et al, 2016).

A. Constraints Types in Timetable Problem (TTP)

Constraints are divided into (Saleh Elmohammed et al,

1998; Ojugo et al, 2007; 2016) thus:

a. Hard constraints are specific to room-time conflicts.

They cannot be physically violated or overlapped as

such event constraints must be satisfied. We can

schedule only one examination per class per time for an

instructor, student or room as thus: (a) courses taught by

the same instructor, (b) examination of courses that

were taught in same room, (c) lectures or labs of the

same class, (d) courses cannot be assigned to a

particular room unless the room capacity is greater or

equal to number of student enrollment for same class,

and (e) laboratory courses or classes require a certain

type of room.

b. Medium constraints are all instructors/students

preference that are based on room-time conflict that

also cannot be physically violated (e.g. a student cannot

be in more than one class at the same time). However, it

is not possible to as a rule of thumb to always satisfy all

students. Thus, we aim to avoid via adjustments so that

though we are not expected to satisfy all student-lecture

preferences – in some cases, students can adjust their

preferences to satisfy student-lecture preference if such

course class conflicts or is oversubscribed. Some

students will carry-over certain courses, and these must

be taken into account. Medium constraints do not have

costs as high as hard constraints attached to them; But,

it is aimed seriously that in a final schedule, such cost(s)

or penalty must be minimized and preferably, reduced

to zero where possible. Examples are: (a) avoid timeslot

conflicts for lectures with students in common, (b)

eligibility criteria for the class must be met, and (c) do

not enroll athletes in classes that conflict with their

sport practice time, etc.

c. Soft constraints are preferences of time conflicts, and

they have lowest penalty associated to them. Example

include: (a) for each student level, have a fully-packed

3-days of the week (Mondays, Wednesdays and

Fridays) and less-packed 2-days (Tuesdays and

Thursdays), (b) spread time lectures over the entire

week, (c) lecture classes may involve contiguous time,

(d) balance student enrollment in multi-section lecture

classes, (e) breaks may be specified, (f) instructor may

request periods in which their lectures and classes are

not taught, (g) instructors have preference for specific

rooms or types of rooms, and (h) minimize distance

between room where classes are taught or assigned and

the building housing the home department.

Thus, we aim at an event schedule of classes to instructors

and their ranks with rooms assigned based on students

enrollment and their preferences of which lecture or class to

attend (when and their engagement in other activities during

other timeslots), room capacity or size, class types and

locations, distances between buildings where these rooms are

located, priorities of each building as used by different

departments, amongst other constraints. Thus, our objective

is to constructs a feasible, optimal and complete schedule for

students, taken by instructors that satisfies all hard

constraints, and minimizes all soft and medium constraints

(Brailsford et al, 1998; Saleh Elmohammed et al, 1998;

Zhang and Lau, 2005; Michalewicz, 1998; Ojugo et al,

2016).

This implies that all hard constraints must be satisfied and

their corresponding associated cost should be eliminated;

while our medium and soft constraints (involving instructors’

and students’ preferences) should be satisfied where possible,

or can be minimized such that the cost associated with them

is brought to its minimum (though – preferences involving

instructors takes precedence and higher priority over those of

students). A feasible, optimal schedule is one that satisfies all

hard constraints, minimizes all medium and soft constraints

where they are not satisfied (Ojugo et al, 2016). The study

was conducted via a semi-automated prediction. Its cost

function measures quality of the current schedule that

involves the weighted sum of penalties associated with the

different constraint or violation types. The study thus, aims to

find the optimal solution using stochastic, evolutionary

methods that minimizes the cost function (Miners et al,

1995).

B. Related Literature on TTP

Ojugo et al (2016) employed simulated annealing

algorithm with 3-heating strategy (with reheating, adaptive

cooling and exponential cooling methods) for academic

scheduling at the University of Benin, and adopted a rule-

based preprocessor model to yield initial solutions. Their

results showed that SA with exponential cooling proved best

with solution converging after 2.112seconds, and that

convergence of SA is dependent on parameters like start

population, initial/ final temperature as well as random swaps

applied in the cooling strategies. While the model offers great

insight into the task at hand, it does not provide us with the

ability to discern from the experimentation if the results

compares better to other methods. Also, there is no means of

storing the schedules so that model can backtrack its previous

schedules and pick the best for the semester at any single

time.

Alowosile et al (2016) investigated a number of existing

works for solving University examination timetabling

problem with a view to resolving the conflict issues and

inability to keep memory the best solution(s) encountered

while using the automated design. They used the modified

International Journal on Data Science and Technology 2017; 3(2): 24-33 26

genetic algorithm and compared their results against standard

genetic algorithm performance in generating possible

timetables schedule. In their quest for better convergence of

an optimal solution, their results of the modified GA used to

schedule 2013/2014 rain semester exam at Ladoke Akintola

University of Technology, Ogbomoso, Nigeria with a task

involving 19,127students, 200-courses, 53-venues and 2-

weeks (excluding Saturdays and Sundays) outperforms

standard GA and maintains its accuracy level with increase in

problem size; whereas standard GA lost its effectiveness as

the problem size grows. While, their work provides useful

insight into further investigation of TTP, we observe these:

(a) their study had no sample output schedule, (b) did not

account for course-room-time conflict (if schedule yields

complete assignment of instructors to courses with venues

and timeslots with no conflicts) – then there will be no need

for study as classes have rooms appropriately allocated to

them, (c) instructor preferences out-weights those of student

and was not also accounted for, (d) instructors have ranks

that must be catered for as senior ranked instructors are often

times engaged in administrative duties, (e) challenges with

adjunct instructors was not accounted for, (f) though, study

considered only examination – distance between venues for

students with concurrent examination was not accounted, and

(h) their study initially set out to simulate and store results

generated in each iteration so that they can easily detect

conflicts via results, the best schedule over time (this goal

was not achieved).

C. Statement of Problem

1. Seek further insight into the field of problem solving in

Computer Science, exchange idea in the domain as well

as further equip policymakers with adequate useful data

required for such scheduling. Thus, we employ

statistical stochastic models and heuristics as in Section

II/III.

2. As a non-Euclidean, complex, chaotic, dynamic, highly

multi-dimensioned and multi-objective task with its

range of applications as a scheduling task makes it

critical as a determinant in many activities that

resonates a University system. Supervised schedules are

time-wasting and often redundant, yielding inconclusive

cum unsatisfying result and lots of copy and paste work

– with many unresolved instructor-

student_enrollment_room_size conflicts as well as

swaps in instructor/student preference amongst others.

This leads to increased ‘unresolved’ non-complete and

non-optimal schedules. To curb this, see Section III.

3. Such studies are often hampered by such ever-evolving

feats like instructors ranks/preferences, student

enrollment and preferences, distances between

buildings, class type and capacity etc – yielding the

unavailability of a precise and concise datasets as its

dataset is often littered with ambiguities, noise and

partial truth. This must be resolved via a robust search

method as in Section III.

4. Resolution of speed defects that often traps hill-

climbing method at local maxima as used by

evolutionary models is here resolved via hybridization

of statistical methods as in Section III as no one method

yields better solution than hybrids. These hybrids, also

in turn impose conflicts of statistical dependency from

dataset used and from the idea of merging heuristics.

This is resolved via discretization of model and data

encoding as in Section III, which will also help model

avoid overtraining, over parameterization and over-

fitting.

D. Objective of Study and Rationale

The goal is: (a) implement a genetic algorithm trained

fuzzy neural network model, (b) ensure model is statistically

sound to simulate such complex, chaotic and dynamic event,

and lastly, (c) compare its statistics/result to those of other

hybrids, using the same dataset.

Rationale for this choice is that for evolutionary models,

no single heuristics is as good as hybrids. The case in point

being that the genetic algorithm trained fuzzy neural network

model will simply have the following benefits:

1. The fuzzy set provides the initial solution for the model

to perform its simulation and prediction.

2. We employ the Jordan neural network constructed from

a multi-layered perceptron network with

Backpropagation and momentum-in-time learning rate

that allows network to store output progress and use

same output as feedback into the system to create

another generation of schedule.

3. Model exploits GA’s speed to ensure that the model is

never trapped at local maxima.

4. Model implores GA’s flexibility and exploratory ability

to seek at each generation, a global maxima or optimal

(best schedule) is found as each generation forms the

backdrop for a better (schedule) pool. And, in turn,

makes model more robust and can be easily tuned.

2. Proposed Model Framework /

Methodology

Soft computing is an inexact science that seeks to

propagate observed data, as the model seeks the underlying

probabilities of data feats of interest to yield an expected

output, chosen from a set of possible solution space and is

guaranteed of high quality even with noise, ambiguity and

impartial truth applied at its input. It exploits numeric data to

perform quantitative processing via a search algorithm that

explores solution space and ensures qualitative knowledge as

output, and experience as its new language (Ojugo et al,

2013). Our hybrid model hinges on 4-methods: (a) fuzzy

logic, (b) genetic algorithm, (c) artificial neural network and

(d) decision support system.

A. Fuzzy Logic System

Fuzzy system chooses between different control actions

and transforms them into a fuzzy set value, (Nascimento,

1991; Ludmila, 2008; Ojugo et al, 2016) which is divided

into:

a. Fuzzy classifier assigns a class label to an object based

27 Eboka Andrew Okonji et al.: Intelligence Classification of the Timetable Problem: A Memetic Approach

on an object’s description, so that it can predict each

class label. Object descriptions are vector values with

attributes relevant for classification task. Classifier

learns to predict a class labels via training algorithm and

its accompanying dataset. If training data is not

available, the classifier is designed to learn apriori so

that when trained, it classifies data focusing on If-Then

rules with actions and outcomes, constructed as a user

specifies class rules and linguistic variables (fuzzy set)

that helps tune a fuzzy set in line with such class rules

(Ludmila, 2008).

b. Fuzzy Cluster groups data as linguistic variables into

homogeneous classes known as clusters so that items in

the same class are as similar as possible, and vice-versa

(Yang and Wang 2001). Based on data and task, it uses

different measures to identify classes and to control how

clusters are formed. Such measures include

connectivity, distance and intensity (Ojugo et al, 2012).

In some cases (non-fuzzy/hard clusters), data is divided

into clusters so that each data point belongs to exactly

one cluster; But, in fuzzy clusters, a data can belong to

more than one cluster. Each data is associated with

member-grades that indicate degree to which a data

point belongs to different clusters.

Linguistic variable(s) helps to convey data about a task or

data under observation (Inan and Elif, 2005). They can

overlap to share feats about other data under observations

also. In this study, it is used to indicate distance between

rooms where lectures occur and buildings in department – via

the term far. We all may have slightly different ideas about

the exact distance that far represents even when this distance

is consistent (Berks et al 2000). Some students may agree it

is not far and at some point, they also agree that it is far. The

space between far and not far indicates distance to some

degree, which is actually a bit of both. Thus, the horizontal

axis measures the value of distance; while, its vertical axis

measures the degree to which the linguistic variable fits the

measured data (Inan and Elif, 2005; Ojugo et al, 2016).

To represent linguistic variable(s), we use fuzzy cluster

mean that attempts to partition a finite set of elements into a

set of clusters in relation to given criterion (Berks et al 2000;

Ojugo et al, 2016) by computing arithmetic means of all data.

See Ojugo et al (2016) for FCM algorithm and the adopted

fuzzy logic system performance tuning.

We adopt the fuzzy model by Ojugo et al (2015) – which

yields a recursive heuristic that assigns an event of

time_space to lecture-class_student-enrollment slots suited to

the problem domain. Also, the model’s basics function has

the data files of lecture-classes, room_space/buildings,

department_buildings, distance_matrix, student_enrollment

and inclusion data. Thus, using these structures – the system

builds an internal database used to perform the scheduling.

Its internal processes are such that checks distances between

buildings, room_space_type and time allotted, and compares

cum resolves all room_space and time_slot conflicts. It also

tracks and updates hours already scheduled. Thus: scheduling

is done by department, so that each move is generated as loop

over all the departments. The departments are chosen in order

of size, with those having the most classes or lectures being

scheduled first. The model first scans all currently

unscheduled lectures. It then attempts to assign them to the

first unoccupied rooms and timeslots that satisfy the rules

governing constraints. Constraints for room capacity is

difficult to satisfy, larger classes are scheduled first to result

iteration and speed of processing as well as avoid conflicts in

room exhaustion (Ojugo et al, 2015).

In most cases, only rooms and timeslots satisfying all rules

will already by occupied by previously schedule; And in such

case, the system attempts to move a lecture/class into a room

and timeslot and allow the unscheduled lecture class to be

scheduled. Next, system searches the schedule to select those

with higher cost by checking all medium and soft constraints

(e.g. how close a room match a class-size, how many

students have lecture-time conflicts or clashes, which

sporting activity conflicts with lecture-time, the student

enrollment affected, if a lecture is in a preferred timeslot,

room or building, and so on). If a poorly scheduled lecture

class is identified, the model searches the space, maps or

swaps it into a more comfortable timeslot – so that the hard

constraint are still satisfied, but the overall cost of

medium/soft constraints are reduced. Room swapping

process continues, provided all the rules are satisfied and no

cycling (swapping of the same lecture) occurs. Once all the

departments have been schedule, iteration cycle is complete.

The model continues until complete iteration yields no

further change in a schedule. There are many rules dealing

with room_time conflict, room type, room_priority etc –

many of which are complex. Our fuzzy model yields partial

schedule as output (though, it is unable to assign all the given

classes to room_time slots). Output is grouped into: list of

unassigned classes from constraint conflict, and list of all

assigned cum associated instructors/student_enrollment to

room_time. The basic rules for implementing these

constraints include (Ojugo et al, 2015):

a. IF room_size > student_enrollment AND {no conflict in

room} THEN ASSIGN Room to the Lecture-Class.

b. IF Instructor = (Professor > Adjunct > Reader > Senior

Lecturer > LecturerI > LecturerII) AND {NO

room_time conflict} THEN (allot room to most senior

instructor as preference).

c. IF (Time = allotted lecture) AND Student_has_Sports

THEN Adjust Student OR Class_Time.

Our fuzzy model will yield a partial schedule as output (as

it is unable to assign all the given lectures to rooms and

timeslots). Output is grouped these: (a) list of unassigned

lecture classes from constraint conflict, and (b) classes and

all the associated instructors/students_enrolled_set as

assigned to various rooms [26,39,41].

B. Artificial Neural Network (ANN)

ANN is a data processing model, inspired by neurons in

the human brain – and consists of interconnected neurons

(nodes) with the ability to learn by example. Thus, as it

processes data, its nodes shares data, adjusting each node’s

weight and bias and consequently, strengthens nodal

International Journal on Data Science and Technology 2017; 3(2): 24-33 28

connections (Caudill, 1987 and Fausett, 1994). As learning

takes place, model adjust its node weights and biases as well

as converts the data so that depending on the task, it uses an

activation/transfer function to modulate the associated input

(Mandic and Chambers, 2001) and nonlinear feats exhibited

in the task to yield an output via Eq. 1. Its weights are

correlated as Wi.j which sums all weights between input and

hidden layers, Woj is the bias and xi is TTP input data. Thus,

it yields an output via the tangent/sigmoid function that sums

its weighted input as in Eq. 2 and Eq. 3 (Minns, 1998;

Chakraborty, 2010).

      



 (1)

     



  (2)

  

 !"#$ % & (3)

There are 2-types of ANN: feedforward and recurrent. For

this study, we use recurrent (Jordan) network with

unsupervised learning (Ojugo et al, 2016). The Jordan net is

constructed by adding a context layer to (modify) a

multilayered feedforward and using a backpropagation-

momentum-in-time unsupervised learning to train the data.

This will help it retain data between iterations. As algorithm

starts, the context layer is initialized to 0, so that output from

the first iteration is fed back as input into its hidden layer

(Perez and Marwala, 2011; Ojugo et al, 2016). Thus, in next

time step, previous contents of the hidden layer is processed

to yield an output, which is also resent into context layer as

new input (and repassed as input into hidden layer in another

time-step to yield output). Process continues till solution is

found (Regianni and Rientjes, 2005). Weights are

recomputed in same manner for new connections fro/to its

context layer from hidden layer. Training aims at best fit data

weights computed via Tansig function that assumes an

approximation influence of data points at its center.

'( )*

( +, 

 *

( ..' % /..

 (4)

Arriving at best schedule (optimal solution) requires

previous knowledge. So, model incorporates previous data

and model previous output (fed back as input) into hidden

units (Rajurkar et al, 2004; Karunanthis et al, 1994) to yield

another output. Our model (net) resolves the structural

dependencies imposed by dataset and by the hybrid

heuristics used through its ability to store earlier data

generated from previous layer(s) (Kuan, 1994; Ojugo et al,

2016) and through the encoding decimal encoding used in the

GA. Feedforward nets can be expanded and extended to

represent complex dynamic patterns such as this – since, it

treats all data as new so that previous data do not help to

identify data feats, even if such observed datasets exhibits

temporal dependence; But, as the network grows larger, it

becomes practical difficult. However, Jordan net overcomes

this difficulty through these internal feedbacks, and the

Jordan net is more plausible and computationally more

powerful than other adaptive models.

Its learning algorithm allows output at time t to be used

alongside new input to compute another output at time t+1 in

response to dynamism. Thus, first output is fed-back as input

to hidden layers with a time delay, so that outputs at time t−1

is input at time t (Mandic and Chambers, 2001) computed by

its activation function yk in Eq. 4, which sums input, receives

target value of input training pattern, computes error data,

weight correction updates in layers (cj

k) and bias weights

correction updates (co

k). The errors are sent from output layer

back to input nodes via backpropagation (which helps

correct the weights and to find weights that approximate

target output with selected accuracy). Weights are modified

by minimizing error between target and computed outputs;

And, if the error is higher than selected value, process

continues – else, training stops with weights updated via

mean square error until model achieve minimal error (Ursem

et al, 2002; Ojugo et al, 2016).

C. Genetic Algorithm (GA)

GA is inspired by survival of fittest evolution and consists

of population (data) chosen for selection with potential

solutions to a specific task. Each potential solution is an

individual for which optimal is found using four operators:

initialize, select, crossover and mutation (Coello et al, 2004

and Reynolds, 1994). Individuals with genes close to

optimal, is said to be fit. Fitness function determines how

close an individual is to optimal solution. Ojugo et al

(2013a,b) GA operators include: (a) initialize (encodes input

data into a suitable form, uses fitness function to evaluate

how close each solution is to its optimal so that they can be

selected for mating if found to be good. The fitness function

has knowledge of task and if more solutions are found, the

higher its fitness value, (b) selection pick solutions that meets

fitness criteria and ensures the fittest are chosen for mating

on first come basis; Since, if waits to select only best fit after

process ends, model may end up with an elitist solution,

which often leads to local optima or poor convergence), (c)

crossover ensures best fit individual genes are exchanged to

yield a new, fitter pool via a (1-, 2- or multi-point) cross with

genes of a parent), and (d) mutation (helps to alter or

introduce greater diversity or chaos to ensure that the new

pool yields the best or converges to global minima, and the

algorithm stops if optimal is found, or after number of runs if

new pools are created).

For this study, we use Cultural GA with a belief space

define as thus: (a) Normative (has specific value ranges to

which an individual is bound), (b) Domain (has data about

task domain), (c) Temporal (has data about events’ space is

available), and (d) Spatial (has topographical data). In

addition, an influence function mediates between belief space

and the pool – to ensure and alter individuals in the pool to

conform to belief space. CGA is chosen to yield a pool that

does not violate its belief space and helps reduce number of

29 Eboka Andrew Okonji et al.: Intelligence Classification of the Timetable Problem: A Memetic Approach

possible individuals GA generates till an optimum is found

(Reynolds, 2004).

3. Experimental Model

A. Experimental Model Framework

We adoptOjugo et al (2015) model proposed in the study

as:

a. Knowledgebase of historic, decimal encoded data

(feats) and database of data matrix of TTP using fuzzy

If-Then rules represented as linguistic variables with

optimized membership functions. The fuzzy set consists

classifier to propagate if-then rule values of selected

data, enhanced as predefined linguistic variables and

classified into TTP classes. It uses the fuzzy cluster

means universe discourse equation to enhances

linguistic variables partitioned into data-point.

b. Inference Engine consists of our genetic algorithm

trained neural network model. It infers conclusion

derived from selected data encoded as fuzzy rules to

yield a centralized, fuzzy function boundary in

determining high/low degree membership function. We

use Jordan net to provide self-learning optimized via

crossover and mutation with an aim to re-introduce

greater diversity and chaos that will help resolve all

conflicts to autonomous-scheduled events.

c. Decision support consists of the predicted output and

the output database that is updated automatically in time

as patients are diagnoses as long as it encounters and

read sin new data. The decision support predicts system

output based on the cognitive and the emotional filers as

display by the output device.

Model starts off with Proposed Fuzzy Classifier and

Cluster Mean Universe Discourse Equation (PFCMUDE) as

in Eq. 6 to generate a fuzzy Linguistic variable Universe of

discourse:

012345 67 87 1 9  0 (6)

A, B, C… = selected questions option; P(x) = probability

assigned to questions option fuzzy range value.

Model starts off with Proposed Fuzzy Classifier and

Cluster Mean Universe Discourse Equation (PFCMUDE) as

in Eq. 6 to generate a fuzzy Linguistic variable Universe of

discourse:

012345 67 87 1 9  0 (7)

A, B, C… = selected questions option; P(x) = probability

assigned to questions option fuzzy range value.

Table 1. Fuzzy Encoded Universe of Discourse for TTP.

Code Fuzzy Linguistic Variable Member Function

H01 No instructor can teaching more than one lecture or class at a time 0.70

H02 Not more than one instructor can be in a class for a lecture for a time 0.70

H03 No student can sit in more than one (1) class at any given time 0.70

H04 Total student_enrollment assigned to room_space cannot exceed room_size or room_capacity 0.70

H05 Time duration of each class must not exceed or violate assigned contiguous time allotted to the class/lecture 0.70

H06 Classes/lectures of certain types (e.g. labs or others) are assigned to room types that fits class description 0.70

M01 2/more classes by same instructor cannot be assigned at same time 0.30

M02 Assign all adjunct_instructors first as they take precedence over full time and contract instructors 0.30

M03 Eligibility criteria must be met as a student cannot attend all lectures just because he/she belongs to that level; But, only

classes that he/she has registered for and is eligible 0.20

M04 Classes assigned timeslot follows instructors’ order of seniority so long it does not violate common_student-

student_enrollment_size-room_size conflict condition/rule 0.20

M05 2-classes with common student_set in cannot be assigned to same timeslot 0.20

M06 Classes/lectures with same students in common cannot be assigned to same / different room space(s) at same time 0.20

M07 Class and sporting cannot be assigned at same time with common_student(s) i.e. do not enroll student athletes in class

that conflicts with sporting time 0.20

M08 Minimize distance between rooms where classes having common student set are taught 0.30

S01 Fully packed lectures for all days of the week except for Wednesdays that lectures ends by 2pm 0.10

S02 Lectures can involve contiguous time but breaks are specified to relax brain of students as they prepare for other

lectures same day 0.10

S03 Balance student enrollment in multi-section lectures 0.10

S04 Instructors may reschedule and request timeslots in which their class or lectures are not taught 0.10

S05 Instructors may have preference for specific room_types for their lectures 0.10

B. Genetic Algorithm Trained Neural Network (GANN)

GANN is initialized with 30-individuals rules whose

fitness is computed and new pool is selected via tournament

method, which determines individual solutions selected for

mating. We apply a multi-point crossover to help net learn all

dynamic and non-linear feats in dataset (feats of interest). We

then apply mutation, to add further diversity and reintroduce

chaos so that best fit schedules are chosen. Data are

randomly generated via Gaussian distribution corresponding

to crossover points (since all genes are from a single parent

initially). As new parents contribute to yield new solutions

whose genes are combination of both parents, mutation yield

3-random genes that further undergoes another mutation as

they are allocated new random values that still conforms to

our belief space via swaps. Number of mutation applied

depends on how far CGA has progressed (how fit is the

fittest solution in pool), which equals fitness of fittest

solution divided by 2. New solutions replace older ones of

International Journal on Data Science and Technology 2017; 3(2): 24-33 30

low fitness to yield new pool. Process continues until

individual with a fitness value of 0 is found – indicating that

the solution has been reached (Branke, 2001).

Initialization/selection via ANN ensures that first 3-beliefs

are met; mutation ensures fourth belief is met. Its influence

function influences how many mutations take place, and the

knowledge of solution (how close its solution is) has direct

impact on how algorithm is processed. Algorithm stops when

best individual has fitness of 0 (Campolo et al, 1999; Dawson

and Wilby 2001b). Ojugo et al (2016) CGA belief rules are:

a. Normative belief – each instructor and students is bound

to only a class/lecture as a time given by 0.5).

b. Domain – events occurs daily from 8am-5pm,

excluding Saturday and Sundays. It lists all department

building and room_types to be allotted, and

student_enrollment.

c. Temporal – is data structure of instructors (adjuncts)

enrolled for both semester detailing each semester feats,

student_enrollment for each lecture and those for sports.

d. Spatial – creates the data structure of instructors

enrolled, student enrollment for each lecture, buildings

and their distances, rooms allocation and distances

between all the rooms in various building, laboratory,

pavilions etc

e. Influence function mediates between belief space and

the pool – to ensure and alter individuals in the pool to

conform to belief space.

GANN model is as thus:

INPUT:

1. Pool_ size (k), crossover (c), mutation (v), influence

function (Ic) and n; // Initialization and Selection

2. Randomly generate K possible solution

3. Save solution in population Kok; // Loop till terminal

point

4. For m = 1 to n do; // Crossover

5. Number of crossover nc = (k – Ifnc)/2;

6. For u = 1 to n do;

7. Select two solutions randomly EA and FG for K;

8. Generate GV and HN by multi-point crossover to EA

and FG;

9. Save GV and HN to K2;

10. End For; //Mutation

11. For u = 1 to n do;

12. Selection a solution Yh from K2;

13. Mutate each bit of Yh under Ifnc

14. Generate a new solution Yh

15. If Yh

i is impossible

16. Recompute Yh

i with possible solution by modifying Yh

17. End if

18. Recompute Yh

with Yh

i in K2

19. End for //Recompute

20. Recompute K = K2;

21. Return Best solution in Y

Model stops if stop criterion is met. GANN utilizes number

of epochs to determine stop criterion. Initial selection

(solution) that yields the 2nd generation is given as:

1. R1: If H01 Then C1 = 0.50

2. R2: If H01 & H02 Then C2 = 0.50

3. R3: If H01, H02 & H03 Then C3 = 0.50

4. R4: If H01, H02, H03 & H04 Then C4 = 0.50

5. R5: If H01, H02, H03, H04 & H05 Then C5 = 0.50

6. R6: If H01, H02, H03, H04, H05 & H06 Then C6 =

0.50

7. R7: If C6 & M01 Then C7 = 0.40

8. R8: If C6, MO1 & M02 Then C8 = 0.37

9. R9: If C6, MO1, MO2 & M03 Then C9 = 0.33

10. R10: If C6, MO1, MO2, MO3 & M04 Then C10 =

0.30

11. R11: If C6, MO1, MO2, MO3, MO4 & M05 Then C11

= 0.30

12. R12: If C6, MO1, MO2, MO3, MO4, MO5 & M06

Then C12 = 0.30

13. R13: If C6, MO1, MO2, MO3, MO4, MO5, MO6 &

M07 Then C13 = 0.29

14. R14: If C6, MO1, MO2, MO3, MO4, MO5, MO6,

MO7 & M08 Then C14 = 0.30

15. R15: If C6, C14 & S01 Then C15 = 0.30

16. R16: If C6, C14, SO1 & S02 Then C16 = 0.25

17. R17: If C6, C14, SO1, SO2 & S03 Then C17 = 0.22

18. R18: If C6, C14, SO1, SO2, SO3 & S04 Then C18 =

0.22

19. R19: If C6, C14, SO1, SO2, SO3, SO4 & S05 Then

C19 = 0.21

Fitness function (f) is resolved with initial pool (Parents) as:

R1:50 R2:50 R3:50 R4:50 R5:50 R6:50

R7:40 R8:37 R9:33 R10:30

R11:30

R12:30

R13:29

R14:30

R15:30

R16:25

R17:22

R18:22

R19:21

Fitness function (f) is resolved with first pool (dual

Parents):

R1:53 R2:51 R3:48 R4:29 R5:55 R6:53

R7:31 R8:19 R9:25 R10:18

R11:40

R12:17

R13:54

R14:38

R15:45

R16:42

R17:39

R18:28

R19:32

Table 2. 1st and 2nd Generation of population from Parents.

No Selection Chromosomes (Binary 0 or 1) Fitness Function

Parent 2nd Gen Crossover Parent 3rd Gen

1 50 0110010 1 and 7 0110101 53

2 50 0110010 2 and 8 0110011 51

3 50 0110010 3 and 13 0110000 48

4 50 0110010 4 and 9 0011101 29

5 50 0110010 5 and 10 0110111 55

31 Eboka Andrew Okonji et al.: Intelligence Classification of the Timetable Problem: A Memetic Approach

No Selection Chromosomes (Binary 0 or 1) Fitness Function

Parent 2nd Gen Crossover Parent 3rd Gen

6 50 0110010 6 and 11 0110101 53

7 40 0101000 7 and 12 0011111 31

8 37 0100101 8 and 16 0010011 19

9 33 0100001 9 and 17 0011010 26

10 30 0011110 10 and 19 0010010 18

11 30 0011110 11 and 14 0110010 40

12 30 0011110 12 and 15 0010001 17

13 29 0011101 13 and 16 0110110 54

14 30 0011110 Mutation 0110000 38

15 30 0011110 15 and 19 0101101 45

16 25 0011001 Mutation 0101010 42

17 22 0010110 Mutation 0101001 39

18 22 0010110 18 and 2 0011100 28

19 21 0010101 19 and 1 0100000 32

Table 3. 3rd and 4th Generation of population from Parents.

No Selection Chromosomes (Binary 0 or 1) Fitness Function

Parent 2nd Gen Crossover Parent 3rd Gen

1 53 0110101 1 and 7 1000000 64

2 51 0110011 2 and 8 0101101 45

3 48 0110000 3 and 13 0011001 23

4 29 0011101 4 and 9 0110110 54

5 55 0110111 5 and 10 0111011 59

6 53 0110101 6 and 11 0111100 60

7 31 0011111 7 and 12 1000111 71

8 19 0010011 8 and 16 0100000 32

9 26 0011010 9 and 17 0010101 21

10 18 0010010 10 and 19 0110001 49

11 40 0110010 11 and 14 0110100 52

12 17 0010001 12 and 15 0111001 57

13 54 0110110 13 and 16 0111000 56

14 38 0110000 Mutation 0110111 55

15 45 0101101 15 and 19 0110111 55

16 42 0101010 Mutation 0101111 47

17 39 0101001 Mutation 0100011 35

18 28 0011100 18 and 2 0110011 51

19 32 0100000 19 and 1 0110010 50

Tables 2 and 3 shows generation of optimized fuzzy

linguistic variables of both single and dual parents by

choosing first and second bits from the left as our crossover

and mutation points. Third generation is our stop criterion

with best fitness function of 71 (row 7) – implies that clusters

of the various universe of discourse variable values as

searched, has been optimized to 0.71 (with base value 0.50).

Thus, if parameter combination yields a membership function

less than 0.50, it is said to be a low-degree membership;

while, those ≥ 0.50 is said to be high-degree membership

function. It was also discovered that the more crossover and

mutation is applied to the fuzzy linguistic variable as in

tables 2 and table 3 respectively, the better and higher fitness

function is reached by each solution. Thus, event scheduling

accuracy increases as more time-steps are given allowing for

better scheduling and random swaps.

4. Result Findings and Discussion

A schedule yields an assignment that satisfies the

following:

1. R1: IF schedule satisfies only one hard constraint,

without resolving any medium cum soft constraints;

THEN we classify such assignment as C1, which is

non optimal and incomplete.

2. R2: IF schedule satisfies two hard constraints, without