An Event Grouping Based Algorithm for University Course Timetabling Problem
📝 Abstract
This paper presents the study of an event grouping based algorithm for a university course timetabling problem. Several publications which discuss the problem and some approaches for its solution are analyzed. The grouping of events in groups with an equal number of events in each group is not applicable to all input data sets. For this reason, a universal approach to all possible groupings of events in commensurate in size groups is proposed here. Also, an implementation of an algorithm based on this approach is presented. The methodology, conditions and the objectives of the experiment are described. The experimental results are analyzed and the ensuing conclusions are stated. The future guidelines for further research are formulated.
💡 Analysis
This paper presents the study of an event grouping based algorithm for a university course timetabling problem. Several publications which discuss the problem and some approaches for its solution are analyzed. The grouping of events in groups with an equal number of events in each group is not applicable to all input data sets. For this reason, a universal approach to all possible groupings of events in commensurate in size groups is proposed here. Also, an implementation of an algorithm based on this approach is presented. The methodology, conditions and the objectives of the experiment are described. The experimental results are analyzed and the ensuing conclusions are stated. The future guidelines for further research are formulated.
📄 Content
(IJCSIS) International Journal of Computer Science and Information Security, Vol. 14, No. 06, June 2016
An Event Grouping Based Algorithm for University Course Timetabling Problem
Velin Kralev, Radoslava Kraleva, Borislav Yurukov
Department of Informatics, South West University “Neofit Rilski”, Blagoevgrad, Bulgaria
Abstract — This paper presents the study of an event grouping
based algorithm for a university course timetabling problem.
Several publications which discuss the problem and some
approaches for its solution are analyzed. The grouping of events
in groups with an equal number of events in each group is not
applicable to all input data sets. For this reason, a universal
approach to all possible groupings of events in commensurate in
size groups is proposed here. Also, an implementation of an
algorithm based on this approach is presented. The methodology,
conditions and the objectives of the experiment are described.
The experimental results are analyzed and the ensuing
conclusions are stated. The future guidelines for further research
are formulated.
Keywords – university course timetabling problem; heuristic;
event grouping algorithm
I.
INTRODUCTION
The University Course Timetabling Problem (UCTP) is an
optimization problem and has been widely explored for the last
55 years. For the first time the key aspects of this problem were
presented in [1]. In order to solve a UCTP a finite number of
events E = {e1, e2, …, en} synchronized in time and fixed on a
timetable that consists of a finite number of time slots T = {t1,
t2, …, tk} is needed. The arrangement of the events must be
done in such a way that it satisfies the finite number of hard
constraints (Ch) and violates the fewest possible ones from a
finite number of soft constraints (Cs). A timetable is acceptable
when it meets all hard constraints and is better than another one
when it violates fewer soft constraints [2].
The UCTP is NP-hard [3], but it has been intensively
studied because of its great practical relevance [4], [5] and
others. In recent years, the interest in the heuristic and hybrid
approaches towards solving this problem has increased. These
approaches give better results than the approaches based on
constructive heuristics [6], [7] and [8].
There are different approaches that are used to solve the
UCTP, for instance: constructive heuristics, meta-heuristics and
constraints-based approaches. They are discussed in detail in
the scientific literature [4], [9], [10], [11] and [12]. In addition
to these approaches others are well known as well, for instance:
multicriteria approaches, case-based reasoning, knowledge-
based approaches and hyper-heuristic approaches [13].
A. Constraint-based approaches
In addition to the use of constraints in the constraint-based
approaches, other supporting methods are used, such as:
“Depth First Search”, object-oriented modeling of graphs and
trees,
“backtracking”,
combined
methods
and
genetic
algorithms [14]. The experimental results show that it is
possible for certain acceptable time to find good solutions that
are close to the optimal one, but it refers only to timetables
with a small number of events. This can be done by not
considering temporary solutions that are not promising.
B. Graph-based approaches
Graph-based approaches show how the UCTP can be
represented by a graph [4]. The graph coloring problem and its
relationship with the UCTP are widely discussed in the
scientific literature, for instance in [15].
C. Meta-heuristic and hyper-heuristic approaches
Meta-heuristic and hyper-heuristic approaches are methods
of high level which are used to find the solution to problems
with a large computational complexity. For instance, such are:
“tabu search” [16]; “simulated annealing” [17]; “variable
neighborhood search” [18] and “ant colony optimization” [19].
The purpose of these approaches is maximum satisfaction
of the soft constraints. They are one of the most effective
strategies for the practical solution to optimization problems.
The published results indicate that the proposed methods find
good solutions when they are used for UCTP. Their
disadvantage is the need to set up additional parameters that
control the performance of the algorithms.
D. Case-based reasoning and knowledge-based approaches
Case-based reasoning approaches (CBR) are characterized
by the fact that additional heuristic methods are used. For
instance, graphs in which the attributes of the vertices and the
edges store more information about the interconnection
between events. In this way, the algorithm that generates a
timetable shall decide how to continue the process from here
(or to improve the final solution) [12] and [13]. Knowledge-
based approaches use an expert system of rules with pre-
defined strategies (for instance, “Depth-first search” [20].
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