Model and Solutions to Campus Parking Space Allocation Problem

144 Pages·2013·1.84 MB·English

Model and Solutions to Campus Parking
Space Allocation Problem
By
Luke Oluwaseye Joel
(211559858)
Submitted in fulfilment of the academic requirements
for the degree of Master of Science
in the School of Computer Science
University of Kwazulu-Natal
Westville Campus, South Africa.
Supervisor
Dr. A. O. Adewumi
June, 2013
COLLEGE OF AGRICULTURE, ENGINEERING AND SCIENCE
DECLARATION
The work described by this thesis was carried out at the University of Kwazulu-Natal, School of
Mathematics, Statistics and Computer Science, University of Kwazulu-Natal, Westville Campus,
under the supervision of Dr. Adewumi A. O.
This thesis is entirely, unless specifically contradicted in the text, the work of the candidate and
has not been previously submitted, in whole or in part, to any other tertiary institution. Where
use has been made of the work of others, it is duly acknowledged in the text.
Signed: Student Name:
As the candidate’s supervisor I have/have not approved this dissertation for submission.
Signed: Supervisor Name:
ii
COLLEGE OF AGRICULTURE, ENGINEERING AND SCIENCE
DECLARATION - PLAGIARISM
I, ..............................................................., declare that
1. The research reported in this dissertation, except where otherwise indicated, is my original
research.
2. This dissertation has not been submitted for any degree or examination at any other univer-
sity.
3. This dissertation does not contain other persons data, pictures, graphs or other information,
unless specifically acknowledged as being sourced from other persons.
4. Thisdissertationdoesnotcontainotherpersons’writing,unlessspecificallyacknowledgedas
being sourced from other researchers. Where other written sources have been quoted, then:
(a) Their words have been re-written but the general information attributed to them has
been referenced
(b) Where their exact words have been used, then their writing has been placed in italics
and inside quotation marks, and referenced.
5. This dissertation does not contain text, graphics or tables copied and pasted from the Inter-
net, unless specifically acknowledged, and the source being detailed in the dissertation and
in the References sections.
Signed
...................................................
Declaration Plagiarism 22/05/08 FHDR Approved
iii
Dedication
This thesis is dedicated to the members of my family in memory of our loving and caring
mother.
iv
Acknowledgements
My ultimate thanks, praise, and honour go to the Omniscient, Omnipotent and Omnipresent God
who saw me through this study.
I owe gratitude to my supervisor, Dr. Adewumi Aderemi, for his guidance, support and pa-
tience towards me during my entire period of study. I am also grateful to Dr. B. A. Sawyerr and
Dr. Blamah for their programming assistance, and the optimization and modelling research group
members for their moral support and contributions.
I offer my profound gratitude to my family members for their spiritual, financial and moral sup-
port, may the Almighty God bless you abundantly.
I am thankful to the following people: the technical personnel- Mr Greenwood and Mr Jay, Mrs
Chairmaine, Mrs Moodley and Mrs Sheeren of the School of Mathematical, Statistics and Com-
puter Science.
A million thanks to the Deeper Life Bible Church leaders and workers in Westville, Howard, and
Edgewood campuses for their prayers. I also want to express my gratitude to my dear colleagues
in the masters’ LAN, and all my friends far and near.
Finally, I am indebted to every other person not mentioned here who might have in one way
or the other contributed to the success of this project and my overall stay in South Africa during
my masters’ study. May God in his infinite mercy bless you all abundantly (Amen).
v
Abstract
Parking is considered a major land use challenge in campus planning. The problem can be in
terms of scarcity (few available spaces compared to demand) or management (inefficient usage of
available facilities). Many studies have looked at the parking problem from the administrative
and management points of view. However, it is believed that mathematical models and optimiza-
tion can provide substantial solution to the parking problem. This study investigates a model for
allocating car parking spaces in the university environment and improves on the constraints to
address the reserved parking policy on campus. An investigation of both the exact and heuristic
techniques was undergone to provide solutions to this model with a case study of the University
of KwaZulu-Natal (UKZN), Westville Campus.
The optimization model was tested with four different set of data that were generated to mimic
real life situations of parking supply and demand on campus for reserved and unreserved parking
spaces. These datasets consist of the number of parking lots and office buildings in the case study.
The study also investigate some optimization algorithms that can be used to obtain solutions to
this problem. An exact solution of the model was generated with CPLEX solver (as incorporated
in AIMMS software). Further investigation of the performance of the three meta-heuristics to
solve this problem was done. A comparative study of the performance of these techniques was
conducted. Results obtained from the meta-heuristic algorithms indicate that the algorithms used
cansuccessfullysolvetheparkingallocationproblemandcangivesolutionsthatarenearoptimal.
The parking allocation and fitness value for each of the meta-heuristic algorithms on the sets of
data used were obtained and compared to each other and also to the ones obtained from CPLEX
solver. TheresultssuggestthatPSwarmperformsbetterandfasterthantheothertwoalgorithms
and gives solutions that are close to the exact solutions obtained from CPLEX solver.
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Contents
Declaration ii
Declaration - Plagiarism iii
Dedication iv
Acknowledgements v
Abstract vi
List of Figures xi
List of Tables xiii
List of Abbreviations xiv
Outcome of Research Work - Publication xv
1 Introduction 1
1.1 Background of Study . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.1.1 Types of Parking . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2
1.1.2 Parking Restrictions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3
1.2 Statement of Problem . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
1.3 Motivation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6
1.4 Objective of the Study . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6
1.5 Definition of Terms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7
1.6 Thesis Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8
2 Background and Related Works 9
2.1 Introduction to Optimization . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9
2.1.1 Optimization Process . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11
2.1.2 Classification of Optimization Problems . . . . . . . . . . . . . . . . . . . . 11
2.2 Combinatorial Optimization Problem. . . . . . . . . . . . . . . . . . . . . . . . . . 13
vii
2.2.1 Knapsack Problem . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14
2.2.2 Travelling Salesman Problem . . . . . . . . . . . . . . . . . . . . . . . . . . 15
2.2.3 Assignment Problem . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16
2.2.4 Space Allocation Problem . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16
2.3 Optimization Techniques . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17
2.3.1 Exact Optimization Techniques . . . . . . . . . . . . . . . . . . . . . . . . . 18
2.3.1.1 Simplex Algorithm . . . . . . . . . . . . . . . . . . . . . . . . . . . 18
2.3.1.2 Interior Point Algorithm . . . . . . . . . . . . . . . . . . . . . . . 20
2.3.1.3 Branch and Bound Algorithm . . . . . . . . . . . . . . . . . . . . 21
2.3.2 Meta-heuristic Optimization Techniques . . . . . . . . . . . . . . . . . . . . 22
2.4 Genetic Algorithm . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22
2.4.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22
2.4.2 GA Encoding . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23
2.4.2.1 Binary Encoding . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23
2.4.2.2 Value Encoding . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24
2.4.2.3 Permutation Encoding. . . . . . . . . . . . . . . . . . . . . . . . . 24
2.4.2.4 Tree Encoding . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24
2.4.3 GA Operator . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26
2.4.3.1 Selection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26
2.4.3.2 Crossover . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27
2.4.3.3 Mutation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28
2.4.4 Application of GA . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29
2.5 Pattern Search . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29
2.5.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29
2.5.2 Application of PS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30
2.6 Particle Swarm Pattern Search Algorithm . . . . . . . . . . . . . . . . . . . . . . . 31
2.6.1 Particle Swarm Optimization . . . . . . . . . . . . . . . . . . . . . . . . . . 31
2.6.2 Particle Swarm Pattern Search . . . . . . . . . . . . . . . . . . . . . . . . . 32
2.7 Penalty Method for Constrained Optimization. . . . . . . . . . . . . . . . . . . . . 32
2.7.1 Death Penalty . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34
2.7.2 Static Penalty. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34
2.7.3 Dynamic Penalty . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34
2.7.4 Annealing Penalty . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36
2.7.5 Adaptive Penalty . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37
2.8 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38
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3 Campus Space Allocation Problem 39
3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39
3.2 Related Works on PSA . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39
3.3 Campus Parking Space Allocation Model . . . . . . . . . . . . . . . . . . . . . . . 44
3.4 Solution Idea . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47
3.5 Exact Optimization Solver . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49
3.6 Genetic Algorithm . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50
3.7 Pattern Search Algorithm . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53
3.8 Particle Swarm Pattern Search Algorithm . . . . . . . . . . . . . . . . . . . . . . . 55
3.9 Data Representation for the CPSA Model . . . . . . . . . . . . . . . . . . . . . . . 57
3.10 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59
4 Experimental Setting and Results 60
4.1 Dataset . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60
4.2 Experimental Settings . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61
4.2.1 GA Parameter Settings . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61
4.2.2 PS Parameter Settings . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62
4.2.3 PSwarm Parameter Settings . . . . . . . . . . . . . . . . . . . . . . . . . . . 62
4.3 Exact Results Using CPLEX Solver . . . . . . . . . . . . . . . . . . . . . . . . . . 62
4.3.1 Fitness Values across Datasets . . . . . . . . . . . . . . . . . . . . . . . . . 62
4.3.2 Distribution of Parking Spaces . . . . . . . . . . . . . . . . . . . . . . . . . 64
4.3.2.1 Dataset 1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64
4.3.2.2 Dataset 2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65
4.3.2.3 Dataset 3 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67
4.3.2.4 Dataset 4 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69
4.4 Meta-heuristic Results Performances . . . . . . . . . . . . . . . . . . . . . . . . . . 72
4.4.1 Fitness Values across Datasets . . . . . . . . . . . . . . . . . . . . . . . . . 72
4.4.2 Execution Time of the Algorithms for Different Datasets. . . . . . . . . . . 72
4.4.3 Distribution of Parking Spaces . . . . . . . . . . . . . . . . . . . . . . . . . 76
4.4.3.1 Dataset 1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 79
4.4.3.2 Dataset 2 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 79
4.4.3.3 Dataset 3 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85
4.4.3.4 Dataset 4 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 91
4.5 Meta-heuristics Comparison with Exact Results . . . . . . . . . . . . . . . . . . . . 98
4.6 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 100
5 Conclusion and Future Research 102
5.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 102
ix
5.2 Organisation of Objectives . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 102
5.3 Summary of Research Study . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 103
5.4 Future Research . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 104
5.5 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 105
A Dataset 1 116
B Dataset 2 119
C Dataset 3 122
D Dataset 4 126
E Conference paper 130
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