ARTIFICIAL BEE COLONY IN OPTIMIZING PROCESS PARAMETERS OF SURFACE ROUGHNESS IN END MILLING AND ABRASIVE WATERJET MACHINING NORFADZLAN BIN YUSUP A dissertation submitted in partial fulfillment of the requirements for the award of the degree of Master of Science (Computer Science) Faculty of Computer Science and Information Systems Universiti Teknologi Malaysia FEBRUARY 2012
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ARTIFICIAL BEE COLONY IN OPTIMIZING PROCESS PARAMETERS OF
SURFACE ROUGHNESS IN END MILLING AND ABRASIVE WATERJET
MACHINING
NORFADZLAN BIN YUSUP
A dissertation submitted in partial fulfillment of the
requirements for the award of the degree of
Master of Science (Computer Science)
Faculty of Computer Science and Information Systems
Universiti Teknologi Malaysia
FEBRUARY 2012
To my beloved family and friends, thank you for the endless support and
encouragement.
ACKNOWLEDGEMENT
Firstly I would like to thank Allah SWT the Most Merciful, Most
Compassionate. It is by God willing; I was able to complete this project within the
time given. I want to express gratitude to my supervisors, Assoc. Prof. Dr. Siti
Zaiton Mohd Hashim and Dr. Azlan Mohd Zain. This project would not be
accomplished without their guidance and support throughout period of time on doing
this project. I learned a lot of knowledge under their guidance. Thank you very much
Dr. Azlan Mohd Zain for improving both of my research and writing skills. I would
also like to thank to Kementerian Pengajian Tinggi (KPT) Malaysia and Universiti
Malaysia Sarawak (UNIMAS) for the scholarship that they provided during the
period of my study.
Special thanks to my examiners Prof. Dr. Siti Maryam Shamsudin and Dr.
Roselina Sallehuddin. Thank you for their constructive comments in evaluating my
project. Thank you to my family and friends for their support. And lastly thank you
to all post graduate staff and lectures Faculty of Computer Science and Information
System (FSKSM), UTM for their help and support.
V
ABSTRACT
The machining operation can be generally classified into two types which are
traditional machine and non-traditional (modem) machine. There are two types of
machining employed in this research, end milling (traditional machining) and
abrasive waterjet machining (non-traditional machining). Optimizing the process
parameters is essential in order to provide a better quality and economics machining.
This research develops an optimization algorithm using artificial bee colony (ABC)
algorithm to optimize the process parameters that will lead to minimum surface
roughness (Ra) value for both end milling and abrasive waterjet machining. In end
milling, three process parameters that need to be optimized are the cutting speed,
feed rate and radial rake angle. For abrasive waterjet, five process parameters that
need to be optimized are the traverse speed, waterjet pressure, standoff distance,
abrasive grit size and abrasive flow rate. These machining process parameters
significantly impact on the cost, productivity and quality of machining parts. The
ABC simulations are developed to achieve the minimum Ra value in both end milling
and abrasive waterjet machining. The results obtained from the simulation are
compared with experimental, regression modelling, Genetic Algorithm (GA) and
Simulated Annealing (SA). In end milling, ABC reduced the Ra by 10% and 8%
compared to experimental and regression. In abrasive waterjet, the performance was
much better where the Ra value decreased by 28%, 42%, 2% and 0.9% compared to
experimental, regression, GA and SA respectively.
vi
ABSTRAK
Secara umumnya, operasi pemesinan boleh dikelaskan kepada dua jenis iaitu
mesin tradisional dan mesin bukan tradisional (mesin moden). Terdapat dua jenis
pemesinan yang digunakan dalam penyelidikan ini, mesin pengisaran hujung
(pemesinan tradisional) dan mesin pelelas je t air (pemesinan bukan tradisional).
Mengoptimumkan proses parameter adalah penting untuk menyediakan kualiti yang
lebih baik dan ekonomi pemesinan. Penyelidikan ini membangunkan algoritma
pengoptimuman menggunakan algoritma koloni lebah buatan (ABC) bagi kedua-dua
mesin pengisaran hujung dan mesin pelelas jet air. Terdapat tiga parameter mesin
pengisaran hujung yang perlu dioptimumkan iaitu kelajuan memotong, kadar suapan
dan sudut meraih jejarian. Bagi mesin pelelas je t air terdapat lima parameter yang
perlu dioptimumkan iaitu kelajuan traverse, tekanan jet air, jarak standoff, saiz kersik
melelas dan kadar aliran yang melelas. Parameter pemesinan memberi kesan yang
ketara ke atas kos, produktiviti dan kualiti bahagian-bahagian pemesinan. Simulasi
ABC dibangunkan untuk mencapai nilai minimum Ra dalam kedua-dua mesin
pengisaran hujung dan mesin pelelas jet air. Keputusan yang diperolehi daripada
penyelidikan dibandingkan dengan eksperimen, pemodelan regresi, Algoritma
Genetik (GA) dan simulasi penyepuhlindapan (SA). Dalam mesin pengisaran hujung,
ABC mengurangkan Ra sebanyak 10% dan 8% berbanding dengan eksperimen dan
regresi. Di mesin pelelas jet air, prestasi adalah lebih baik dimana nilai Ra menurun
sebanyak 28%, 42%, 2% dan 0.9% berbanding dengan eksperimen, regresi, GA dan
TABLE OF CONTENT
CHAPTER TITLE PAGE
DECLARATION ii
DEDICATION iii
ACKNOWLEDGEMENT iv
ABSTRACT v
ABSTRAK vi
TABLE OF CONTENT vii
LIST OF TABLES x
LIST OF FIGURES xiv
LIST OF ABBREVIATION xvi
LIST OF SYMBOLS xvii
1 INTRODUCTION 1
1.1 Introduction 1
1.2 Statement of problems 4
1.3 Objectives of the Study 5
1.4 Scope of the Study 5
1.5 Significance of the Study 6
1.6 Organization of the Report 6
2 LITERATURE REVIEW 7
2.1 Minimization of surface roughness 7
2.2 Optimization of end milling and AWJ machining process 8
2.3 ABC optimization technique 10
2.3.1 Flow of ABC algorithm 13
V lll
2.3.2 ABC Pseudocode 14
2.3.3 Abilities and limitation of ABC 16
2.4 Previous research on ABC algorithm in various domain 17
2.5 Previous research in optimizing machining process parameters using soft computing technique 21
2.6 Experimental data of case studies 36
2.6.1 End milling machining 3 6
2.6.1.1 Experimental design 37
2.6.1.2 Experimental results 39
2.6.2 AW J machining 41
2.6.2.1 Experimental design 41
2.6.2.2 Experimental results 42
2.7 Summary 43
METHODOLOGY 44
3.1 Introduction 44
3.2 Research flow 47
3.3 Assessment of real experimental data 47
3.4 Regression modeling development 47
3.4.1 Regression modeling in end milling 48
3.4.1.1 Regression Model for Each Cutting Tool 49
3.4.2 Regression modeling in abrasive waterjet 54
3.5 ABC algorithm for optimization of process parameters 56
3.5.1 Justification of ABC control parameters 59
3.5.2 Steps for determination of the optimal process parameters 59
3.6 Validation and evaluation of ABC results 61
3.7 ABC optimization performances 61
3.7 Summary 65
ABC OPTMIZATION
4.1 Introduction
4.2 ABC optimization execution
4.3 Initial Phase
4.4 Employed-bee Phase
66
66
67
73
74
IX
4.5 Onlooker-bee Phase 75
4.6 Scout-bee Phase 76
4.7 Experiment 1 - ABC optimization parameters for endmilling 76
4.7.1 Colony size of 10 and limit of 30 77
4.7.2 Colony size of 20 and limit of 60 90
4.7.3 Colony size of 50 and limit of 60 103
4.7.4 Colony size of 100 and limit of 300 116
4.8 Experiment 2 - ABC optimization parameters for AWJ 129
4.8.1 Colony size of 10 and limit of 50 129
4.8.2 Colony size of 20 and limit of 100 142
4.8.3 Colony size of 50 and limit of 250 155
4.8.4 Colony size of 100 and limit of 500 168
4.9 Summary of end milling experimental results 181
4.10 Summary of AWJ experimental results 183
5 ANALYSIS OF RESULTS 186
5.1 Introduction 186
5.2 Analysis of results 187
5.2.1 Validation and evaluation of end milling results 187
5.2.2 Validation and evaluation of AWJ results 190
5.3 Summary 195
6 CONCLUSION AND FUTURE WORK 196
6.1 Introduction 196
6.2 Summary of work 197
6.3 Research summary and conclusion 198
6.4 Suggestion for future work 201
6.5 Summary 202
REFERENCES 203
X
TABLE NO TITLE PAGE
2.1 Control parameters of ABC 20
2.2 Previous researches in optimizing processparameters of Ra for traditional machining 23
2.3 Previous researches in optimizing processparameters of Ra for modem machining 30
2.4 Mechanical properties of Ti-6A1-4V 36
2.5 Properties of the cutting tool used in theexperiments 37
2.6 Levels of independent variables and codingidentification 38
2.7 Specification of the CNC machine 38
2.8 Ra values for real machining experiments 40
2.9 Levels of process parameters and codingidentification 41
2.10 Ra values for real machining 42
3.1 Uncoated Tool coeffients value 49
3.2 TiAIN coated Tool coeffients value 49
3.3 SNTr coated Tool coeffients value 50
3.4 Ra predicted values of regression modelling 51
3.5 Statistics and correlations for paired samples 52
3.6 Paired samples test 53
3.7 Predicted Ra values of AWJ Regression model 55
3.8 Justification of ABC control parameters 59
3.9 Parameters used in the numerical benchmarkfunction experiments 62
4.1 Control variables combination with limit of 30 77
4.2 The best value returned from 10 max cycles perran with limit of 30 79
LIST OF TABLES
4.3
4.4
4.5
4.6
4.7
4.8
5.9
4.10
4.11
4.12
4.13
4.14
4.15
4.16
4.17
4.18
4.19
4.20
4.21
4.22
4.23
4.24
XI
The best value returned from 20 max cycles perrun with limit of 30 81
The best value returned from 50 max cycles perrun with limit of 30 83
The best value returned from 100 max cycles perrun with limit of 30 86
Control variables combination with limit of 60 90
The best value returned from 10 max cycles perrun with limit of 60 92
The best value returned from 20 max cycles perrun with limit of 60 94
The best value returned from 50 max cycles perrun with limit of 60 96
The best value returned from 100 max cycles perrun with limit of 60 99
Control variables combination with limit of 150 103
The best value returned from 10 max cycles perrun with limit of 150 105
The best value returned from 20 max cycles perrun with limit of 150 107
The best value returned from 50 max cycles perrun with limit of 150 109
The best value returned from 100 max cycles perrun with limit o f l5 0 112
Control variables combination with limit of 300 116
The best value returned from 10 max cycles perrun with limit of 300 118
The best value returned from 20 max cycles perrun with limit of 300 120
The best value returned from 50 max cycles perrun with limit of 300 122
The best value returned from 100 max cycles perrun with limit of 300 125
Control variables combination with limit of 50 129
The best value returned from 10 max cycles perrun with limit of 50 131
The best value returned from 20 max cycles perrun with limit of 50 133The best value returned from 50 max cycles perrun with limit of 50 135
4.25
4.26
4.27
4.28
4.29
4.30
4.31
4.32
4.33
4.34
4.35
4.36
4.37
4.38
4.39
4.40
4.41
4.42
5.1
5.2
5.3
X l l
The best value returned from 100 max cycles perrun with limit of 50 138
Control variables combination with limit of 100 142
The best value returned from 10 max cycles perrun with limit of 100 144
The best value returned from 20 max cycles perrun with limit of 100 146
The best value returned from 50 max cycles perrun with limit of 100 148
The best value returned from 100 max cycles perrun with limit of 100 151
Control variables combination with Limit of 250 155
The best value returned from 10 max cycles perrun with limit of 250 157
The best value returned from 20 max cycles perrun with limit of 250 159
The best value returned from 50 max cycles perrun with limit of 250 161
The best value returned from 100 max cycles perrun with limit of 250 164
Control variables combination with limit of 500 168
The best value returned from 10 max cycles perrun with limit of 500 170
The best value returned from 20 max cycles perrun with limit of 500 172
The best value returned from 50 max cycles perrun with limit of 500 174
The best value returned from 100 max cycles perrun with limit of 500 177
Summary of ABC optimization results usingdifferent colony size and limit in end milling 183
Summary of ABC optimization results usingdifferent colony size and limit in end milling 185
Conditions to define the scale for optimal process parameters of end milling 189
Comparison of the optimal process parameters inend milling 190
Conditions to define the scale for optimal process parameters of AWJ 192
5.4 Comparison of the optimal process parameters in AWJ 193
5.5 Comparison of optimal Ra in end milling and AWJ machining 194
6.1 Reduction percentage of minimum surface roughness in end milling 198
6.2 Reduction percentage of minimum surface roughness in AWJ 199
6.3 Summary of minimum bee colony size and max number of cycles 200
6.4 Summary of level of the optimal process parameters 201
xiv
FIGURE NO
1.1
2.1
2.2
2.3
3.1
3.2
4.1
4.2
4.3
4.4
4.5
4.6
4.7
4.8
4.9
4.10
4.11
4.12
4.13
4.14
4.15
4.16
4.17
4.18
LIST OF FIGURES
TITLE
Parameters that affect Ra
Categories of milling
AWJ major components
Flow of ABC optimization
Flow of searching for optimum process parameters
Evolution of mean best values for Rosenbrock function
ABC Matlab program interface
Results of 10 max cycles per run with limit of 30
Results of 20 max cycles per run with limit of 30
Results of 50 max cycles per run with limit of 30
Results of 100 max cycles per run with limit of 30
Results of 10 max cycles per run with limit of 60
Results of 20 max cycles per run with limit of 60
Results of 50 max cycles per run with limit of 60
Results of 100 max cycles per run with limit of 60
Results of 10 max cycles per run with limit of 150
Results of 20 max cycles per run with limit of 150
Results of 50 max cycles per run with limit of 150
Results of 100 max cycles per run with limit of 150
Results of 10 max cycles per run with limit of 300
Results of 20 max cycles per run with limit of 300
Results of 50 max cycles per run with limit of 300
Results of 100 max cycles per run with limit of 300
Results of 10 max cycles per run with limit of 50
PAGE
2
8
9
13
46
63
68
78
80
82
85
91
93
95
98
104
106
108
111
117
119
121
124
130
4.19 Results of 20 max cycles per run with limit of 50 132
4.20 Results of 50 max cycles per run with limit of 50 134
4.21 Results of 100 max cycles per run with limit of 50 137
4.22 Results of 10 max cycles per run with limit of 100 143
4.23 Results of 20 max cycles per run with limit of 100 145
4.24 Results of 50 max cycles per run with limit of 100 147
4.25 Results of 100 max cycles per run with limit of 100 150
4.26 Results of 10 max cycles per run with limit of 250 156
M l Results of 20 max cycles per run with limit of 250 158
4.28 Results of 50 max cycles per run with limit of 250 160
4.29 Results of 100 max cycles per run with limit of 250 163
4.30 Results of 10 max cycles per run with limit of 500 169
4.31 Results of 20 max cycles per run with limit of 500 171
4.32 Results of 50 max cycles per run with limit of 500 173
4.33 Results of 100 max cycles per run with limit of 500 176
4.34 Comparison of the effect of colony size in end milling experiment 181
4.35 Comparison of the effect of colony size in AWJ Experiment 184
LIST OF ABBREVIATIONS
ABC - Artificial Bee Colony
AI - Artificial Intelligence
ANN - Artificial Neural Network
AWJ - Abrasive Waterjet
BP - Backpropagation
DE - Differential Evolution
EA - Evolutionary Algorithm
GA - Genetic Algorithm
NFL - No Free Lunch
NN - Neural Network
PSO - Particle Swarm Optimization
RSM - Response Surface Methodology
SA - Simulated Annealing
SNtr - Supemitride
TiAIN - Titanium Aluminum Nitrate
LIST OF SYMBOLS
Radial rake angle
Abrasive grit size
Feed rate
Standoff distance
Abrasive flow rate
W ateijet pressure
Surface Roughness
Cutting speed
Traverse speed
CHAPTER 1
INTRODUCTION
1.1 Introduction
In highly competitive manufacturing industries nowadays, the manufacturer
ultimate goals are to produce a high quality product with less cost and time
constraints. Thus, the flexible manufacturing system (FMS) has been introduced
since 1960 to achieve this goals by introducing the fully automation of computer
numerically controlled (CNC) machine tools. The idea of FMS is to provide a fully
automated machine that required a minimum supervision in 24 hours per day. In the
traditional FMS, it consists of a huge number of CNC which handled by complex
software and it is undeniable very costly. Nowadays, a smaller version of FMS is
being used which is commonly refer as Flexible Manufacturing Cell (FMC) where it
consists two or more CNC machines only. According to Mike et al. (1998), CNC
machine tools require less operator input, provide greater improvements in
productivity, and increase the quality of the machined part. Generally, the machining
operations can be classified into two types which are traditional and non-traditional
(modem). The traditional machining operations include turning, milling, boring, and
grinding while non-traditional or modem machining operations include abrasive
w aterjet machining, electron beam machining and photochemical machining.
2
According to Rao and Pawar (2009), the selection of machining process
parameters is a very crucial part in order for the machine operations to be success. To
choose the process parameters, it is usually based on the human (or manufacturing
engineers) judgement and experience. However, the chosen of process parameters
usually did not give an optimal result. This is due to in the machining processing; a
number of factors also could interrupt thus preventing in achieving high process
performance and quality (Bemados and Vosniakos, 2002). Figure 1.1 below showed
the machining parameters that affect surface roughness, Ra. To improve this quality,
one of the indications is by referring to the machining performances measures, Ra
(Zain et al, 2010a). In manufacturing, the quality of the product focused on the
surface texture particularly the Ra because it affects the product end results such as
the appearance, function and reliability. There are many factors to produce a specific
roughness such as in end milling where it depends on the cutting speed, feed rate,
velocity of the traverse, cooling fluids and the mechanical properties of the piece
being machined. Any small changes in one of these factors could affect the results of
the surface produced.
C - H i n n T n n i e P m n Br t i « Machining Parameters
SURFACEROUGHNESS
Cutting force variation
Workpiece Properties Cutting Phenomena
Figure 1.1 Parameters that affect Ra (Benardos and Vosnaikos, 2003
Various techniques have been considered by a number of researchers to
model and optimize machining problems. This technique includes statistical
regression, conventional optimization technique such as Taguchi method, response
3
surface methodology (RSM) and iterative mathematical search technique. Other
techniques such as Artificial neural network (ANN) and Fuzzy set-theory based
modelling also have been applied. Apart from that, a number of researches also have
been done using the concept of non conventional optimization technique such as
Non-traditional machining such as AWJ used a high forceful flow of water in
order to slash the workpiece. The high pressure of water (usually more than 900
mph) incredibly enables it to cut the hard workpiece such as metal and has been used
in the industries since 1980. The advantage of AWJ is that it never gets dry and
overheat compared to other cutting machining. Today, the CNC AWJ is usually used
to slash softer materials while the recent developed AWJ machining technology is
used for slashing harder materials. An example of major AWJ components
machining is illustrated in Figure 2.2.
Figure 2.2 AWJ major components (Echert et al, 1989)
According to Caydas and Hascalik (2008), the various advantages of AWJ
are including no thermal distortion, high machining versatility and flexibility, also
small cutting forces which means the machining has less pressured on the workpiece.
AWJ downsides and restrictions include producing deafening sound and untidy
10
operational setting. At a high traverse rates, the cutting of the material may build
narrowed edges on the kerf. Azmir and Ahsan (2008).
Five controlled tuning process parameters of AWJ that are considered in the
study. According to Hashish (1991) the most significance and precisely controllable
process parameters are water pressure (P), abrasive flow rate (Mj), je t traverse rate
(V) and diameter of focusing nozzle (d).
2.3 ABC optimization technique
Currently, there has been intensifying demand in growth of computational
models or methods that motivated by how animals interact and communicate among
each other to find food sources. Many optimization algorithms have been designed
and developed by adopting a form of biological-based swarm intelligence including
ABC algorithm. ABC is a swarm-based algorithm that mimics the foraging
behaviour of swarm honey bee. Similar to the concept of ACO and PSO, this
exploration algorithm is capable of tracing good quality of solutions. Honey bee is a
good example of well known social insects with self organisation and division of
labour for food collection through information sharing between employed and
unemployed foragers.
Three types of bees in the colony include employed, onlookers and scouts
bees. Each type of bee bears a different task. Employed bees that are currently
exploiting and searching are linked with the food sources. The unemployed bees or
scouts bees are associated with establishing new food sources either by searching the
environment surrounding the hives or waiting for the employed bees to share the best
food source location in the hives. Unemployed bees can be regarded as scouts and
onlookers bees. Without any supervision, the scout bees explore the location for new
11
food sources. It is a very exceptional situation if the scouts’ bees find out loaded
indefinite food sources by chance. In contrast, the onlookers bees that watched the
waggle dance are positioned on the food sources by using a probability based
selection process. The probability value which the food source is favoured by
onlookers increases while the quantity of the nectar amount increases. The employed
bees will share the information by performing a special dance called the waggle
dance in the hive dance floor. This dance contains much valuable information about
the food sources such as the location and the quality of the nectar. Based on the
dance, the scout bees later will explore the reveal food sources. The main steps of the
ABC algorithm are initialize the population, then position the employed bees on their
food sources, consign onlooker bees on the food sources based on the quality of the
nectar, followed by sending off the scouts to explore neighbourhood for learning new
food sources and finally revise the best food source found so far. The process of
searching for food is repeated in anticipation of the satisfied termination criteria
(Karaboga, 2005).
The three control parameters that perform significant role in the ABC
algorithm are as follows:
i. the number of colony size (SN) - the number of food sources or the
population size of the colony (the number of employed bees or
onlooker bees).
ii. the predefined value of limit (L) - the food source is assumed to be
deserted if a location or position cannot be enhanced (for unimproved
loop).
iii. the maximum loop for searching food (M)
The colony of the bees is made up of two groups. The first group of the
colony composed of the employed bees and the next group consist of the onlooker’s
bees. For each food source, there is no more than one employed bee. Consequently,
if a solution indicating a food source is not enhanced by a predetermined number of
trials, in that case the food source is deserted by the employed bee soon transformed
12
to scout bees. For the second group, the onlooker’s bee in the hives waits for the
employed bees to perform a special dance routine called the waggle dance and
chooses the food position according to the information given by the employed bees
in the dance.
13
2.3.1 Flow of ABC algorithm
Figure 2.3 below illustrates the flow of ABC algorithm.
Figure 2.3 Flow of ABC optimization (Karaboga, N., 2009
14
In Figure 2.3, there are three steps for each cycle after the initialization food
source position phase. The first step is initializing the employed bees to the food
source and determined the nectar quantity. Then the onlooker bees are initialized to
the food source and determined the nectar quantity. At the last step for the cycle, the
scout bees determined and the bees are initialized to the food sources at random.
During the initialization step, a set of food source position that signify a potential
solution are produced randomly. Then, the control parameters values are assigned.
Employed bees search for the best quality of food around the neighbourhood. The
bees will assess the nectar quality in the food source area. If the bees calculated a
high quantity of the nectar, it will memorize the food source position until it founds
new food sources that have much higher quantity of the current one. Thus, the pollen
or nectar quantity of the food source match to the quality of the solution signifies by
that food source. Once the process of searching for food source is finished, the
employed bees will go back to their hives and share the information (the best food
source position) to the onlooker bees. By doing a unique type of dance called the
waggle dance, the employed bees will start dancing while the onlookers bees will
extract information from this dance. The food source that has the most quantity and
quality will be chose the majority by the onlooker bees. After that, every onlooker
bees that has been assigned to each of the food source within the neighbourhood will
calculate the nectar amount.
2.3.2 ABC Pseudocode
The detailed pseudocode to solve the optimization is as follows, (Karaboga
and Akay, 2009):
1: Initialize the population of solutions xi,j
2: Evaluate the population
3: Cycle=l
4: Repeat
5: Produce new solutions (food source positions) x»i,j in the neighbourhood of xi,j for
the employed bees using the formula ui,j = xi,j + Oij(xi,j - xk,j) (k is a solution in the
neighbourhood of i, O is a random number in the range [-1,1] ) and evaluate them
15
6: Apply the greedy selection process between xi and x»i
7: Calculate the probability values Pi for the solutions xi by means of their fitness
values using the equation (2.1):
n (2 .1)
In order to calculate the fitness values of solutions we employed the following
equation (2.2):i
i , i f f > 0 f i t t = \ i+ fi * (2 .2)
( l + abs f ( i ) , i f f t < 0
Normalize Pi values into [0,1].
8: Produce the new solutions (new positions) x»i for the onlookers from the solutions
xi, selected depending on Pi, and evaluate them.
9: Apply the greedy selection process for the onlookers between xi and x»i.
10: Determine the abandoned solution (source), if exists, and replace it with a new
randomly produced solution xi for the scout using the equation (2.3):
Xij=minj+rand( 0,1)* (maxj -minj) (2.3)
11: Memorize the best food source position (solution) achieved so far
12: Cycle=cycle+1
13: Until cycle= Maximum Cycle Number (MCN)
16
2.3.3 Abilities and limitation of ABC
The abilities of ABC algorithm may possibly include the following (Rao et al,
2008; Karaboga N., 2009; Benala et al, 2009; Akay and Karaboga, 2010; Karaboga
D. and Akay, 2009; Rao and Pawar, 2010; Akay and Karaboga, 2009):
i. ABC algorithm does not need external parameters such as cross over
rate and mutation rate as in GA and DE.
ii. ABC algorithm introduces neighbourhood source production
mechanism which is the same as mutation process.
iii. ABC algorithm has less computation time required and offered
optimal solution due to its excellent global and local search capability.
iv. the probability of falling into the local optimum is low in ABC
algorithm because of the combination of local and global search.
v. ABC algorithm only employs fewer control parameters.
vi. the convergance rate of ABC algorithm is very high and only requires
a little iteration for convergence to the optimal solution.
vii. ABC algorithm combines both stochastic selection scheme and greedy
selection scheme.
viii. ABC algorithm does not need big number of colony size to solve
optimization problems with high dimensions.
The limitations of ABC may perhaps include the following (Kurban and
Besdok, 2009; Pei et al, 2009; Saeedi et al, 2009):
i. slow convergance rate.
ii. the artificial bee, can only move straight to one of the nectar sources of those
are discovered by the employed bees.
iii. the number of tunable parameters it employs.
17
2.4 Previous research on ABC algorithm in various domain
ABC is a recent swarm based intelligent algorithm that has been applied in
various applications to solve numerous problems and the performance of ABC
proved that it is an excellent algorithm. This is confirmed by a number of researches
that has successfully implemented ABC in different domain and problems.
In the domain of electrical and network-based, ABC algorithm has been used
to solve network configuration problem in distribution system (Rao et al, 2008). The
experiments results obtained showed that ABC outperforms the GA, differential
evolution (DE) and SA in terms of quality of the solution and computation
effectiveness. The authors stated that the advantages of ABC are it does not need
external parameters such as cross over rate and mutation rate as in GA and DE.
Moreover, ABC algorithm introduces neighborhood source production mechanism
which is the same as mutation process. In a research by Karaboga et al. (2010), ABC
has been proposed as a hierarchical clustering approach for wireless sensor networks
to maintain energy reduction of the network in lowest amount. From the results, it
showed that ABC algorithm outperformed over direct transmission and LEACH
algorithm. Also, ABC algorithm seems to be a promising solution for successful
operations in cluster based. In the research of Abu-Mouti and El-Hawary (2009), the
authors positive that ABC algorithm has excellent solution quality and convergence
characteristics. In the experiments, ABC has been used to minimize total system real
power loss for determining the optimal size, location and power factor for a
distributed generation (DG). The efficiency of ABC algorithm is confirmed where
the standard deviation of the attained results for 30 independent runs at every test
case is practically equivalent to zero.
In the domain of signal processing, ABC algorithm was implemented for
designing digital HR filters and its performance is compared with conventional
optimization algorithm (LSQ-nonlin) and PSO (Karaboga, 2009). ABC algorithm
shows a less computation time required and offered optimal solution compared to
18
PSO and LSQ-nonlin due to its excellent global and local search capability. The
algorithm is recommended as alternative approach for designing digital low- and
high-order HR filters.
In the domain of image processing, Benala et al. (2009) used ABC algorithm
to enhance image edge for hybridized smoothening filters as ABC algorithm claims
to be the most powerful neutral optimization technique for sampling a large solution
space. The results are then compared to GA. It was found out that ABC
outperformed GA in terms of speed in optimization and accuracy of results. The
authors claimed that in ABC algorithm the probability of falling into the local
optimum is low. This is because of the combination of local and global search since
the aim of the algorithm is to improve the local search ability of the GA without
degrading the global search ability.
In the domain of bioinformatics, ABC algorithm has been used by Bahamish
et al. (2009) to search the protein conformational search space to find the lowest free
energy conformation. In the research, four types of experiments are conducted and
100 independent runs were performed for each experiment. The results indicated that
the algorithm was able to find the lowest free energy conformation for a test protein
(i.e. Met enkephaline) of -12.910121 kcal/mol usign ECEPP/2 force field. Another
research attempted by Benitez and Lopes (2010). ABC algorithm was used to predict
protein structure using the three-dimensional hydrophobicpolar model with side-
chains (3DHP-SC). From the results, the researchers stated that the colony size
(number of bees) per hive has a significant influence in the quality of solutions and
suggested that larger colony leads to better results than the smaller ones.
In the scheduling and assignment problem, ABC algorithm was used to
identify optimum parameters for scheduling the manufacture and assembly of
complex products to minimize the combination of earliness and tardiness penalties
cost (Pansuwan et al., 2010). According to the authors, ABC algorithm performance
can be enhanced significantly after implementing the optimum parameter setting
19
identified through statistical design and analysis. In solving small to medium size
generalized assignments problems by Baykasoglu et al. (2010), the researchers
assured that ABC algorithm discovered all optimal solutions effortlessly compared to
the other 12 algorithms that was tested in the experiments.
In the domain of numerical optimization, a comparative study by
Krishnanand et al. (2009) shows that ABC gives an optimal result compared to the
other four biological inspired optimization algorithms which are Artificial Immune
(AI), Invasive Weed Optimization (IWO), GA and PSO. In the experiments, all five
algorithms are applied using multivariable Rosenbrock function and global minima
are constantly attained in ABC for extremely undersized dimensional problem. A
modified ABC algorithm is applied by Akay and Karaboga (2010) to solve real-
parameter optimization problem. In the study, ABC algorithm has been tested with
two group of functions which are unimodal function such as Sphere and Rosenbrock
function and composite function. The results show that ABC is efficient in terms of
local and global optimization due to the selection schemes employed and the use of
neighbouring production method. In Karaboga D. and Akay (2009), ABC was used
for optimizing a large set of numerical test functions and the results produced by
ABC algorithm are compared with the results obtained by GA, PSO, DE and
evolution strategies. Results show that the performance of the ABC is better than or
similar to those of other population-based algorithms with the advantage of
employing fewer control parameters.
2 0
Table 2.1: Control parameters of ABC
No Author, Year Number of test/
experiments
Number of colony size (SN)
Limit (L) Maximum loop (M)
1 Rao et al. (2008)
3 30 Not stated 20
2 Bahamish et al. (2009)
4 20 Not stated 1000
3 Karaboga(2009)
4 20 40 100
4 Baykasoglu et al. (2010)
2 150 Not stated 100
5 Abu-Mouti and El- Hawary (2009)
4 30 227 20
6 Benitez and Lopes (2010)
4 250 Not stated 6000
Table 2.1 shows the value of three control parameters of ABC optimization
such as number of colony, limit and maximum loop that has been used by various
researchers.
2.5 Previous research in optimizing machining process parameters using soft
computing techniques
From the literature review, there is a deficiency of research using ABC in
optimizing process parameters of Ra in machining areas particularly for traditional
and non-traditional machining. A research by Rao and Pawar (2010) applied non-
traditional optimization algorithm such as ABC, PSO and SA to optimize process
parameter in multi-pass milling machining. The results show that the convergence
rate of ABC and PSO algorithms are very high and involves only a little iteration for
convergence to the optimal solution. The accurateness of solution achieved by ABC
algorithm is better than the result obtained by using SA algorithm.
In Zain et al (2010a, 2010b, 2010c) GA and SA have been applied in
optimizing cutting condition for both end milling and AWJ. The results of GA and
SA show a significant potential and accomplishment in both machining operations.
In end milling machining, GA and SA decreased the Ra by 27%, 26% and 50%
compared to experiment data, regression model and RSM technique correspondingly.
While in abrasive waterjet machining, GA minimize the Ra by 27% and 41%
compared to experimental data and regression model respectively. The outcomes of
SA show a modest increments where it minimize the Ra by 28% and 42% compared
to data and regression model respectively.
Based on No Free Lunch (NFL) theorem, whichever two algorithms are
equivalent when their performance is averaged across all possible problems (Wolpert
and Mcready, 1997). Although GA and SA show good results in minimizing the Ra
values in both end milling and AWJ machining, ABC optimization algorithm is
applied in order to achieve more optimal values of Ra for both machining operations.
The NFL outcomes point out that matching algorithm to problems gives superior
average performance than does applying a fixed algorithm to all (Wolpert and
Mcready, 2005). The NFL is impossibility theorem where universal optimization
22
approach is impractical and a single approach can surpass another if it is specialized
to the structure of the particular problem under consideration (Ho and Pepyne, 2002).
Table 2.2 and Table 2.3 briefly summarized the previous research works that
have been accomplished in traditional and modem machining respectively to
optimize process parameters of Ra using a variety of optimization techniques.
Table 2.2: Previous researches in optimizing process parameters of Ra for traditional machining
Author/Year Techniques Cutting condition Process Results
lao and Pawar 2010)
ABC, PSO, SA
Feed per tooth, cutting speed, depth of cut
Milling The convergence rate of ABC algorithms is v high and involves only a little iteration for convergence to the optimal solution. The accurateness of solution achieved by ABC algorithms is better than results obtained by u SA algorithm.
lossain et al. 2009)
ANN Feed per tooth, cutting speed, depth of cut
Milling Performance of the neural network is very go( terms of concurrence with the experimental d<
Cadirgama et 1. (2008)
RSM,RBFN
Cutting speed, feed rate, axial depth and radial depth
Milling The feed rate has been identified as the most significant factors effecting Ra in the first ord( model and RBFN. RBFN predict Ra more pre compared to RSM.
Wang et al. 2009)
NN Spindle rate, feed rate, axial depth
Milling The maximal prediction error is about 10%, w the machining variables are chosen out of the variables range which is used for the NN moc training. The model is capable to predict the h well.
Wang et al. 2009)
GA Spindle rate, feed rate, axial depth
Milling The optimization results shows that the maxir removal rate can be attained in the certain ran Ra by selecting the right cutting parameters.
ring et al. 2005)
PSO Feed rate, depth of cut, grit size
Grinding PSO establishes the optimization of silicon ca grinding and hence assists the effective use of quality ceramics in industrial applications.
3odi and 'ingjian (2009)
ANN, GA Cutting speed, feed rate, depth of cut, diameter, slenderness ratio
Milling ANN and GA are both successful and efficien slender bar turning operations.
'ain et al. 2010a, 2010b)
GA, SA Feed per tooth, cutting speed, depth of cut
Milling, In end milling GA and SA decreased the Ra b; 27%, 26% and 50%.
Escamilla et al. 2009)
ANN, PSO Feed per tooth, cutting speed, depth of cut
Milling The results indicate that a system where neura network is used to model and predict process outputs andPSO is used to obtain optimum process param can be successfully applied to multi-objective optimization of titanium’s machining process
’l-Mounayri et 1. (2003)
PSO Feed per tooth, cutting speed, depth of cut
Milling The final model is able to predict the output (l Ra) of the system for new inputs (i.e. Feed rat depth of cut and spindle speed) with over 79°/ confidence.)
'ain et al. 2009)
ANN Feed per tooth, cutting speed, depth of cut
Milling The ANN technique has decreased the minim value of the experimental sample data by aboi 0.0126(j,m, or 5.33%.
Milling Statistically all three models predicted roughn with satisfactory goodness of fit, the test performance of ANFIS was better than ANN MRA.
amanta, B. 2009)
ANFIS, GA Spindle speed, feed rate, and depth of cut
Milling The results show the effectiveness of the prop approach in modelling the Ra.
Uiarathi Raja nd Baskar 2010)
PSO Cutting speed, feed, depth of cut,
Turning It is observed that the machining time and Ra on PSO are nearly same as that of the values obtained based on confirmation experiments; it is found that PSO is capable of selecting appropriate machining parameters for turning operation.
rakasvudhisam t al. (2009)
SupportVectorMachine(SVM),PSO
Feed rate, spindle speed, and depth of cut
Milling The cooperation between both techniques can achieve the desired Ra and also maximize productivity simultaneously.
Turning HPSO can be taken into account as a useful ai powerful technique for optimizing machining problems.
iao et al. 2008)
GeneticSimulatedAnnealing(GSA)
Feed rate, cutting speed and depth of cut
Milling The result shows that optimum machining parameters are superior to the handbook value can effectively shorten machining time.
ayuti et al. 2011)
Taguchi Spindle speed, feed rate, depth of cut, lubrication mode, tool type, tool diameter and tool wear.
Grinding The results showed an improvement of 8.91 °/ the measured Ra.
alanikumar, K. 2006)
Taguchi Cutting speed, feed rate, and depth of cut.
Turning The experimental results suggest that the mos significant process parameter is feed rate folic by cutting speed. The study shows that the Ta method and Pareto ANOVA are suitable for optimizing the cutting parameters with the minimum number of trials.
'"anda et al. 2010)
Taguchi Cutting speed, feed rate and depth of cut
Turning Low surface finish was obtained at high cutting speed and low feed rate. Therefore tin' cost saving are significant especially is real in application, and yet reliable prediction is obta by conducting machining simulation using FE software Deform 3D. The results obtained for using the proposed simulation model were in good agreement with the experiments.
/lotorcu, A.R. 2010)
Taguchi Cutting speed, feed rate, depth of cut
Turning The obtained results indicate that the feed rate found out to be a dominant factor among controllable factors on the Ra, followed by de cut and tool’s nose radius. The second order regression model shows that the predicted val were very close to the experimental one for R
Lilickap et al. 2010)
RSM, GA Cutting speed, feed rate, and cutting environment
Drilling The predicted and measured values were quite close, which indicates that the developed moc be effectively used to predict the Ra. The give model could be utilized to select the level of drilling parameters. A noticeable saving in machining time and product cost can be obtaii using this model.
/lurthy andLajendran2010)
ANN Cutting speed, depth of cut and feed rate
Milling The results show that the highest cutting spee medium feed rate and medium depth of cut produces lowest Ra. This study provides the optimum cutting conditions for end milling oi aluminium 6063 under minimum quantity lubrication machining.
uisalam andJarayanan2010)
IGA Speed, feed, and depth of cut
Turning The proposed algorithm was compared with t conventional genetic algorithm (CGA), and w found that the proposed IGA is more effective previous approaches and applies the realistic machining problem more efficiently than does conventional genetic algorithm (CGA).
s.lam et al. 2008)
RSM Spindle speed, feed rate, and depth
Milling A very good performance of the RSM model, terms of agreement with experimental data, w achieved. It is observed that cutting speed has most significant influence on Ra followed by and depth of cut.
)ktem, H. 2009)
ANN, GA Spindle speed, feed rate, and depth
Milling GA improves the Ra value from 0.67 to 0.59 p with approximately 12% gain. Then, machining time has also decreased from 1.28^ 1.0316 min by about 20% reduction based on cutting parameters before and after optimizati process using the analytical formulas. The fin measurement experiment has been performed verify Ra value resulted from GA with that of material surface by 3.278% error.
Lazfar and 'adeh (2009 )
NN, GA Spindle speed, feed rate, and depth
Milling Genetically optimized neural network system (GONNS) is proposed for the selection of the optimal cutting conditions from the experimei data when an analytical model is not available GONNS uses back-propagation (BP) type NN represent the input and output relations of the considered system. The GA obtains the optim operational conditions through using the NNs From this, it can be clearly seen that a good agreement is observed between the predicted and the experimental measurements.
lossain et al. 2008)
ANN Cutting speed, feed, and axial depth of cut.
Milling A very good predicting performance of the n< network, in terms of concurrence with experir data was attained. The model can be used for analysis and prediction for the complex relatk between cutting conditions and the Ra in meta cutting operations and for the optimization of for efficient and economic production.
/Tanna and alodkar (2008)
Taguchi Cutting speed, feed rate and depth of cut
Turning The developed optimality condition affects th economics of machining conditions. The grap representations also help to understand and an the effects of various input constraints at the optimum point and their significant influences production cost. The analysis can propose an effective methodology in advance for proper of machining parameters in practice, which m reduce the cost of unit production.
laq et al. 2008)
Taguchi Cutting speed, feed and point angle
Drilling Experimental results have shown that the resp in drilling process can be improved effectiveb through the new approach.
'hang et al. 2007)
Taguchi Feed rate, spindle speed and depth of cut
Milling An orthogonal array of Lg(34) was used; ANC analyses were carried out to identify the signi factors affecting Ra, and the optimal cutting combination was determined 1 seeking the best Ra (response) and signal-to-n ratio. Finally, confirmation tests verified that Taguchi design was successful in optimizing milling parameters for Ra.
Table 2.3: Previous researches in optimizing process parameters of Ra for modem machining
Author/Year Techniques Cutting condition Process Results
'ain et al. 2010c)
GA, SA Water pressure, abrasive flow rate, jet traverse rate, diameter of focusing nozzle
AWJ GA minimize the i?„by 27% and 41% and 28% and 42%.
Colahan and Qiajavi (2009)
SA Water pressure, abrasive flow rate, jet traverse rate, diameter of focusing nozzle
AWJ Computational results show that the propos solution procedure is reasonably effective.
aha et al. 2008)
Back-propagationneuralnetwork
Pulse on-time, pulse off- time, peak current, and capacitance
Wire electrodischarge machining (WEDM)
4-11-2 network architecture has been founc the optimal one, which can predict cutting and Ra with 3.29% overall mean prediction
Lao et al. 2010)
ABC, Harmony Search (HS), PSO
Amplitude of ultrasonic vibration, frequency of ultrasonic vibration, mean diameter of abrasive particles, volumetric concentration of abrasive particles, and static feed force.
Ultrasonicmachining(USM).
The results of the presented algorithms are compared with the previously published re obtained by using genetic algorithm (GA).
j u o et al. 2006)
ANN Beam angle, movement, speed and laser power
3D Laser cutting The ANN is very successful for optimizing parameters, predicting cutting results and deducing new cutting information.
4aji and ratihar (2010)
RegressionAnalysis,GA
Peak current, pulse-on- time and pulse-duty-factor
Electric discharge machining (EDM)
More or less 10% deviations in prediction responses had been reported for both of the the test cases.
asam et al. 2010)
Taguchi,GA
Ignition pulse current, Short pulse duration,Time between two pulses,Servo speed, Servo reference voltage, Injection pressure, Wire speed and Wire tension
WEDM Optimum values of control parameters for selected range and workpiece material are obtained.
omashekhar t al. (2009)
GA Gap voltage, capacitance and feed rate.
Micro Wire Electric Discharge Machining (|j,- WEDM)
Experiments were planned and conducted i DoE techniques. ANOVA was performed t out the significance of each factor. Regress models were developed for the experiment, results of Ra and overcut of the micro slots produced on aluminium. Then Genetic Algorithm (GA) was employed to detemiin values of optimal process parameters for th desired output value of micro wire electric discharge machining characteristics.
in et al. 2009)
Taguchi Machining polarity, peak current, auxiliary current with high voltage, pulse duration, no load voltage, and servo reference voltage
EDM Experimental results showed EDM is a fea process to shape conductive ceramics, and relationships between machining character] and parameters were examined. Moreover, machining parameter optimal combination in machining conductive ceramics via EDN were also determined.
'hen et al. 2010)
BPNN, SA Pulse on-time, pulse off- time, peak current, and capacitance
WEDM The results of proposed algorithm and confirmation experiments are show that the BPNN/SAA method is effective tool for th optimization of WEDM process parameters
Luo and Chang 2007)
Taguchi Rotational speed, feed, and depth of cut
Laser-assisted machining (LAM)
The findings indicate that feed, with a contribution percentage as high as 37.26%, the most dominant effect on LAM system performance, followed by rotational speed depth of cut. LAM’s most important advant its ability to produce much better workpiec surface quality than does conventional machining, together with larger material re rates (MRR).
LamakrishnanndLarunamoorthy2006)
Taguchi Pulse on time, wire tension, delay time, wire feed speed, and ignition current intensity.
WEDM Multi response S/N (MRSN) ratio was app measure the performance characteristics deviating from the actual value. Analysis o variance (ANOVA) is employed to i dent if) level of importance of the machining paran
on the multiple performance characteristics considered. Finally experimental confimiat was carried out to identify the effectiveness this proposed method. A good improvemer obtained.
'hen et al. 2010)
Taguchi Peak current, pulse-on- time and pulse-duty-factor
EDM The experimental results show that peak cu and pulse duration significantly affected M and SR, and the adhesive conductive mater was the significant parameter correlated wi EWR. In addition, the optimal combination levels of machining parameters were also determined from the response graph of sigr noise ratios for each level of machining parameters.
ahoo et al. 2009)
RSM Pulse current, pulse on time and pulse off time
EDM The roughness models, as well as the significance of the machining parameters, 1 been validated with analysis of variance. A attempt has also been made to obtain optim machining conditions using response optimisation technique.
Lanagarajan et 1. (2008)
Nondominatedsortinggeneticalgorithm(NSGA-II)
Pulse current, pulse on time, electrode rotation and flushing pressure
EDM The experimental results are used to develc statistical models based on second order polynomial equations for the different proc characteristics. Non-dominated solution se1 been obtained and reported.
/larkopoulos et 1. (2006)
ANN Pulse current and the pulse-on time
EDM A feed-forward artificial ANN trained wit Levenberg-Marquardt algorithm was finall selected. The proposed neural network take consideration the pulse current and the puls time as EDM process variables, for three different tool steels in order to determine tt center-line average (Ra) and the maximum of the profile (Rt) Ra parameters.
arkar et al. 2006)
ANN Pulse on time, pulse off time, peak current, wire tension, dielectric flow rate and servo reference voltage
WEDM The model is capable of predicting the resp parameters as a function of six different co parameters. Experimental results demonstr that the machining model is suitable and th optimisation strategy satisfies practical requirements.
enthilkumar t al. (2010)
NSGA - II Electrolyte concentration, electrolyte flowrate, applied voltage, and tool feed rate.
Electrochemicalmachining
The non -dominated sorting genetic algorit (NSGA-II) tool was used to optimize the E process parameters to maximize MRR and minimize Ra. A non -dominated solution se been obtained and reported.
Lao and Pawar 2010)
ABC Pulse-on time, pulse-off time, peak current, and servo feed setting
WEDM ABC is applied to find the optimal combin< of process parameters with an objective of achieving maximum machining speed for a desired value of surface finish.
/lohammadi et Taguchi Power, time-off, voltage, Turning wire The variation of Ra and roundness with1. (2008) servo wire tension, wire electrical machining parameters was mathematically
speed, and rotational discharge modelled by using the regression analysisspeed machining method. The presented model is verified b)
(TWEDM) of verification tests.
37
2.6 Experimental data of case studies
In this section, the experimental data of case studies of end milling and AWJ,
research attempted by Mohruni (2008) and Caydas and Hascalik (2008) are being
referred respectively. The experimental design and results are discussed.
2.6.1 End milling machining
The experiments conducted were using a material workpiece annealed alpha-
beta titanium alloy or named as Ti-6A1-4V. The chemical composition of Ti-6A1-4V
includes A l 6.37%, V 3.89%, Fe 0.16%, C 0.002%, Mo <0.01%, Mn <0.01%,
Si<0.01% and balance value of Ti. The mechanical properties of Ti-6A1-4V are
shown in Table 2.4. There are three category of end milling machining that employed
in the study namely uncoated carbide (WC-Co), two TiAIN coated carbide tools
which consist of PVD-TiAIN coated carbide tool and PVD with enriched Al-content
TiAIN coated carbide tools, also named Supemitride coating (SNTR). The properties
for each cutting tools are shown in Table 2.5.
Table 2.4: Mechanical properties of Ti-6A1-4V
Mechanical properties
Tensile strength (MPa) 960-1270Yield strength (MPa) 820Elongation 5D (%) >8Reduction in area (%) >25Density (g/cm3) 4.42Modulus of elasticity tension (GPa) 100-130Hardness (Hv) 330-370Thermal conductivity (W/mK) 7
38
Table 2.5: Properties of the cutting tool used in the experiments
Tool type WC- Co TiAIN coated Supemitridecoated
Substrate(wt%)
WC 94 94 94
Co 6 6 6
PropertiesGrade K30 K30 K30
Grain size (jam) 0.5 0.5 0.5
Coating
Process - PVD-HIS PVD-HIS
Coating thickness Monolayer (3-4
|am)
Monolayer (1
8 |am )
Film composition (mol-%AIN)
- Approx. 54 Approx. 65-67
2.6.1.1 End milling experimental design
In end milling machining Ti-6A1-4V, the 23-factorial design used level -1,0
and +1 coding variables which based on the design of experiments (DOE). Table 2.6
shows the level of independent variables and coding identification. Two of the
variables are kept constant which is axial and depth of cut with value of 5mm and
2mm correspondingly. The machining experiments are completed on a CNC MAHO
700S machining centre in wet state. The specification of the CNC machine is given
in Table 2.7. A device named Taylor Hobson Surftronic +3 was used to record and
compute the minimum Ra values for each cutting tool type. A total of five
measurements were accomplished at the setting of the length of cut on the
workpiece.
39
Table 2.6: Levels of independent variables and coding identification
Level in coded form
Independent
Variables
Units -1.4142 -1 0 +1 +1.4142
Cutting
speed, v
m/min 124.53 130.00 144.22 160.00 167.03
Feed ra te ,/ mm/tooth 0.025 0.03 0.046 0.07 0.083
Radial rake
angle, y
o 6.2 7.0 9.5 13.0 14.8
Table 2.7: Specification of the CNC machine
Brand CNC Flexible Machining Cell
Model MAHO 700S 5 Axis
Electrical data (Motor) 3 x 300 V 50Hz
No. of axes 5
Tool capacity 60
Spindle speed 20-6300 rpm
Controller Philip 432
40
2.6.1.2 End milling experimental results
There are eight data sources from each of two levels DOE 2k full factorial,
four centre and twelve axial points are performed on the 24 experimental
assessments for each cutting tool type. From the experimental results, the lowest Ra
values for /?uncoated is 0.23 jam which was given by the minimal process parameters
of v = 167.03m/min,/ = 0.046mm/tooth and y = 9.5°. For /?TiAlN the lowest Ra
values is 0.232(j,m which obtained by v = 160m /m in,/= 0.03mm/tooth and y = 13°.
And lastly for /?SNtr the lowest Ra values is 0.190|am which also achieved by v =
160m/min, / = 0.03mm/tooth and y = 13°. The minimum and average Ra are
calculated and results are shown in Table 2.8.
41
Table 2.8: Ra values for real machining experiments
where y is the logarithmic value of the predictive (estimated) Ra.
Equation (3.9) can be extended to form a second-order polynomial regression
for surface roughness predicted equation and given as follows:
55
y = Ra = bo + bi V + bjP + b^h + b t\,d + b 5m + bn V~ + bjj P~ + b33 hr + b^ct + b 5 5 777“+ bnF^ + b i3^ + b i4F<i+ b\sVm + bi^Ph + bi_aPd + b25-Pw + b ^ h d + b 3 5 /? 777 +b45<iw (3.10)
As of the results of Caydas and Hascalik (2008), the final regression model
for surface roughness obtained is written as follows:
Ra = -5.07976+0.08169F +0.07912P - 0.34221 h - 0.08661 d - 0.34866m -0.00031V2 - 0.00012P2 + 0.10575h2 +0.00041 d2 +0.07590w2 -0.00008Fw -0.00009Pw +0.03089//w+0.00513Jw (3.11)
The predicted Ra results of AWJ Regression model are given in Table 3.7
Table 3.7: Predicted Ra values of AWJ Regression model (Zain et al, 2010c)
No Setting values of experimental process parameters Z?fl(nm)
V (m/min) P (MPa) h (mm) d (jam) m (g/s)
2 50 125 1 60 2 2.62915
4 50 175 2.5 90 0.5 4.00520
6 50 175 2.5 90 3.5 5.42532
8 50 250 4 120 2 7.69815
10 100 125 2.5 120 0.5 3.66819
12 100 125 2.5 120 3.5 5.55233
14 100 175 4 60 2 7.36548
16 100 250 1 90 0.5 7.96455
18 100 250 1 90 3.5 9.21330
20 150 125 4 90 2 4.98615
22 150 175 1 120 0.5 6.07837
24 150 175 1 120 3.5 7.79815
26 150 250 2.5 60 2 9.23448
Ra (minimum) 2.62915
Subsequently, (3.11) will be assigned as the objective function for optimization
solution of ABC.
3.5 ABC algorithm for optimization of process parameters
56
There are three important control parameters in ABC optimization algorithm,
which have been stated in section 2.3. The process flow of ABC algorithm is
illustrated in Figure 2.3. There are seven steps to optimize process parameters of end
milling and AWJ that will lead to minimum Ra values. The steps are discussed
below.
i. Selection of control parameter
ii. Evaluation of the nectar quantity in every food source
iii. Probabilities determination using the nectar quantity
iv. Compute the number of onlookers bees to be sent to the food sources
V . Compute the fitness of each onlooker bee
vi. Assess the most excellent solution
vii. Update the scout bee
Step 1: Selection of control parameter
The possible solution to the problem to be optimized is generally represented
by food source position. A set of food source position is produced randomly and the
values of control parameters (SN, L, M) of ABC algorithm are determined. The
number of food sources must be equal to the number of employed bees. The value of
each food source depends on the fitness value of the objective function given by
equation (3.5c) for end milling and equation (3.11) for AWJ. In Rao and Pawar
(2010), the results are not better than the results obtained using number of employed
bees of 5 and colony size is 16 (number of employed bees and onlooker bees). ABC
performs better with a smaller population size and the ideal population size depends
on the optimization goal (Aderhold, et al, 2010). The value of control parameters
selected is defined in Table 3.8.
57
Step 2: Evaluation of the nectar quantity in every food source
A new food source is determined by each of employed bees by moving them
to the food source within the neighbourhood and after that the amount of nectar is
evaluated. If the new food sources contain a higher amount of nectar, the employed
bees will forget the historical food sources and memorizes the new food sources.
Once the process of searching is completed, the employed bees will come back to
their hive and share the information (the food source position) with onlooker bees by
performing a waggle dance on the dance area. The value of each food source depends
on the fitness value of the objective function given by equation (3.5c) for end milling
and equation (3.11) for AWJ.
Step 3: Probabilities determination using the nectar quantity
The prospect of the food source is preferred by onlooker bee increases as the
nectar amount food source increased. The chance with of the food source located at
0i is selected by an onlooker bee can be calculated by using equation (2.1) and
equation (2.2).
Step 4: Compute the number of onlookers bees to be sent to the food sources
As mentioned in the previous step, the majority of onlookers bees determine a
food source area with a probability based on higher amounts of nectar. The number
of onlookers bees that send to the food sources is by multiplying the probability
values, Pi in step 3 with the total number of onlookers bees. This repetitive process is
stop once all the onlooker bees are distributed onto high nectar amounts of food
sources that have been decided by employed bees.
58
Step 5: Compute the fitness of each onlooker bee
The information of the particular prospect food source will be shared in the
hives by doing an attention-grabbing waggle dance. This waggle dance will be
observed by unemployed bees which later will hunt to make use of the food source.
Based on the waggle dance, the onlooker bee take off to the food sources located at
0i. The position of selected neighbourhood food sources is calculated in equation
(3.12):
0i(c+l) = 0i(c) + 0 (0i (c) - 0k (c)) (3.12)
where c is number of generation. In order to find out food source with more nectar
around 0i, <f>(c) is a randomly produced. A randomly produced index k is dissimilar
from i. The difference of the equivalent parts of 0i(c) and 0k(c) gives the value of
(j>{c). If the nectar amount Fi (c + 1) at 0i (c + 1) is higher than at 0i (c), then the bees
go to the hive and share information with others and the position 0i (c) of the food
source is changed to 0i (c + 1) otherwise 0i (c) is kept as it is. If the position 0i of the
food source i cannot be improved through the predetermined number of trials, then
that food source 0i is abandoned by its employed bee and then the bee becomes a
scout. The scout starts searching new food source, and after finding the new source,
the new position is accepted as 0i.
Step 6: Assess the most excellent solution
In each food source the most excellent position of onlooker bee is identified.
In each generation, the global best of the honeybee swarm in possibly will replace
the global best at preceding generation if it has improved fitness value.
59
Step 7: Update the scout be
The employed solution of employed bees will be compared to the scout
solution of the scout bees. Employed solution will replace the scout solution if it has
improved solution. If not, employed solution is shifted to the next generation with
no modification.
3.5.1 Justification of ABC control parameter
Based on the control parameters used by previous researchers that have been
summarized in Table 2.1, the three control parameters to develop the ABC
optimization algorithm for optimizing process parameters in end milling and AWJ
machining is justified in Table 3.8:
Table 3.8: Justification of ABC control parameters
Control parameters Justification
the number of colony size (SN) 16
the predefined value of limit (L) 100
maximum loop for searching food (M) 150
3.5.2 Steps for determination of the optimal process parameters
The main intention of the optimization process in this research is to find out
the optimal values of the process parameters that lead to the lowest value of Ra.
Therefore, the Regression models in (3.5c) and (3.11) will be proposed to be the
fitness function of the optimization solution for end milling and AWJ respectively.
The minimization of the fitness function values of equations (3.5c) and (3.11)
are subjected to the restrictions of the process parameters. The process parameters of
60
each machining are set by a range of values and initial points to present the
boundaries of the optimization solution.
In end milling, there are three process parameters which are the cutting speed
(v), feed rate if) and radial rake angle (y). The best possible value of feed rate if)
must be in the range of,
/m m < /< /m a x (3.13)
where /m,n is the minimum feed rate and /max is the maximum feed rate.
The cutting speed (v) must meet the range of equation (3.14),
Vmin — V ^ Vmax (3-14)
where vm]n is the minimum cutting speed and vmax is the maximum cutting speed.
The upper bound and the lower bound of radial rake angle must be in the range of,
Y m m < Y < Y m a x (3.15)
where is the minimum y min radial rake angle and is y max the maximum radial rake
angle.
For AWJ, there are five process parameters which are traverse cutting speed
rate (m). The minimum cutting speed ( V) value must be in the range determined by
minimum and maximum values of the cutting speed of AWJ.
Vmm < V < Vmax (3.16)
Where is the minimum cutting speed and Vmax is the maximum cutting speed.
The waterjet pressure (P), must meet the range of equation of 3.17.
P mill — P — P max (3.17)
where P mm is the minimum waterjet pressure and P max is the maximum waterjet
pressure.
The machining standoff distance range is given by equation (3.18),
h m ill — h < h max (3.18)
61
where h m]n is the minimum standoff distance and h max is the maximum standoff
distance.
The upper bound and lower bound of abrasive grit size (d) must be in the range of,
^n iin ^ d ̂ d max ( 3 - 1 9 )
where d mm is the minimum abrasive grit size and d max is the maximum grit size.
The upper bound and lower bound of abrasive flow rate are given in equation (3.20),
M mm — fx JTI max (3.20)
where m min is the minimum abrasive flow rate and m max is the maximum abrasive flow rate.
3.6 Validation and evaluation of ABC results
After the minimum Ra value is estimated based on the ABC optimization
algorithms, the results later will be validated and evaluated. The minimum Ra value
that estimated by ABC is optimistically a lesser amount of experimental, Regression
modelling, SA optimization and GA optimization. The equations in (3.13) to (3.15)
for end milling and equations (3.16) to (3.20) for AWJ that achieved at the last
iteration of ABC are preferred to be the range of values of the process parameters.
The values of the process parameters will lead to the minimal Ra value.
3.7 ABC optimization performances
ABC has been used recently by researchers to find optimal solution in
numeric optimizations problems. Some of the advantages of ABC algorithm include
strong robustness, fast convergence and high flexibility and employed less control
parameters. The performance of ABC is competitive with other algorithm such as
GA, PSO, DE and EA on many benchmark functions. The performance of ABC have
62
been assessed by Karaboga and Basturk (2008) to evaluate the performance of ABC
in optimizing the numerical benchmark function such as Schaffer, Sphere, Griewank,
Rastrigin and Rosenbrock. The results of ABC later is compared with differential
evaluation (DE), PSO, and evolutionary algorithms (EA). Table 3.9 below shows the
parameter values used in the experiments for each soft computing technique.
Table 3.9: Parameters used in the numerical benchmark function
experiments (Karaboga and Basturk, 2008)
Technique Parameters
1. DE i. Population size = 50ii. Crossover factor (CF) = 0.8iii. Scaling factor if) = 0.5
2. PSO i. Population size = 20ii. Inertia weight, (nr) = 1.0 —> 0.7iii. Lower bound of the random velocity rule weight, (cpmin) = 0iv. Upper bound of the random velocity rule weight, (cpmax) = 2.0
3. EA i. Population size =100ii. Crossover ratQ,p& =1.0iii. Mutation rate pm = 0.3iv. Mutation variance am = 0.01v. Elite size, n =10
4. ABC i. Colony size =100ii. Onlooker number, no = 50%iii. Employed bee number, no = 50%iv. Scout number, ns = 1v. Limit = «ex Dimension of the problem (D)
The experiments was repeated 30 times with different random seeds, and the
average function values of the best solutions found have been recorded as in Table
63
For Schaffer and Sphere numerical function, DE, EA and ABC could find the
optimum value but not PSO. For Griewank and Rastrigin function, DE and ABC
showed equal performance and found the optimum value but PSO and EA showed
the poorest results. For the Rosenbrock function, ABC gives the best optimum results
compared to the other four soft computing techniques.
The ABC algorithm is tested further to analyze its behavior under different
colony size which ranges from 10 to 100 and also the limit values for about 1000
iterations. From the results, as the population increases the algorithm produce better
results. As shown in Figure 3.2 below for Rosenbrock function, the optimum value
with 10 colony achieved is 9.2173464. The optimum value decrease to 0.159732
after the colony size increased to 50. The colony size is then increased to 100 and the
optimum value achieved for the function is 0.0852967. According to Karaboga and
Basturk, after a sufficient value for colony size, any increment in the value does not
improve the performance of the ABC algorithm.
Cyde
Figure 3.2 Evolution of mean best values for Rosenbrock function (Karaboga
and Basturk, 2008)
64
From the experiments, it shows that the performance of ABC is very good in
terms of the local and global optimization due to the stochastic selection schemes
employed and the neighbor production mechanism used (Karaboga and Basturk,
2008). They conclude that ABC is simple to use and robust optimization algorithm
and can be used efficiently in the optimization of multimodal and multi-variable
problems.
In this research, ABC was chosen as the optimization technique because of
some advantages it has compared to other optimization technique. For example, ABC
has less control parameters compared to other optimization techniques. ABC also
does not need a crossover operator like GA or DE. A simple operation based on
taking the difference of randomly determined parts of the parent and a randomly
chosen solution from the population is applied in ABC to produce a new solution
from its parent. This process increases the convergence speed of search into a local
minimum. In GA, DE and PSO the best solution found so far is always kept in the
population and it can be used for producing new solutions in the case of DE and GA,
new velocities in the case of PSO. However, in ABC, the best solution discovered so
far is not always held in the population since it might be replaced with a randomly
produced solution by a scout. For that reason, ABC produces superior results
compared to other optimization technique.
65
This chapter has discussed the methodology of the research. The process flow
and steps of searching the combination optimum process parameters that will lead to
minimum Ra are shown and further explained. The process flows consists of four
main phases. The first phases are the assessment of real experiments data based on
work by Mohruni (2008) for end milling and Caydas and Hascalik (2008) for AWJ.
In the second phase, the regression model is built and the best equation that gave
minimum Ra values will be selected and chosen as ABC fitness function. For the
third phase, ABC optimization algorithm will be used to find the best combination of
process parameters that give a minimum Ra value. Finally, the results will be
evaluated and compared with experimental, regression modelling, SA optimization
and GA optimization.
3.8 Summary
CHAPTER 4
ABC OPTIMIZATION
4.1 Introduction
The objective of this chapter is to describe the ABC optimization execution
and presents the experimental results of the study. In the previous chapter, the
methodology of the research has been discussed.
In this chapter, experiments for end milling and AWJ machining have been
conducted to find the minimum Ra value and the set of optimal process parameters
using ABC algorithm. There are four main phases in ABC optimization. These four
phases are discussed in details in the next section.
67
The execution process of ABC algorithm in optimizing process parameters of
Ra value in end milling and AWJ machining are divided into four main phases:
i. Initial phase
ii. Employed-bee phase
iii. Onlooker-bee phase
iv. Scout-bee phase.
The program is developed and run using MATLAB 2010 software. Figure 4.1 shows
the interface of the program. There are two objective functions that were used in
order to optimize the process parameters and find minimum Ra value in both end
milling and AWJ machining. For end milling, the objective function is:
Where x\ is the traverse cutting speed (V) in mm/min, xi is the waterjet pressure (P)
in MPa, X3 is the standoff distance (h) in mm, X4 is the abrasive grit size (d) in jam
and lastly, X5 the abrasive flow rate (m) in g/s.
4.2 ABC optimization execution
68
Q Artificial Bee Algorithm Program
P r o c e s s P a r a m e t e r s O p t i m i z a t i o n o f S u r f a c e R o u g h n e s s i n E n d M i l l i n g a n d A b r a s i v e W a t e r j e t M a c h i n i n g
U s i n g A r t i f i c i a l B e e C o l o n y A l g o r i t h m
R r * = 0 . 2 3 7 — ( 0 . 0 0 1 7 5 x x l > + ( S . 6 9 3 x x 2 > + ( 0 . 0 0 1 5 9 x x 3 >
where p is the parameter pair index and determined randomly.
75
The next step is evaluating each parameter value inside the Solution. If the
value is below the LT then the program set the value to LT, and if the value is above
the UT then the program sets the value to UT. And then the program calculates the
objective value and the fitness value for this Solution.
i. If the fitness value of Solution is higher than the previous Fitness value
(before any value inside that parameters pair is changed), then replace the
parameters pair with the Solution. Reset the corresponding Trial value to
zero
ii. If the fitness value of Solution is lower than the previous Fitness value
(before any value inside that parameters pair is changed), then increment
the corresponding Trial value.
This process is repeated until the iteration equal to the number of food source.
When iteration is done, the program calculates the probabilities value by:
Probability (/) = Fitness (/) / sum(Fitness) (5.4)
In other words, the probability is the fitness of fitness value. This probability
value will be evaluated later in onlooker-bee phase.
4.5 Onlooker-bee Phase
In the Onlooker-bee phase, the mutation of value as in Employed-bee phase
above was repeated, but the difference is the control variables that determine what
condition the iteration should stop. The iteration will be stop if a control variable,
named T, and is equal to the number of food sources. The value of T is incremented
only if a value in probability array is higher than a random number.
76
At first time before the iteration run, T is initiated to 0. Then each probability
value is evaluated. Once the probability value P(/) (from Employed-bee phase) is
higher than a value (generated randomly), it is time to do mutation as in Employed-
bee phase and also increment T value. But if Probability P(/) value is lower the
random value, the evaluation is as follows:
i. next Probability value P(i+1), if i not equal the number of food sources
(indicates last index in Probability array)
ii. first Probability value P(z'), if i equal to the number of food source. If T is
equal to the number of food source then iteration is stopped. After the
iteration is stopped, the program will find the best of parameters value and
store in the matrix GV and GP.
4.6 Scout-bee Phase
This phase is the last step of ABC algorithm execution. In this phase, the
maximum value inside trial array was discovered. If it is bigger than limit, then the
program do initial step again for related parameter. For example, if the program find
trial (x) is bigger than limit (this means the parameter P(x) cannot be optimized
anymore) then the program will generate a new parameters pair P(£), and replace
P(x) with P(£) in food matrix, recalculate again objective and fitness value.
4.7 Experiment 1 - ABC optimization parameters for End Milling
For the experiments, a colony size of 10, 20, 50 and 100 have been tested in
the program to find the most minimum Ra value. The combination of control
variables with the bee colony size of 10 are shown in Table 4.1.
77
Table 4.1: Control variables combination with limit of 30
Colony Size Max cycles per run Limit (abandoned
food)
10 10 30
10 20 30
10 50 30
10 100 30
4.7.1 Colony size of 10 and limit of 30
The experiments initialize the control variables with a bee colony size of 10,
max cycles per run are 10 and limit is set to 30. The value of bee colony size and
max cycles per run will be increased to observe whether the minimum Ra value will
be improved.
When the program is executed, the results are depicted in Figure 4.2. The first
combination of control variables gives a minimum Ra value of 1.1719|am in the first
78
^ Artificial Bee Algorithm Program «=>'
P r o c e s s P a r a m e t e r s O p t i m i z a t i o n of S u r f a c e R o u g h n e s s i n E n d M i l l i n g a n d A b r a s i v e W a t e r j e t M a c h i n i n g
U s i n g A r t i f i c i a l B g g C o l o n y A l g o r i t h m
R a = 0.23-7 — (0.00 175 X x l ) + - (S.693 x x2) -+- (0.00159 X i3 )
Function for: End Milling
Colony S ize :
Number of Run:
Max Cycles per Run
Limit (abandoned food)
Parameters Range------
X1 X2 X3 X4 X5
Uppest Threshold:
167.03 1 0.083 14.B 120 , J }
________________Lowest Threshold :
124.53 0.025 6.2 | 60 || 0.5
All best values/run
run Num.Cycles , MinValue XI
1 10 j. 167.0301 >
2 10 0.4832 146.321:
3 10 0.2645 136.589: =
4 10 0.2080 146.3671
5 10 0.1786 167.0301
6 10 0.1932 155.552
7 10 0.1737 167.0301 -
1 1 nr j
I Sflow OlatlReady
0.9
0.8
0.7
0 . 6
0.4
0.3
0.2
0 1
Min Value, Fitnes & Mean of Fitness/Cycle
Best fitness
tMean fitness
■ Best Fitness- Mean Fitness- Min.Value
Min Ra value
3 4 5 6 7 Cycle
9 10
Figure 4.2 Results of 10 max cycles per run with limit of 30
From the results of the first control variables combinations, the set values of
process parameters that lead to the minimum values of Ra value are 167.0300 m/min
for cutting speed, 0.0250 mm/tooth for feed and 6.200 0 for radial rake angle. The
best fitness value is 0.8533. The minimum Ra value is achieved at cycle six as shown
in Table 4.2.
79
Table 4.2: The best value returned from 10 max cycles with limit of 30
Cycle Min Ra XI (v) X2 if) X3(y) Best
fitness
Mean
fitness
1 0.2232 167.0300 0.0307 7.5555 0.8175 0.6864
2 0.2230 167.0300 0.0307 7.4056 0.8177 0.7005
3 0.2230 167.0300 0.0307 7.4056 0.8177 0.7018
4 0.1738 167.0300 0.0250 7.4056 0.8519 0.7098
5 0.1738 167.0300 0.0250 7.4056 0.8519 0.7113
6 0.1719 167.0300 0.0250 6.2000 0.8533 0.7149
7 0.1719 167.0300 0.0250 6.2000 0.8533 0.7409
8 0.1719 167.0300 0.0250 6.2000 0.8533 0.7415
9 0.1719 167.0300 0.0250 6.2000 0.8533 0.7480
10 0.1719 167.0300 0.0250 6.2000 0.8533 0.7506
The second combination of control variables is tested where the number of max cycle
per run is increased to 20. The results are shown in the Figure 4.3. The minimum Ra
value achieved is 0.1719(j,m.
80
Artificial Bee Algorithm Progr; l— -i.
P r o c e s s P a r a m e t e r s O p t i m i z a t i o n of S u r f a c e R o u g h n e s s i n E n d M i l l i n g a n d A b r a s i v e W a t e r j e t M a c h i n i n g
U s i n g A r t i f i c i a l B e e C o l o n y A l g o r i t h m
R a = 0 237 — (0.00175 x icl) -+- (3 693 x x2) ■+■ (0.00 159 x tc3>
Function fo r: End Milling
Colony S ize :
Number of Run:
Max Cycles per Run:
Limit (abandoned food):
j— Parameters Range------
X1 X2 X3 X4 X5
Uppest Threshold
167.03 0.083 14 c 3.5
Lowest Threshold
124.53 0.025 6.2
All best valuesfrun
run Num.Cycles MinValue X I
1 20 0.1719 167.030( >
2 20 0.2094 148.21 S«
3 20 0.1914 160 556;
4 20 0.1719 167.0301
5 20 0.1843 159.918i
6 20 0.1741 167.030(7 r>n n i tjm ̂C7 mnr
- l i" Z] 1
Ready
Min Value, Fitnes A Mean of Fitness/Cycle
Figure 4.3 Results of 20 max cycles per run with limit of 30
In Table 4.3, the results of the second control variables combinations also
gives the best fitness value of 0.8533 at cycle six and the set values of process
parameters that lead to the minimum Ra value are 167.0300 m/min for cutting speed,
0.0250 mm/tooth for feed and 6.200 0 for radial rake angle.
81
Table 4.3: The best value returned from 20 max cycles per run with limit of 30
Next, the value of max cycles per run is increased to 50. The results are
shown in Figure 4.4 where the minimum Ra value achieved is 0.1719|am in the first
82
S3 Artificial Bee Algorithm Progn ’ 'I---
P r o c e s s P a r a m e t e r s O p t i m i z a t i o n of S u r f a c e R o u g h n e s s in E n d M i l l i n g a n d A b r a s i v e W a t e r j e t M a c h i n i n g
U s i n g A r t i f i c i a l B e e C o l o n y A l g o r i t h m
R a = 0.237 — (0.00175 x x l ) -+- (3.693 x x2) (0.00159 X x3>
Function fo r : End Milling
Colony S ize :
Number of Run:
Max Cycles per Run
Limit (abandoned food):
I— Parameters Range------
X1 X2 X3
50
X4 X5
Uppest Threshold:
167.03 0.083 14.8 120 3.5
Lowest Threshold:
124.53 0 025 ' 6 ;
All best valuesAun
run Num.Cycles MinValue X I
1 50 0.1719 167.Q30( >
2 50 0.1719 167.Q3DI
3 50 0.1719 167.03014 50 0.1719 167.Q3DE
5 50 0.1730 166.3781
6 50 0.1719 167.030(7 m CM 7-1 0 ̂e? n n̂r
v III _1 t
| S to w Detail |
Ready
Min Value, Fitnes & Mean of Fitness/Cycle
Figure 4.4 Results of 50 max cycles per run with limit of 30
In Table 4.4, the results of the third control variables combinations also gives
the best fitness value of 0.8533 at cycle six and the set values of process parameters
that lead to the minimum Ra value are 167.0300 m/min for cutting speed, 0.0250
mm/tooth for feed and 6.200 0 for radial rake angle.
83
Table 4.4: The best value returned from 50 max cycles per run with limit of 30
Finally, the number of max cycles per run is increased to 100. The results are
shown in Figure 4.5 where the minimum Ra value achieved is 0.1719|am in all 10
runs.
Artificial Bee Algorithm Progr; _____ 'P r o c e s s P a r a m e t e r s O p t i m i z a t i o n of S u r f a c e R o u g h n e s s i n E n d M i l l i n g a n d A b r a s i v e W a t e r j e t M a c h i n i n g
U s i n g A r t i f i c i a l B e e C o l o n y A l g o r i t h m
R a = 0.237 — (0.00175 x tc 1} -4- (3 693 x x2) •+■ (0.00159 x x3>
10
Function fo r: End Milling
Colony S ize :
Number of Run:
Max Cycles per Run:
Limit (abandoned food):
I— Parameters Range------
X1 X2 X3
30PUN
X4 X5
Uppest Threshold:
167 03 0.083 14 8 3.5
Lowest Threshold:
124.53 0.025 6 2 \
All best valuesAun
run Num.Cycles MinValue X I
1 100 0.1719 167.030( *
2 100 0.1719 167.0301
3 100 0.1719 167.0301
4 100 0.1719 167.030E
5 100 0.1719 167.030(
6 100 0.1719 167.030(7 inn fH71Q a err mnr
< | m Z l r
i 1 i
Ready
Min Value, Fitnes & Mean of Fitness/Cycle
Cycle
Figure 4.5 Results of 100 max cycles per run with limit of 30
The results of the last control variables combinations also gives the best
fitness value of 0.8533 at cycle six and the set values of process parameters that lead
to the minimum Ra value are 167.0300 m/min for cutting speed, 0.0250 mm/tooth for
feed and 6.200 0 for radial rake angle. This is shown in Table 4.5.
86
Table 4.5: The best value returned from 100 max cycles per run with limit of 30
The number of bee colony size is increased to 20 with limit of 60 to
investigate whether it will give superior results from the previous size of bee colony.
The combination of control variables are given in Table 4.6 below.
Table 4.6: Control variables combination with limit of 60
Colony Size Max cycles per
run
Limit (abandoned
food)
20 10 60
20 20 60
20 50 60
20 100 60
When the program is executed using the first control variables combination,
the minimum Ra value achieved is 1.725jam. This is the minimum Ra value from the
10 runs as shown in the Figure 4.6.
91
P 3 Artificial Bee Algorithm Program
P r o c e s s P a r a m e t e r s O p t i m i z a t i o n of S u r f a c e R o u g h n e s s in E n d M i l l i n g a n d A b r a s i v e W a t e r j e t M a c h i n i n g
U s i n g A r t i f i c i a l B e e C o l o n y A l g o r i t h m
R a = 0.237 — (0.00175 x x l ) -+- (3.693 x x2) -+- (0.00159 x x3)
Function fo r : End Milling
Colony S ize : 20
Number of Run: 10
Max Cycles per Run :— RUN
Limit (abandoned food): 60
I— Parameters Range------
X1 X2 X3 X4 X5
Uppest Threshold:
167.03 0.083 I 14.8 120 || 3.5
Lowest Threshold:
| 124.53 |f 0.025 | 6.2 |
All best valuesAun
run Num. Cycles MinValue X I* * ■ . M
5 10 0.1816 167.030(
6 10 Q.1725 167.030(
7 10 0.2036 155.623: —
8 10 0.1792 163.588? =9 10 0.1781 167.0301
10 10 0.1994 151.411' -
< III □ 1
|Sftow Detail |
Ready
10
Min Value, Fitnes & Mean of Fitness/Cycle
Cycle
Figure 4.6 Results of 10 max cycles per run with limit of 60
From Table 4.7, the minimum Ra value achieved is 0.1725(j,m at cycle 10.
The best fitness value is 0.8529 and the set values of process parameters that lead to
the minimum Ra value are 167.0300 m/min for cutting speed, 0.0250 mm/tooth for
feed and 6.5963 0 for radial rake angle.
92
Table 4.7: The best value returned from 10 max cycles per run with limit of 60
The max per cycle per run is increased to 20 and the results are better
compared to the previous control variables combination. Figure 4.7 shows that the
minimum Ra value was achieved at the seventh runs.
93
r a Artificial Bee Algorithm Progr;
P r o c e s s P a r a m e t e r s O p t i m i z a t i o n of S u r f a c e R o u g h n e s s i n E n d M i l l i n g a n d A b r a s i v e W a t e r j e t M a c h i n i n g
U s i n g A r t i f i c i a l B e e C o l o n y A l g o r i t h m
R a = 0 237 — (0.00 175 x x l ) -+- (3 693 x x2) -+- (0.00 159 x x3>
20
Function fo r: End Milling
Colony S ize :
Number of Run:
Max Cycles per Run:
Limit (abandoned food):
j— Parameters Range------
X1 X2 X3 X4 X5
Uppest Threshold
167.03 0.083 14 8 3.5
124.53 0.025 6.2
Lowest Threshold
I 0 5All best valuesAun
run Num.Cycles MinValue X IAw u ■1 “■1 1 Jl .WW 1
5 20 0.1754 165.044:
6 20 0.1806 162.073J
7 20 □ .1719 167.030(
8 20 0.1719 167.030t
9 20 0.1719 167.030(
10 20 0.1719 167.030( -< | It! 2 »
Ready
Min Value, Fitnes A Mean of Fitness/Cycle
C yc le
Figure 4.7 Results of 20 max cycles per run with limit of 60
From Table 4.8 below, the minimum Ra value is achieved at cycle 11 with the
best fitness value of 0.8533. The set values of process parameters that lead to the
minimum Ra value are 167.0300 m/min for cutting speed, 0.0250 mm/tooth for feed
and 6.200 0 for radial rake angle.
94
Table 4.8: The best value returned from 20 max cycles per run with limit of
The number of max cycles per run is then increased to 50 and the results are
shown in Figure 4.8. The minimum Ra value achieved is 0.1719|am at all 10 runs.
H Artificial Bee Algorithm Progn
P r o c e s s P a r a m e t e r s O p t i m i z a t i o n of S u r f a c e R o u g h n e s s i n E n d M i l l i n g a n d A b r a s i v e W a t e r j e t M a c h i n i n g
U s i n g A r t i f i c i a l B e e C o l o n y A l g o r i t h m
R a = 0.237 — (0.00175 x x l ) > (S.693 x x2) -+- (0.00159 X x3>
Function fo r:
Colony S ize :
Number of Run:
Max Cycles per Run :
Limit (abandoned food):
p— Parameters Range —
X1 X2
End Milling
X3 X4 X5
Uppest Threshold:
167.03 0.083 14.8 3.5
Lowest Threshold
124.53 0.025 6.2
All best valuesA'un
run Num.Cycle; MinValue X I
5 50 0.1719 167.030( +
6 50 0.1719 167.03Q(
7 50 0.1719 167.030(
8 50 0.1719 167 0301
9 50 0.1719 167.030(
10 50 0.1719 167.0301 -* 1 rer 1
Ready
Min Value, Fitnes & Mean of Fitness/Cycle
Figure 5.8 Results of 50 max cycles per run with limit of 60
In Table 4.9, the minimum Ra value is achieved at cycle 10 with the best
fitness value of 0.8533. The set values of process parameters that lead to the
minimum Ra value are 167.0300 m/min for cutting speed, 0.0250 mm/tooth for feed
and 6.200 0 for radial rake angle.
96
Table 4.9: The best value returned from 50 max cycles per run with limit of 60
Lastly for limit of 60, the max cycles per run is increased to 100. The results
are shown in the Figure 4.9 below. The minimum Ra value achieved is 0.1719|am at
all 10 runs.
Artific ia l Bee A lgorithm Progr<
P r o c e s s P a r a m e t e r s O p t i m i z a t i o n o f S u r f a c e R o u g h n e s s i n E n d M i l l i n g a n d A b r a s i v e W a t e r j e t M a c h i n i n g
U s i n g A r t i f i c i a l B e e C o l o n y A l g o r i t h m
Ra = 0.237 — (0.00175 x x l) -4- (3 693 x x2) + (0.00159 x tc3>
10
Function fo r: End Milling
Colony S iz e :
Number of R un:
Max Cycles per R un:
Limit (abandoned fo od):
I— Parameters Range--------
X1 X2 X3
PUN
X4 X5
Uppest Threshold:
167 03 0.083 14 8 3.5
124.53 0.025
Lowest Threshold:
1 60 I 05All best valuesAun
run N u m .C yc le s M in V a lu e X I
5 100 0.1719 167.030(*
6 100 □ .1719 167.030(
7 100 0.1719 167.030(
8 100 0.1719 167.030E T9 100 0.1719 167.0301
10 100 0.1719 167.030( -4 L Kl t
Ready
Min Value, Fitnes & Mean of Fitness/Cycle
Figure 4.9 Results of 100 max cycles per run with limit of 60
The best returned value of 100 max cycles per runs is achieved at the sixth
runs. In Table 4.10 below, the minimum Ra value of 0 .17 19|am is achieved at cycle
four with the best fitness value of 0.8532. The set values of process parameters that
lead to the minimum Ra value are 167.0300 m/min for cutting speed, 0.0250
mm/tooth for feed and 6.200 0 for radial rake angle.
99
Table 4.10: The best value returned from 100 max cycles per run with limit of 60
The bee colony size is increased to 50 with the limit of 150 to examine
whether it will improve the results from the bee colony size of 10 and 20. The control
variables combination for the experiments are shown in Table 4.11
Table 4.11: Control variables combination with limit of 150
4.7.3 Colony size of 50 and limit of 150
Colony Size Max cycles per
run
Limit (abandoned
food)
50 10 150
50 20 150
50 50 150
50 100 150
104
In Figure 4.10, the experimental results showed that the minimum Ra value achieved
is 0.1719|am in the sixth and tenth runs only.
H Artific ia l Bee A lgorithm Progn
P r o c e s s P a r a m e t e r s O p t i m i z a t i o n o f S u r f a c e R o u g h n e s s i n E n d M i l l i n g a n d A b r a s i v e W a t e r j e t M a c h i n i n g
U s i n g A r t i f i c i a l B e e C o l o n y A l g o r i t h m
Ra = 0.237 — (0.00 175 x x l) -»- (3.693 x x 2 ) ■+• (0.00 159 x x3)
Function fo r: End Milling
Colony S iz e :
Number of R un:
Max Cycles per R un:
Limit (abandoned fo od):
I— Parameters Range-------
X1 X2 X3
150
X4 X5
Uppest Threshold:
167 03 0 003 14 8 3.5
Lowest Threshold:
124.53 0.025 6 J || USAll best values/run
run N u m .C yc le ? M in V a lu e X I
1 10 0.1729 167.030( *2 10 0.1741 167.030E
3 10 0.1765 167.0301
4 10 0.1737 167.030E
5 10 0.1739 167.030(
6 10 0.1719 167.030(7 AH n 1 QCG A CQ oi ns
4 | m r
" js ih o w D e ta i l
Ready
0 9
0.8
0 7
3 0 5 a>04
0 3
02
0 1
Min Value, Fitnes & Mean of Fitness/Cycle
_l_________l_
Best fitness
Mean fitness
Min R„ value
5 6 Cycle
0
Figure 4.10 Results of 10 max cycles per run with limit of 150
From the results, the sixth runs give the best value returned from 10 max
cycles per run. The set values of process parameters that lead to the minimum Ra
value are 167.0300 m/min for cutting speed, 0.0250 mm/tooth for feed and 6.200 0
for radial rake angle. The minimum Ra value of 0.1719(_im is achieved at cycle 9 with
the best fitness value of 0.8533. This is shown in Table 4.12.
105
Table 4.12: The best value returned from 10 max cycles per run with limit of 150
The max cycle per run is increased to 20 and the results are shown in Figure
4.11. From the experiment results, the minimum Ra value achieved is 0.1719|am in
all runs except in the second, fourth and tenth run where the minimum Ra values
achieved are 0.1720(j,m, 0.1736(j,m and 0.1770(j,m respectively.
106
n Artificial Bee Algorithm Progr;
P r o c e s s P a r a m e t e r s O p t i m i z a t i o n o f S u r f a c e R o u g h n e s s i n E n d M i l l i n g a n d A b r a s i v e W a t e r j e t M a c h i n i n g
U s i n g A r t i f i c i a l B e e C o l o n y A l g o r i t h m
Ra = 0 237 — (0.00 175 X icl) + (3 693 x x2) ■+■ (0.00 159 X tc3>
Function fo r: End Milling
Colony S iz e :
Number of R un:
Max Cycles per R un:
Limit (abandoned fo od):
j— Parameters Range---------
X1 X2 X3 X4 X5
Uppest Threshold
167.03 0.083 iro 3.5
Lowest Threshold
124.53 0.025 6.2
All best valuesA'un
run N u m .Cycles MinValue X I
5 20 0.1719 167.030( *
6 20 0.1719 167.Q30(
7 2 0 1 0 .1 71 9 1 167.030( “
8 20 0.1719 167.0301 S9 20 0.1719 167.030C
10 20 0.1770 164.121 ( -
< | ff[ □ »
jjhovv Detailj
Ready
Min Value, Fitnes A Mean of Fitness/Cycle
Figure 4.11 Results of 20 max cycles per run with limit of 150
In Table 4.13 below, the best value returned from 20 max cycles is in the
seventh run. The minimum Ra value achieved is 0.1719|am in cycle 9 with the best
fitness of 0.8533. The set values of process parameters that lead to the minimum Ra
value are 167.0300 m/min for cutting speed, 0.0250 mm/tooth for feed and 6.200 0
for radial rake angle.
107
Table 4.13: The best value returned from 20 max cycles per run with limit of 150
Next the max cycle per run value is increased to 50 to test the performance of
ABC algorithm. The results of control variables 50 max per cycles with limit of 150
are shown in Figure 4.12 where the minimum Ra value achieved is 0.1719(_im in all
tenth runs.
108
2 Artificial Bee Algorithm Progr<
P r o c e s s P a r a m e t e r s O p t i m i z a t i o n o f S u r f a c e R o u g h n e s s i n E n d M i l l i n g a n d A b r a s i v e W a t e r j e t M a c h i n i n g
U s i n g A r t i f i c i a l B e e C o l o n y A l g o r i t h m
Ra = 0.237 — (0.00 175 X i l ) + (3 693 x + (0.00159 X x3>
Function fo r: End Milling
Colony S iz e :
Number of R un:
Max Cycles per R un:
Limit (abandoned fo od):
j— Parameters Range---------
X1 X2 X3 X4 X5
Uppest Threshold
167.03 0.083 3.5
Lowest Threshold
124.53 0.025 6.2
All best valuesfrun
run Sum .Cycles M in Value X I
5 50 0.1719 167.0300 *
6 501 a .1719 B 167.03007 50 0.1719 167.0300 —
8 50 0.1719 167.0300 m
9 50 0.1719 167.0300
10 50 0.1719 167.0300 -4 eii »
Ready
Min Value, Fitnes A Mean of Fitness/Cycle
Figure 4.12 Results of 50 max cycles per run with limit of 150
In Table 4.14 below, the results of the experiments showed that the minimum
Ra value of 1.1719|am is achieved at cycle three with the best fitness value of 0.8533.
The set values of process parameters that lead to the minimum Ra value are 167.0300
m/min for cutting speed, 0.0250 mm/tooth for feed and 6.200 0 for radial rake angle.
109
Table 4.14: The best value returned from 50 max cycles per run with limit of 150
For the final combination of bee colony size of 50, the max cycles per run
value is increased to 100 with the limit of 150. The results of the experiments are
shown in Figure 4.13 where the minimum Ra value achieved is 0.1719|am in all tenth
runs.
I l l
Q Artificial Bee Algorithm Progr;
P r o c e s s P a r a m e t e r s O p t i m i z a t i o n o f S u r f a c e R o u g h n e s s i n E n d M i l l i n g a n d A b r a s i v e W a t e r j e t M a c h i n i n g
U s i n g A r t i f i c i a l B e e C o l o n y A l g o r i t h m
Ra = 0.237 — (0.00 175 X icl) + (3 693 x ■+■ (0.00 159 x tc3>
Function fo r: End Milling
Colony S iz e :
Number of R un:
Max Cycles per R un:
Limit (abandoned fo od):
j— Parameters Range---------
X1 X2 X3
100
X4 X5
Uppest Threshold
167.03 0.083 120 3.5
124.53 1 ^ 0 2 5 | 6.2 ]|
Lowest Threshold
II 0 5All best valuesA'un
run N u m .Cycles MinValue X I
1 100 0.1719 167.030( >
2 100 0.1719 167.030E
3 100| □ .1719 167.030E
4 100 0.1719 167.0301
5 100 0.1719 167.030(
6 100 0.1719 167.030(7 ̂nn ni7iQ ̂C7 mnr
< | in “ 1 r
^ o w D e ta i l j
Ready
Min Value, Fitnes A Mean of Fitness/Cycle
Figure 4.13 Results of 100 max cycles per run with limit of 150
Table 4.15 below shows the minimum Ra value 0.1719|am is achieved in
cycle two with the best fitness of 0.8533. The set values of process parameters that
lead to the minimum Ra value are 167.0300 m/min for cutting speed, 0.0250
mm/tooth for feed and 6.200° for radial rake angle.
11 2
Table 4.15: The best value returned from 100 max cycles per run with limit of
For the last control variables combination of end milling, the colony size
value is increased to 100 with the limit of 300. The control variables combinations
are described in Table 4.16.
Table 4.16: Control variables combination with limit of 300
4.7.4 Colony size of 100 and limit of 300
Colony Size Max cycles per
run
Limit (abandoned
food)
100 10 300
100 20 300
100 50 300
100 100 300
When the program is executed, the results of the first control variables
combination are shown in Figure 4.14. The minimum Ra value achieved is 0.1719|am
in the first and seventh run.
117
2 Artificial Bee Algorithm Progr<
P r o c e s s P a r a m e t e r s O p t i m i z a t i o n o f S u r f a c e R o u g h n e s s i n E n d M i l l i n g a n d A b r a s i v e W a t e r j e t M a c h i n i n g
U s i n g A r t i f i c i a l B e e C o l o n y A l g o r i t h m
Ra = 0 237 — (0.00 175 X icl) + (3 693 x ■+■ (0.00 159 x x3>
Function fo r: End Milling
Colony S iz e :
Number of R un:
Max Cycles per R un:
Limit (abandoned fo od):
j— Parameters Range---------
X1 X2 X3 X4 X5
Uppest Threshold
167.03 0.083 3.5
Lowest Threshold
124.53 0.025 6.2
All best valuesAun
run N u m .Cycles MinValue X I
5 10 0.1744 167.030( •
6 10 Q.1729 167.03Q(
7 10| 0.17 1 9 H 167.030(
8 10 0.1747 167.0301 g
9 10 0.1753 166.098:
10 10 0.1723 167.030( -
< I IB J t
i ^ o v v Detail
Ready
Min Value, Fitnes A Mean of Fitness/Cycle
Cycle
Figure 4.14 Results of 10 max cycles per run with limit of 300
The best value returned is given by the seventh run where the minimum Ra
value 0 .17 19|am can be found in cycle seven. The best fitness value is 0.8533 and the
set values of process parameters that lead to the minimum values of Ra value are
167.0300 m/min for cutting speed, 0.0250 mm/tooth for feed and 6.200 0 for radial
rake angle. This is shown in Table 4.17.
118
Table 4.17: The best value returned from 10 max cycles per run with limit of 300
Subsequently the number of max cycle per run is increased to 20 and the
results are shown in Figure 4.15. The minimum Ra value achieved is 0.1719|am in all
tenth runs.
119
S3 Artific ial Bee A lgorithm Program \^_iP r o c e s s P a r a m e t e r s O p t i m i z a t i o n o f S u r f a c e R o u g h n e s s i n E n d M i l l i n g a n d A b r a s i v e W a t e r j e t M a c h i n i n g
U s i n g A r t i f i c i a l B e e C o l o n y A l g o r i t h m
Ra = 0 237 — (0.00 175 X i l ) + (3 693 x x 2 ) + (0.00159 x x3>
100
Function fo r: End Milling
Colony S iz e :
Number of R un:
Max Cycles per R un:
Limit (abandoned fo od):
j— Parameters Range---------
X1 X2 X3 X 4 X5
Uppest Threshold
167.03 0.083 3.5
Lowest Threshold
124.53 0.025 6.2
All best values/run
run N u m .Cycles MinValue X Iu . 1 ' 1 -■
5 20 0.1719 167.030(
6 20 0.1719 167.Q3CK
7 20 0.1719 167.030( — i8 20 0.1719 167.0301 =
9 20 0.1719 167.0301
10 20 0.1719 167.030( -
4 L HI H I »
IjS ftow b e ta i
Ready
0.9
0.8
0.7
0.6
= 0 .6
0.4
0.3
0.2
0.1
Min Value, Fitnes & Mean of Fitness/Cycle
Mean fitness
/Mill Ra value
10Cycle
15 20
Figure 4.15 Results of 20 max cycles per run with limit of 300
Table 4.18 below shows the best value returned from the fifth run with the
minimum Ra value of 0.1719 jam. This minimum Ra value is found in cycle five with
the best fitness value of 0.8533. The set values of process parameters that lead to the
minimum Ra value are 167.0300 m/min for cutting speed, 0.0250 mm/tooth for feed
and 6.200 0 for radial rake angle.
12 0
Table 4.18: The best value returned from 20 max cycles per run with limit of 300
The value of max cycle per run is increased to 50 and the experimental
results are shown in Figure 4.16. From the results, the minimum Ra value achieved is
0.1719|am in all tenth runs.
H Artific ia l Bee A lgorithm Progn i--------
P r o c e s s P a r a m e t e r s O p t i m i z a t i o n o f S u r f a c e R o u g h n e s s i n E n d M i l l i n g a n d A b r a s i v e W a t e r j e t M a c h i n i n g
U s i n g A r t i f i c i a l B e e C o l o n y A l g o r i t h m
Ra = 0.237 — (0.00 175 x i l ) -1- (3 693 x ■+• (0.00159 x x3>
Function fo r: End Milling
Colony S iz e :
Number of R un:
Max Cycles per R un:
Limit (abandoned fo od):
I— Parameters Range-------
X1 X2 X3 X4 X5
Uppest Threshold:
167.03 0.083 3.5
Lowest Threshold:
124.53 0.025 6.2 60 || 0.5
All best valuesfrun
run Num .Cycles MinValue X I
5 50 0.1719 167.030(*
6 50 0.1719 167.03CH
7 50 0.1719 167.030(
8 50 0.1719 167.030t E
9 50 0.1719 167.030(
10 50 0.1719 167.030(
< | m Z i t
j S J io w D «ta il
Ready
Min Value, Fitnes & Mean of Fitness/Cycle
Figure 4.16 Results of 50 max cycles per run with limit of 300
The best value returned from 50 max cycles per run is given by the ninth runs
where the minimum Ra value is 0.1719 jam. In Table 4.19 below, the minimum Ra
value can be found in the cycle two with the best fitness value of 0.8533. The set
values of process parameters that lead to the minimum Ra value are 167.0300 m/min
for cutting speed, 0.0250 mm/tooth for feed and 6.200 0 for radial rake angle.
12 2
Table 4.19: The best value returned from 50 max cycles per run with limit of 300
Finally, the value of max cycles per run is increased to 100 with the limit of
300. Figure 4.17 shows the results where the minimum Ra value discovered is
0.1719|am in all tenth runs.
P r o c e s s P a r a m e t e r s O p t i m i z a t i o n o f S u r f a c e R o u g h n e s s i n E n d M i l l i n g a n d A b r a s i v e W a t e r j e t M a c h i n i n g
U s i n g A r t i f i c i a l B e e C o l o n y A l g o r i t h m
Ra = 0 237 — (0.00 175 x i l ) -4- (S.693 x x2) + (0.00159 x x3>
10
Function fo r: End Milling
Colony S iz e :
Number of R un:
Max Cycles per R un:
Limit (abandoned fo od):
I— Parameters Range--------
X1 X2 X3
PUN
X4 X5
Uppest Threshold:
167 03 0.083 14 8 3.5
Lowest Threshold:
124.53 0.025 6 2 |
All best valuesAun
run Num .Cycles MinValue X I
3 100 0.1719 167.030( *
4 100| 0.1719H 167.030(
5 100 0.1719 167.030C
6 100 0.1719 167.030C 57 100 0.1719 167.030E —
8 100 0.1719 167.0301n Anr>
* I rtr- H I -»*'>
1
Ready
Min Value, Fitnes & Mean of Fitness/Cycle
Figure 4.17 Results of 100 max cycles per run with limit of 300
From the results in Table 4.20, the minimum Ra value of 0.1719 jam can be
found in cycle seven. The best fitness value achieved is 0.8533 and the set values of
process parameters that lead to the minimum Ra value are 167.0300 m/min for
cutting speed, 0.0250 mm/tooth for feed and 6.200 0 for radial rake angle.
125
Table 4.20: The best value returned from 100 max cycles per run with limit of
Using the same steps of end milling experiment, the AWJ experiment starts
with a bee colony size of 10 with the limit of 50. The control variables combinations
are shown in Table 4.21.
Table 4.21: Control variables combination with limit of 50
4.8 Experiment 2 - ABC optimization parameters for AWJ
Colony Size Max cycles per run Limit (abandoned
food)
10 10 50
10 20 50
10 50 50
10 100 50
4.8.1 Colony size of 10 and limit of 50
Using the first control variables combination, the program is executed for the
first time and the results are shown in Figure 4.18. The minimum Ra value found is
2.7090(j,m in the third run.
130
^ 3 A rtif ic ia l Bee A lg o r ith m P ro g r:
P r o c e s s P a r a m e t e r s O p t i m i z a t i o n o f S u r f a c e R o u g h n e s s i n E n d M i l l i n g a n d A b r a s i v e W a t e r j e t M a c h i n i n g
U s i n g A r t i f i c i a l B e e C o l o n y A l g o r i t h m
Ra =- 5 . 0 7 9 7 6 + ( 0 . 081*9 x s i ) + ( 0. 07912 x i 2 ) - ( 0. 34221 * x 3 ) - (0. 03661 x i 4 j - ( 0. 34866 x5) - ( 0. 00031 x i l * ) - ( 0. 00012 x i 2 s) +
( 0 , 10575 y x 3 J) + ( 0 . 0 00 4 ] x *4=) + ( 0 , 07590 * x 5 J) - ( 0. 00003 x x l x *5) - (O.OODOP x x l * x 5 ) + ( 0 . 03039 x * 3 x x 5 ) + ( 0. 00513 * x 4 x x5>
Function fo r :
Colony S iz e :
Number of R u n :
Max Cycles per Run
Limit (abandoned food)
Parameters Range---------------
X1 X2 X3
10
X4 X5
Uppest Threshold:
150 250 120 3.5
Lowest Threshold:
50 125 60 0.5
All best valuesA’un
run N u m . C yc le s M in V a lu e X I
1 10 4 4476 124.332 >
2 10 5.3259 59,417!
3 io | 2 . 7 H 9 « 73.109! £
4 10 3.1026 61.293!
5 10 3.5687 69.606!
6 10 4.3082 5i
7 10* rrr
4.6279 90.286:►
Show Detail
P.eadyCycle
10
''
Figure 4.18 Results of 10 max cycles per run with limit of 50
The results in Table 4.22 shows the minimum Ra value is achieved in cycle
eight with the best fitness value of 0.2696. The set values of process parameters that
lead to the minimum Ra value are 73.1095m/min traverse speed, 125Mpa waterjet
pressure, 1.4156mm standoff distance, 98.9371 [am abrasive gritsize and 1.0733g/s
abrasive flowrate.
131
Table 4.22 The best value returned from 10 max cycles per run with limit of 50
Next, the max cycle per run is increased to 20 and the results of the
experiment are shown in Figure 4.19. From the results, the minimum Ra value
achieved is 1.6032(j,m which is 41% better than the previous results. This value is
achieved at the seventh run.
132
H Artificial Bee Algorithm Program
P r o c e s s P a r a m e t e r s O p t i m i z a t i o n o f S u r f a c e R o u g h n e s s i n E n d M i l l i n g a n d A b r a s i v e W a t e r j e t M a c h i n i n g
U s i n g A r t i f i c i a l B e e C o l o n y A l g o r i t h m
Ra =-5.079^6 + (O .O S 1 6 9 x i l ) + (0.07911 x 12 ) - (0 .3 4 2 2 1 x e3)-(0.0& )61 x i 4 ) - (0 .3 4 S 6 6 x s 5 ) - (0.00031 x x l - ) - (0.00012 x n2?) +(0 ,1 0 5 7 5 x x 3 2) + (0 .0 0 0 4 1 x * 4 ! ) + (Q .0 7 ? 9 Q x % 5j ) - (0 .0 0 0 0 3 x * ] x x 5 ) - (Q .Q O Q 09 x x 2 x * 5 ) + (0 .0 3 0 3 9 x x 3 x * 5 } + (0 .0 0 5 1 3 x * 4 x x 5 }
Function fo r:
Colony S iz e :
Number of R un:
Max Cycles per R un:
Limit (abandoned food)
i— Parameters Range---------
X1 X2 X3
Abrasive Waterjet
1 250 r
X4 X5
Uppest Threshold
120 3.5
Lowest Threshold
50
All best valuesA'un
run N u m .Cycles M in Value X I
5 20 3.9778 5(•
6 20 3.143Q 66.269f
7 2 0 1 1.6032H 5(
8 20 1.7223 51 =E
9 20 1.8514 5(
10 20 1.8004 5( -
' 1 hi .□ 1
Ready
Cycle Min Value, Fitnes A Mean of Fitness/Cycle
25 5
Figure 4.19 Results of 20 max cycles per run with limit of 50
Table 4.23 below shows the best value returned from 20 max cycles per run
and the minimum Ra value achieved at cycle 20 with the fitness value 0.3841. The set
values of process parameters that lead to the minimum Ra value are 50/min traverse
The value of max cycles per run is increased to 50 and the results are shown
in Figure 4.20. The minimum Ra value achieved is 1.5223 jam at the sixth run.
Compared to the previous results, the minimum Ra value is improved by 5%.
134
S3 Artific ial Bee A lgorithm Progr*
P r o c e s s P a r a m e t e r s O p t i m i z a t i o n o f S u r f a c e R o u g h n e s s i n E n d M i l l i n g a n d A b r a s i v e W a t e r j e t M a c h i n i n g
U s i n g A r t i f i c i a l B e e C o l o n y A l g o r i t h m
Ra «-5 .07976 +■ (0 .OS 169 x *1} + (0.07912 x x2) - C0.34221 x i J ) - (0 .0 S 6 6 1 - i 4 ) - (Q.34S66 * xS) - (0.00031 * x V ) - (0 .000t l x x 2 !> +< 0 ,1 0 5 7 5 x (0 .0 0 0 4 ] * * 4 = ) + (0 .0 7 5 9 0 x * 5 J) - (0 .0 0 0 0 3 s i x * 5 ) - (0 .0 0 0 0 9 x j ] x * 5 ) + (0 .0 3 0 3 9 x * 3 * s 5 ) + (0 .0 0 5 1 3 x x 4 x * 5 )
Function fo r :
Colony S iz e :
Number of Run:
Max Cycles per Run
Limit (abandoned fo od);
I— Parameters Range--------
X1 X2 X3
Abrasive Waterjet
SO
X4 X5
Uppest Threshold:
ISO 250 4 120 3.5
Lowest Threshold:
50 125 | 1 60 OS |
All best valuesAun
run Num .Cycles MinValue X I
1 50 1.5232 5( >
2 50 1.7036 St
3 50 1.6540 50.24CK =
4 50 1.5225 5t
5 50 1.6430 5(
6 50 1.5223 5(7 cn 1 C V T
v III ►
| S h o w Detail |
Ready
Min Value, Fitnes & Mean of Fitness/Cycle
Cycle
Figure 4.20 Results of 50 max cycles per run with limit of 50
In Table 4.24, the minimum Ra value is found at cycle 17 with the best fitness
value of 0.3965. The set values of process parameters that lead to the minimum Ra
value are 50/min traverse speed, 125Mpa waterjet pressure, 1.5630mm standoff
distance, 102.2855|am abrasive gritsize and 0.5000g/s abrasive flowrate.
135
Table 4.24: The best value returned from 50 max cycle per run with limit of 50
Finally, for bee colony size of 10, the max cycle per run is increased to 100.
The results of the experiments are shown in Figure 4.21. From the results, the
minimum Ra value achieved is 1.5223 jam and can be found in all tenth run except at
the second, fifth, eighth and ninth run.
137
Q A r t if ic ^ l Bee A lg o r ith m P ro g ra m
P r o c e s s P a r a m e t e r s O p t i m i z a t i o n of S u r f a c e R o u g h n e s s in E n d M i l l i n g a n d A b r a s i v e W a t e r j e t M a c h i n i n g
U s i n g A r t i f i c i a l B e e C o l o n y A l g o r i t h m
Ra*-5 .079^6 + (O.OS169 x i l ) + (0.07911 x 12 ) - (0.34221 x e3)~(0.0&>61 x i4 ) - (0.34S66 x x 5 ) - (0.00031 x i l : ) - (0.00012 x i i ?) + (0.10575 x *32) + (0.90041 x jt45) + (Q.Q7?9Q x x5j) - (0.00003 * si x *5) - (0.00009 x x2 x *5) + (0.03039 x x3 x *5} + (0.00513 x *4 *
Function fo r:
Colony S iz e :
Number of R un:
Max Cycles per R un:
Limit (abandoned food)
— Parameters Range---------
X1 X2 X3
Abrasive Waterjet
100
Uppest Threshold
120 T 3.5
Lowest Threshold
50 125
All best valuesfrun
run N u m .Cycles MinValue X I
1 100 1.5223 51 >
2 100 1.5229 51
3 100 1.5223 514 100 1.5223 51
5 100 1.5234 51
6 100 1.5223 517 ̂nn 1 COOT £.(
< I Z J r
Ready
Min Value, Fitnes A Mean of Fitness/Cycle
5
Figure 4.21 Results of 100 max cycles per run with limit of 50
The minimum Ra value is given by the third run. As shown in Table 4.25, the
minimum Ra value of 1.5223 jam is found at cycle 41 with the best fitness value of
0.3965. The set values of process parameters that lead to the minimum Ra value are
The bee colony is increased to 20 and the limit is set to 100. The control
variables combinations value are shown in Table 4.26 below.
Table 4.26: Control variables combination with limit of 100
Colony Size Max cycles per run Limit (abandoned
food)
20 10 100
20 20 100
20 50 100
20 100 100
The first control variables combination is tested and the results are shown in
Figure 5.22. From the results, the lowest Ra value achieved is 1,6247|am at the eighth
143
?3 Artific ia l Bee A lgorithm Pre-gram
P r o c e s s P a r a m e t e r s O p t i m i z a t i o n of S u r f a c e R o u g h n e s s in E n d M i l l i n g a n d A b r a s i v e W a t e r j e t M a c h i n i n g
U s i n g A r t i f i c i a l B e e C o l o n y A l g o r i t h m
Ra --5.07976 +■ (0.0S169 x *1) + (0-07912 x i2 ) - (4.34221 x i3) - (0.0S661 x i4 ) (Q.34S66 m i5 ) - (0.00031 « xV) - (0.000t l * x2!> +<0. 10575 x * 3 ' ) + ( 0 . 0004] * *42) + ( 0. 07590 x x 5 J) - ( 0. 00COS * s ] x *5) - ( 0. 00009 x x ] k * 5 ) + ( 0. 03039 x *3 x s 5 ) + ( 0 . 00513 x * 4 * » 5 )
Function fo r :
Colony S iz e :
Number of Run:
Max Cycles per Run
Limit (abandoned fo od):
i— Parameters Range---------
X1 X2 X3
Abrasive W ate r#
X4 X5
Uppest Threshold:
120 3.5
Lowest Threshold:
125 60
All best valuesAun
run Num .Cycles MinValue X I
• • . <n«a i — ■ — < •5 10 4.1813 114.594'
6 10 2.3855 51
7 10 3.2220 83.494
8 10 1.6247 55 £
9 10 1.6682 St
10 10 1.9432 5( -v rri t
| S t o w Detail |
Ready
Min Value, Fitnes & Mean of Fitness/Cycle
Figure 4.22 Results of 10 max cycles per run with limit of 100
Table 4.27 below shows the best value returned from the eighth run. The
minimum Ra is achieved at cycle 10 with the best fitness value of 0.3810. The set
values of process parameters that lead to the minimum values of Ra value are 50/min
To discover better results, the max cycle per run value is increased to 20. The
results are shown in Figure 4.23. The minimum Ra value achieved is 1,5229|am at the
second run.
145
Q Artificial Bee Algorithm Progr*
P r o c e s s P a r a m e t e r s O p t i m i z a t i o n of S u r f a c e R o u g h n e s s in E n d M i l l i n g a n d A b r a s i v e W a t e r j e t M a c h i n i n g
U s i n g A r t i f i c i a l B e e C o l o n y A l g o r i t h m
Ra --5.07976 +■ (0.OS 1*9 x *1} + (0.07912 x x.2) - (0.34221 x i3 )-(0 .0 S 6 6 1 - i 4 ) - (Q.34S66 x x 5 )-(0 .0 0 0 3 1 x xV) - (0.00012 x x2!> +<0,10575 x (0.0004] * *4: ) + (0.07590 x x5J) - (O.OOOOS s i x x5) - (0.00009 x j j x x5)+ (0.03039 x r f x x5) + (0.00513 * x4 * x5)
Function fo r :
Colony S iz e :
Number of Run:
Max Cycles per Run :
Limit (abandoned food)
I— Parameters Range---------
X1 X2 X3
Abrasive Waterjet
20
100
X4 X5
Uppest Threshold:
150 250 120 3.5
Lowest Threshold:
125 | 1
All best valuesAun
run N um . Cycles MinValue X I
1 20 1.9572 5( -2 20 1.5229 SI
3 20 2.1370 5I =
4 20 2.3781 51.143-
5 20 1.8040 5(
6 20 1,52GB 5(7 Tifl 1 o cm cr
V III »
I Snow Detail
Ready
Min Value, Fitnes & Mean of Fitness/Cycle
Figure 4.23 Results of 20 max cycles per run with limit of 100
The best value returned are shown in Table 4.28 below where the minimum
Ra value 1,5229|am can be found at cycle 15. The best fitness value achieved is
0.3964 and the set values of process parameters that lead to the minimum Ra value
are 50/min traverse speed, 125Mpa waterjet pressure, 1.5563mm standoff distance,
103.7480|am abrasive gritsize and 0.5000g/s abrasive flowrate.
146
Table 4.28: The best value returned from 20 max cycle per run with limit of 100
Figure 4.24 below show better results are achieved when the max cycle per
run value is increased to 50. The minimum Ra value achieved is 1.5223[am at the
third, fifth, sixth and ninth run.
147
Q Artificial Bee A lgorithm Program L^j__P r o c e s s P a r a m e t e r s O p t i m i z a t i o n of S u r f a c e R o u g h n e s s in E n d M i l l i n g a n d A b r a s i v e W a t e r j e t M a c h i n i n g
U s i n g A r t i f i c i a l B e e C o l o n y A l g o r i t h m
Ra *-5.079^6 + (0.0S169 X 11) + (0.07911 x 1 2 ) - (0.34221 x E3)-(0 .0 tttfl - i4) - (0.34S66 x i 5 ) - (0.00031 x i l : ) - (0.00012 x r i * ) +(0.10575 x x33) + (0.90041 x jt45) + (0.07590 x x5J) - (0.00003 * s ] x *5) - (0.00009 x x2 x *5) + (0.03039 x x3 x 5*5} + (B.00513 x *4 x *5}
Function fo r:
Colony S iz e :
Number of R un:
Max Cycles per R un:
Limit (abandoned food)
— Parameters Range---------
X1 X2 X3
Abrasive Waterjet
20
T »
X4 X5
Uppest Threshold
120 3.5
Lowest Threshold
SO 125 1
All best valuesAun
run N u m .Cycles MinValue X I
5 50 1.5223 51•
6 50 1.5223 5(
7 50 1.5224 5( ~ |
8 50 1.5257 51
9 50 j 1.5223 H 5(
10 50 1.5226 5( -
' 1 111 □ t
^ o y v Detail
Ready
Min Value, Fitnes A Mean of Fitness/Cycle
10 20 30 40 50Cycle
5
Figure 4.24 Results of 50 max cycles per run with limit of 100
The best value returned from the ninth run is shown in Table 4.29 where the
minimum Ra value is 1.5223pm with the best fitness value 0.3965. The minimum Ra
value is found in cycle 35. The set values of process parameters that lead to the
minimum values of Ra value are 50/min traverse speed, 125Mpa waterjet pressure,
1.5295mm standoff distance, 102.3062pm abrasive gritsize and 0.5000g/s abrasive
flowrate.
148
Table 4.29: The best value returned from 50 max cycle per run with limit of 100
Lastly for limit of 100, the max cycle per run value is increased to 100. The
results are shown in Figure 4.25 where the minimum Ra value achieved is 1.5223 jam
at all 10 run.
H Artificial Bee Algorithm Progn
P r o c e s s P a r a m e t e r s O p t i m i z a t i o n of S u r f a c e R o u g h n e s s in E n d M i l l i n g a n d A b r a s i v e W a t e r j e t M a c h i n i n g
U s i n g A r t i f i c i a l B e e C o l o n y A l g o r i t h m
R* =- 5 .0 7 9 7 6 + ( 0 .0 S 1 6 9 x 1 1) + (0 .0 7 9 1 2 m i 2 ) - (0 .3 4 2 2 1 * x 3 ) - ( 0 .0 S 6 6 1 m i 4 ) - ( 0 . 3 4 S 6 6 > x S ) - (0 .0 0 0 3 1 x i l ? ) - < 0 .0 0 0 1 2 x i 2 ?> +(0.10575 x x33) ■+■ (0.00041 * xtf) + (0.07590 * x5J) - (0.00003 - * l x * 5 ) - (0.00009 *5) + (0.03059 x *3 * *5) + (0.00513 x *4 * *5}
Function fo r:
Colony S iz e :
Number of R un:
Max Cycles per Run :
Limit (abandoned fo od):
p— Parameters Range —
X1 X2
Abrasive Waterjet
X3 X4 X5
Uppest Threshold:
3.5
Lowest Threshold
125 60
All best valuesAun
run Num .Cycles MinValue X I
1 100 1.5223 5(
2 100 1.5223 si3 100 1.5223 5E
4 100 1.5223 SI
5 100 1.5223 5(
6 100 1.5223 5(7 •inn_ 1 c/
< 1 nr r
Ready
Min Value, Fitnes & Mean of Fitness/Cycle
1.5
Figure 4.25 Results of 100 max cycles per run with limit of 100
The best value returned from the third run is shown in Table 4.30. The
minimum Ra value is 1.5223[am with the best fitness value 0.3965 are found in cycle
58. The set values of process parameters that lead to the minimum values of Ra value
are 50/min traverse speed, 125Mpa waterjet pressure, 1.5333mm standoff distance,
102.7407j.im abrasive gritsize and 0.5000g/s abrasive flowrate.
151
Table 4.30: The best value returned from 100 max cycle per run with limit of 100
The bee colony size is increased to 50 and the limit is set to 250. The control
variables combinations value are shown in Table 4.31 below.
Table 4.31: Control variables combination with limit of 250
Colony Size Max cycles per run Limit (abandoned
food)
50 10 250
50 20 250
50 50 250
50 100 250
The results of the first control variables combination with max cycles per run
of 10 is shown in Figure 4.26. From the results, the minimum Ra value achieved is
1.5769(j,m at eighth runs.
156
H Artificial Bee Algorithm Progr< ..... 1------- 1Process P a ra m e te rs O p t im iza t io n of Su rface R oughness in End M i l l in g and A b ra s iv e W a t e r j e t M a c h in in g
Using A r t i f ic ia l Bee Co lo n y A lg o r i th m
R a --5.07976 +■ (0 .OS 1*9 x *1} + (0.07912 x i2 ) - (4.34221 x i 3 ) - (0.03661 - i 4 ) - (Q.34S66 * i 5 ) -(0 .0 0 0 3 1 x x V ) - (0.00012 x x2!> +<0,10575 x (0 .0004] x x 4 ') + (0 .07590 x *5 J) - (0 .00003 s ] x *5) - (0 .00009 x *2 * x 5 ) + (0 .03039 x x3 * x 5 ) + (0 .0 0 5 1 3 x * 4 x x5)
Function f o r : A brasive W aterjet
50
10
10
250RUN
Colony S iz e :
Number of R u n :
M ax Cycles per Run :
Limit (abandoned fo o d ):
j— Parameters R ange---------
X1 X 2 X3 X 4 X5
Uppest Threshold:
150 250 120 3.5
Low est Threshold:
50 125 | I
All best valuesAun
run Num. Cycles MinValue X I
5 10 2.4953 5( *
6 10 1 .8655 5(7 10 1.6656 5(8 10 1.5769 5t =
9 10 3.8389 102.696:10 10 2.1287 5( -
< in □ r
I Snow Detad
Ready
Min Value, Fitnes & M ean of Fitness/Cycle
Figure 4.26 Results of 10 max cycles per run with limit of 250
The best value returned from the eighth run is shown in Table 4.32. The
minimum Ra value achieved is 1.5769pm with the best fitness value 0.3881 at cycle
ten. The set values of process parameters that lead to the minimum Ra value are
To find out better results, the max cycle per run value is increased to 20. The
results are shown in Figure 4.27. The minimum Ra value achieved is 1.5280(j,m at the
first run. This minimum Ra value is 3% much better compared to the previous Ra
value.
158
S 3 A rtific ia l Bee A lg o rith m Progr:
Process P a ra m e te r s O p t im iza t io n of Su rface R oughness in End M i l l in g and A b ra s iv e W a t e r j e t M a c h in in g
Using A r t i f ic ia l Bee Co lo n y A lg o r i th m
R a ■-5.07976 MO OS 1*9 x i l ) + (0.07912 x *2) - (4.34221 * *3) - (0.0S661 - i4 ) - (0.34S66 x x 5 )-<0.04031 x x V ) - (0.44012 >: r 2 !> +<0.10575 x i 3 ' ) + (0.0004] x x42) + (0 .0 7 5 9 0 x *5 J) - <0.00003 ■ x l x *5) - (0 ,00009 x j I k x5 ) + (0 .03039 > i 3 x »5} + (0 .0 0 5 1 3 * * 4 x *5)
Function f o r : A brasive W aterjet
501020
250RUN
Colony S iz e :
Number of R u n :
M ax Cycles per Run :
Limit (abandoned fo o d ):
j— Parameters R ange---------
X1 X 2 X3 X 4 X5
Uppest Threshold:
150 250 1 2 0 3 .5
Low est Threshold:
125 | 1
Ail best valuesAun
run Num. Cycles MinValue X I
1 20 1.5280 5(2 20 1.6384 5t3 20 1.9638 5t F
4 20 1.5735 5t
5 20 2.2999 5(6 20 1.6117 5(7 ~>n T A 11C-
* III □ r
I Snow Detail
Ready
Min Value, Fitnes & M ean of Fitness/Cycle
Figure 4.27: Results of 20 max cycles per run with limit of 250
The results in Table 4.33 show the minimum Ra value achieved at cycle 20
with the best fitness value of 0.3956. The set values of process parameters that lead
to the minimum Ra value are 50m/min traverse speed, 125Mpa waterjet pressure,
The number of max cycles per run is then increased to 50 and the results are
shown in Figure 4.28. The minimum Ra value achieved is 1.5223[am at all 10 runs
except at the third, seven and ninth run.
16 0
H A rtific ia l Bee A lg o rith m Progr;
Process P a ra m e te r s O p t im iza t io n of Su rface R oug hness in End M i l l in g and A b ra s iv e W a t e r j e t M a c h in in g
Using A r t i f i c ia l Bee C o lo n y A lg o r i th m
R a =-5 .0 7 9 ^ 6 + (0.OS169 x i l ) + (0 .07911 x 12 ) - (0 .34221 x e3 )-(0 .0 & > 6 1 - i 4 ) - (0 .34S66 x i 5 ) - (0 .00031 x i V ) - (0 .00012 x r i* ) +(0 ,1 0 5 7 5 x *3 3) + (0.£)0041 x jt45) + (Q.07?9Q x x5 j) - (0 .00003 X i ] x * 5 ) - (0 .0 0 0 0 9 x x2 x * 5 ) + (0 .03039 x * 3 x *5} + (0 .00513 x * 4 x x5}
Function fo r :
Colony Size:
Number of Run:
Max Cycles per Run:
Limit (abandoned food)
i— Parameters Range-------
X1 X2 X3
Abrasive Waterjet
X4 X5
Uppest Threshold
120 3.5
Lowest Threshold
SO 125
All best valuesAunrun N u m .Cycles M in V a lu e X I
1 . ■*« **5 50 1.5223 51
6 50 1.5223 5(
7 50 1.5232 5(
8 50 1.5223 51 =
9 50 1.5226 5(
10 50 ■ ■ ■ E 2 2 E 5t -
* | nr 3 t
j^ovy Detail
Ready
Min Value, Fitnes A Mean of Fitness/Cycle
Cycle
Figure 4.28 Results of 50 max cycles per run with limit of 250
Table 4.34 below show the best value returned from 50 max cycles per run
and the minimum Ra value achieved at cycle 26 with fitness value 0.3965. The set
values of process parameters that lead to the minimum Ra value are 50/min traverse
speed, 125Mpa waterjet pressure, 1.5428 mm standoff distance, 102.5184pm
abrasive gritsize and 0.5000g/s abrasive flowrate.
f
161
Table 4.34: The best value returned from 50 max cycle per run with limit of 250
Lastly for limit of 250, the max cycles per run is increased to 100. The results
are shown in the Figure 4.29 below. The minimum Ra value achieved is 1,5223pm at
all 10 runs.
163
H Artificial Bee Algorithm Progr;
Process P a ra m e te r s O p t im iza t io n of Su rface R oug hness in End M i l l in g and A b ra s iv e W a t e r j e t M a c h in in g
Using A r t i f i c ia l Bee C o lo n y A lg o r i th m
R a =-5 .0 7 9 ^ 6 + (O.OS169 x i l ) + (0.07911 x 12 ) - (0 .34221 x e3 )-(0 .0 & i61 x i 4 ) - (0 .34S66 x i 5 ) - (0 .00031 m i l :) - (0 .00012 x r i s) +(0 ,1 0 5 7 5 x x3 3) + (0 .00041 x * 4 ! ) + (0 .0 7 5 9 0 x x5 J) ~ (0 .00003 X s i x x5 ) - (0 .0 0 0 0 9 x x 2 x * 5 ) + (0 .0 3 0 3 9 x x 3 x 5*5} + (0 .0 0 5 1 3 x * 4 x »5}
Function f o r :
Colony S iz e :
Number of R u n :
M ax Cycles per R u n :
Limit (abandoned food)
i— Param eters R ange---------
X1 X2 X3
Abrasive W aterjet
100
J?
X 4 X5
Uppest Threshold
120 3.5
L ow est Threshold
50 125
All best valuesAun
run N u m .Cycles M in V a lu e | X I
1 100 | 1 5 2 2 3 ® 5( >
2 100 1.5223 51
3 100 1.5223 St r
4 100 1.5223 St
5 100 1.5223 5(
6 100 1.5223 5(7 ̂nn
< | " I1 COOT
2 ----- r
^ o w Detail
Ready
Min V alue , Fitnes A Mean of Fitness/Cycle
Cycle
5
Figure 4.29 Results of 100 max cycles per run with limit of 250
The best returned value of 100 max cycles per runs is achieved at the first
runs. In Table 4.35 below, the minimum Ra value of 1.5223[am is achieved at cycle
26 with the best fitness value of 0.3965. The set values of process parameters that
lead to the minimum Ra value are 50/min traverse speed, 125Mpa waterjet pressure,
1.5522 mm standoff distance, 102.4524|am abrasive gritsize and 0.5000g/s abrasive
flowrate.
164
Table 4.35: The best value returned from 100 max cycle per run with limit of 250
For the final experiments of AWJ, the limit value is increased to 500 to
analyze whether it will give superior results from the prior size of bee colony. The
combination of control variables are given in Table 4.36.
4.8.4 Colony size of 100 and limit of 500
Table 4.36: Control variables combination with limit of 500
Colony Size Max cycles per run Limit (abandoned
food)
100 10 500
100 20 500
100 50 500
100 100 500
The first combination of control variables with limit of 500 gives a minimum Ra
value of 1.7025(j,m in the sixth run as shown in Figure 4.30.
169
H Artificial Bee Algorithm Progr; l—
Process P a ra m e te r s O p t im iza t io n of Su rface R oug hness in End M i l l in g and A b ra s iv e W a t e r j e t M a c h in in g
Using A r t i f i c ia l Bee C o lo n y A lg o r i th m
R a =-5 .0 7 9 ^ 6 + (O.OS169 x i l ) + (0 .07911 x 12 ) - (0 .34221 x e 3 ) - ( O .O & t f l x i 4 ) - (0 .34S66 x i 5 ) - (0 .00031 x i l : ) - (0 .00012 x r f s) +(0 ,1 0 5 7 5 x * 3 J) + (0 .90041 x j*4! ) + (0 .0 7 590 x x5j) - (0 .00003 * s i x j*5) - (0 .0 0 0 0 9 x x 2 x 5*5) + (0 .03039 x x 3 x 5*5} + (0 .00513 x * 4 x »5}
Function f o r :
Colony S iz e :
Number of R u n :
M ax Cycles per R u n :
Limit (abandoned food)
j— Param eters R ange---------
X1 X2 X3
Abrasive W aterjet
] J?
X 4 X5
Uppest Threshold
120 3.5
L ow est Threshold
SO 125
All best valuesAun
run N u m .Cycles M in V a lu e X I
1 10 2.1076 61.798; *
2 10 1.9366 51
3 10 1.8048 51 K
4 10 1.9518 55.547*
5 10 2.8528 78 .727J
6 10 1.7025 517 ̂n _ T11QO R'l 7C.C.'
< I HI r
jjhovy Detail
Ready
Min V alue , Fitnes A Mean of Fitness/Cycle
Cycle
5
Figure 4.30 Results of 10 max cycles per run with limit of 500
From the results of the first control variables combinations, the best fitness
achieved is 0.3700 and the set values of process parameters that lead to the minimum
values of Ra value were 50/min traverse speed, 125Mpa waterjet pressure, 2.1894
mm standoff distance, 105.0051 [am abrasive gritsize and 0.8849g/s abrasive flowrate.
The minimum Ra value is achieved at cycle 10. This is shown in Table 4.37.
170
Table 4.37: The best value returned from 10 max cycle per run with limit of 500
Next, the number of max cycle per run is increased to 50. The results are
shown at Figure 4.31 where the minimum Ra value achieved is 1.5223[am at the fifth
171
P 3 Artificial Bee Algorithm Progn
Process P a ra m e te rs O p t im iza t io n of Su rface R oughness in End M i l l in g and A b ra s iv e W a t e r j e t M a c h in in g
Using A r t i f ic ia l Bee Co lo n y A lg o r i th m
R a is-5.07976 +■ (0.0S169 x i l ) + (0.07912 x i2 ) - (0.34221 x i 3 ) - (0.03661 - i4 ) - (Q.34S66 * x5)-(0.00031 x x V ) - (0.00012 x x2!> +<0.10575 x (0 .0004] * *42) + (0 .07590 x *5 J) - (0 .00003 s i x *5) - (0 .00009 x j j x x 5 )+ (0 .03039 x i 3 * s 5 ) + (0 .0 0 5 1 3 x x 4 * *5)
Abf asjve Waterjet
100Function f o r :
Colony S iz e :
Number of R u n :
M ax Cycles per Run :
Limit (abandoned fo o d ):
I— Parameters R ange---------
X1 X 2 X3 X 4 X5
Uppest Threshold:
500
150 250 120 3.5
Low est Threshold:
50 125 | 1
All best valuesAun
run N u m . Cycles M in V a lu e X I
3 20 1.5290 5( *
4 20 1 .9526 51
5 20 1.5223 5( B
6 2Q 1.8499 5t I7 20 1 .7774 5(
8 20 1.5753 5( -
< IK □ r
! Snow Detail
Ready
Min Value, Fitnes & M ean of Fitness/Cycle
50 0.5
Figure 4.31 Results of 20 max cycles per run with limit of 500
Table 4.38 below shows the best value returned from 20 max cycles per run
and the minimum Ra value is achieved at cycle 19 with fitness value 0.3965. The set
values of process parameters that lead to the minimum Ra value are 50/min traverse
speed, 125Mpa waterjet pressure, 1.5359 mm standoff distance, 102.3683|am
abrasive gritsize and 0.5000g/s abrasive flowrate.
172
Table 4.38: The best value returned from 20 max cycle per run with limit of 500
The number of max cycles per run is then increased to 50 and the results are
shown in Figure 4.32. The minimum Ra value achieved is 1.5223[am at all 10 runs
except at the second and eighth run.
173
H A rtific ia l Bee A lg o rith m Progr; Id - - !■£$■!Process P a ra m e te r s O p t im iza t io n of Su rface R oug hness in End M i l l in g and A b ra s iv e W a t e r j e t M a c h in in g
Using A r t i f i c ia l Bee C o lo n y A lg o r i th m
R a =-5 .0 7 9 ^ 6 + (0 .0 5 1 6 9 x i l ) + (0 .07911 x 12 ) - (0 .34221 x x 3 ) ~ ( 0 .0 t t t f l x i4) - (0 .34S66 x i 5 ) - (0 .00031 x i V ) - (0 .00012 x x2 ?) +(0 ,1 0 5 7 5 x x3 3) + (0.£)0041 x jt45) + (0 .07590 x x5 J) - (0 .00003 x s i x x5) - (0 .0 0 0 0 9 x x 2 x *5 ) + (0 .03039 x * 3 x *5} + (0 .00513 x * 4 * *5}
Function f o r :
Colony S iz e :
Number of R u n :
M ax Cycles per R u n :
Limit (abandoned food)
i— Param eters R ange---------
X1 X2 X3
Abrasive W aterjet
T »
X 4 X5
Uppest Threshold
120 3.5
L ow est Threshold
SO 1 25 1
All best valuesAun
run N u m .Cycles M in V a lu e X I
1 50 1.5223 5( >
2 50 1.5227 51
3 50 1.5223 5[ r
4 50 1.5223. 5t
5 50 1.5223 5(
6 50 1.5223 5(7 cn 1 COOT
< | rtr 3 r
jShow Petal
Ready
Min V alue , Fitnes A Mean of Fitness/Cycle
Cycle
Figure 4.32 Results of 50 max cycles per run with limit of 500
In Table 4.39 below, the minimum Ra value of 1.5223[am is achieved at cycle
15 with the best fitness value of 0.3965. The set values of process parameters that
lead to the minimum Ra value are 50/min traverse speed, 125Mpa waterjet pressure,
1.5479 mm standoff distance, 102.521 ljam abrasive gritsize and 0.5000g/s abrasive
flowrate.
5
174
Table 4.39: The best value returned from 50 max cycle per run with limit of 500
Finally, for limit of 500, the max cycles per run is increased to 100. The
results are shown in the Figure 4.33 below. The minimum Ra value achieved is
1.5223 jam at all 10 runs.
176
H Artificial Bee Algorithm Progr;
Process P a ra m e te r s O p t im iza t io n of Su rface R oug hness in End M i l l in g and A b ra s iv e W a t e r j e t M a c h in in g
Using A r t i f i c ia l Bee C o lo n y A lg o r i th m
R a =-5 .0 7 9 ^ 6 + (0 .0 5 1 6 9 x i l ) + (0 .07911 x 12 ) - (0 .34221 x e 3 )- (0 .0 & > 6 1 - i 4 ) - (0 .34S66 x s5 ) - (0 .00031 x i l 3) - (0 .00012 x r i * ) +(0 ,1 0 5 7 5 x * 3 3) + (0 .EJ0041 x jt45) + (0 .0 7 590 * %5J) - (0 .00003 * x l x * 5 ) - (0 .00009 x x 2 x * 5 ) + (0 .0 3 0 3 9 x x 3 x 5*5} + (0 .0 0 5 1 3 x * 4 x *5 }
Function f o r :
Colony S iz e :
Number of R u n :
M ax Cycles per R u n :
Limit (abandoned food)
i— Param eters R ange---------
X1 X2 X3
Abrasive W aterjet
100
X 4 X5
Uppest Threshold
130 3.5
L ow est Threshold
SO 1 25 1
All best valuesAun
run N u m .Cycles M in V alue X I
5 100 1.5223 5(•
6 100 1.5223 5(
7 100 1.5223 5( ~ 1
8 100 1.5223 51 =
9 103 1.5223 ■ 5(
10 100 1.5223 5( -
' I Hi □ r
i Show Detail
Ready
Min V alue , Fitnes A Mean of Fitness/Cycle
5
Figure 4.33 Results of 100 max cycles per run with limit of 500
The best returned value of 100 max cycles per runs is achieved at the ninth
runs. In Table 4.40 below, the minimum Ra value of 1.5223[am achieved at cycle
eight with the best fitness value of 0.3965. The set values of process parameters that
lead to the minimum Ra value are 50/min traverse speed, 125Mpa waterjet pressure,
1.5504 mm standoff distance, 102.5213[am abrasive gritsize and 0.5000g/s abrasive
flowrate.
177
Table 4.40: The best value returned from 100 max cycle per run with limit of 500