artificial bee colony in optimizing process parameters of surface ...

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




4.8 Experiment 2 - ABC optimization parameters for AWJ 129





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



Control variables combination with limit of 60 90









The best value returned from 100 max cycles perrun with limit o f l5 0 112








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







Control variables combination with Limit of 250 155










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

















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








M l Results of 20 max cycles per run with limit of 250 158







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

genetic algorithm (GA), simulated annealing (SA), particle swarm optimization

(PSO), tabu search (TS) and ant colony optimization (ACO).

The study of insect and animal behaviour has attracted many researchers

attention to better understand their colony and behaviour so that it could be modelled

to solve complex problems in real world. Ant colony optimization (ACO) for

example is one of the swarm intelligence techniques that were introduced by Dorigo

et al. (1996) which were inspired by the foraging behaviour of ants. Similar to the

concept of ACO, recently a new algorithm known as artificial bee colony (ABC)

algorithm was introduced by Karboga in 2005. This algorithm mimics the intelligent

behaviour of the honey bees swarm in foraging foods. ABC algorithm has been

applied in many applications particularly in job scheduling, optimization and data

clustering. A comparative study by Karaboga and Akay (2009) shows that standard

ABC gives an excellent performance for optimizing a large set of numerical test

unimodal function such as Sphere and Rosenbrock. It was found that ABC gave a

better result in terms of local and global optimization due to the selection schemes

employed and neighbouring production mechanism used. The results are then

compared with other swarm optimization algorithms such PSO, differential evolution

algorithm and evolution strategies. From the literature review, there is no research

has been carried out so far to apply ABC optimization techniques for optimization of

process parameters in end milling and abrasive waterjet (AWJ) machining. Recently,

a research was carried out by Rao and Pawar (2009) to optimize the process

parameter such as number of passes, depth of cut for each pass, speed and feed in a

multi-pass milling machining operations using non-traditional optimization

algorithms such as PSO, SA and ABC. The results showed that ABC and PSO

produced a better solution compared to SA where the convergence rate is higher and

the number of iterations is lowered.

4

Based on the previous research by Zain et al. (2010a, 2010b, 2010c), it shows

that the use of GA and SA give a promising result in minimizing Ra both in end

milling and AWJ machining compared to the experimental and regression modelling.

In Zain et al. (2010a, 2010b), GA and SA techniques were used to optimize the

process parameters in end milling machining operation.

The results showed that GA and SA have given a much lower Ra value when

compared to the experimental, regression model and response surface methodology

(RSM) technique by 27%, 26% and 50%, respectively. In Zain et al. (2010c) the

same optimization technique was used to optimize the process parameters in AWJ

machining operations. The results show both techniques produced a minimum

surface roughness value compared to experimental data and regression modelling. In

this study ABC algorithm is considered in minimizing Ra for both end milling and

AWJ machining. Consequently, the Ra of ABC is compared to Ra produced by

experimental, regression modelling, GA optimization and SA optimization.

The research question can be stated as:

How efficient is the performance o f ABC optimization to optimize process

parameters fo r minimizing surface roughness in end milling and AW J machining

operations compared to experimental, regression modelling, GA optimization and SA

optimization.

1.2 Statement of problems

5

Based on the problem statements mentioned above, the objectives of the

study are:

i. To develop ABC based algorithm in optimizing surface roughness of

machining process.

ii. To estimate the optimal set of process parameters in end milling and AWJ for

giving a minimum value of Ra.

iii. To validate the proposed method with the existing techniques such as,

experimental, regression modelling, GA optimization and SA optimization.

1.3 Objectives of the study

1.4 Scope of the study

The scopes of this study are:

i. The experimental data sets are based on the experiment conducted by

Mohruni (2008) for end milling machining operations and Caydas and

Hascalik (2008) for AWJ machining operations.

ii. The optimization approach method used is ABC algorithm.

iii. The performance and results are compared with experimental, regression

modelling, GA optimization and SA optimization.

1.5 Significance of the study

6

This study is to investigate the performance of ABC algorithm in optimizing

process parameters for minimizing Ra in both end milling and AWJ machining

operations. To indicate the effectiveness of this computational approach, the end

results which are the Ra values will be compared with experimental, regression

modelling, GA optimization and SA optimization. From the literature review, there is

no effort taken so far by researchers to apply ABC algorithm for the machining

optimization problems both in end milling and AWJ machining operation. So, it can

be concluded that this study gives a new contribution in the area of machining.

1.6 Organization of the thesis

This thesis consists of six chapters. Chapter 1 describes the introduction to

the research, problem background, problem statement, objective and scope of the

study. Chapter 2 presents the literature review of the study. Chapter 3 discussed

about the research methodology that applied in this study. Chapter 4 discussed the

implementation of ABC optimization while Chapter 5 discussed the analysis of the

results of ABC optimization. Finally, Chapter 6 discussed the conclusion and

recommended the future work of the research.

CHAPTER 2

LITERATURE REVIEW

2.1 Minimization of surface roughness

The evaluation on the appearance of an end manufacturing product usually

depicted as Ra. In order to get a high end quality product with a minimal Ra value, it

must be supported by a precise machine process and depending on the machining

conditions as well. According to Fu (2006), there are three decision variables to

minimize the machining conditions which are the cutting speed, the amount of

moving forward and the cutting depth. These setting are the means to cost-effective

machining operation.

A high quality milled surface must be able to completely improved material

piece in terms of weariness force and oxidization resistance. In order to get a

desirable quality of the detailed Ra, a proper process is needed because the Ra

additionally influences a number of functional qualities of material pieces, which

includes contact causing Ra, wearing, light reflection, heat transmission, ability of

distributing and holding a lubricant, coating, or resisting fatigue (Lou et al 1998).

Roughness is regularly an excellent analyst of the performance of a

mechanical component since irregularities in the surface appearance of nucleation

sites for fractures or oxidization may noticeable. Although roughness is usually

8

unwanted, it is not easy and costly to manage at some stage in manufacturing.

Diminishing Ra will usually exponentially boost its manufacturing expenses. This

often turns out when swapping between the manufacturing cost of a component and

its performance in application (Kadirgama et al, 2008).

2.2 Optimization of end milling and AWJ machining process

In the machining process, to cut the workpiece rapidly, it is usually supplied

into a spinning multiple tooth cutter. There are many combinations of machined

surfaces such as flat, angular, or curved. Traditional machining such as milling

machine, holds the workpiece, rotate the cutter and feeding the workpiece to the

cutter (http://www.mfg.edu/marc/primers/milling/index.html). There are three

categories of milling which are slab, face and end milling. These categories of

machining are shown in Figure 2.1 below.

Figure 2.1 Categories of milling (Kalpakjian and Schmid, 2009)

In manufacturing industries, the most regular process of removing metal is

recognized as end milling. In the end milling, there are three common controlled

parameters which are cutting speed (v), feed rate if) and radial rake angle (y).

(n’t SlahffldiliMr (b) Fare milling (c) End milling'

http://www.mfg.edu/marc/primers/milling/index.html

9

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)


5 Abu-Mouti and El- Hawary (2009)

4 30 227 20

6 Benitez and Lopes (2010)


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%.

amanta et al. 2008)

ANN,adaptiveneuro-fuzzyinferencesystem(ANFIS),multivariateregressionanalysis(MRA)

Spindle speed, feed rate, and depth of cut

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.

rinivas et al. 2007)

PSO Cutting speed, feed, depth of cut

Turning PSO give stable optimal feasible solutions wi1 reasonable computational time.

'osta et al. 2010)

HybridPSO-SA

Cutting speed, feed, depth of cut

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

Setting values of experimental cutting condition

Ra predicted values (jam)

No Datasource

v (m/min) /(mm/tooth)

Y (°) /?uncoated /tTiAIN /?SNtr

1 130 0.03 7 0.365 0.32 0.2842 160 0.03 7 0.256 0.266 0.1963 130 0.07 7 0.498 0.606 0 . 6 6 8

4 160 0.07 7 0.464 0.476 0.6245 130 0.03 13 0.428 0.260 0.2806 DOE

2 k160 0.03 13 0.252 0.232 0.190

7 130 0.07 13 0.561 0.412 0.6128 160 0.07 13 0.512 0.392 0.5769 144.22 0.046 9.5 0.464 0.324 0.329

1 0 144.22 0.046 9.5 0.444 0.380 0.4161 1 144.22 0.046 9.5 0.448 0.460 0.3521 2 144.22 0.046 9.5 0.424 0.304 0.40013 Centre 124.53 0.046 9.5 0.328 0.360 0.34414 124.53 0.046 9.5 0.324 0.308 0.32015 167.03 0.046 9.5 0.236 0.340 0.27216 167.03 0.046 9.5 0.240 0.356 0.28817 144.22 0.025 9.5 0.252 0.308 0.23018 144.22 0.025 9.5 0.262 0.328 0.23419 144.22 0.083 9.5 0.584 0.656 0.6402 0 144.22 0.083 9.5 0.656 0.584 0.6962 1 Axial 144.22 0.046 6 . 2 0.304 0.300 0.3612 2 144.22 0.046 6 . 2 0.288 0.316 0.36023 144.22 0.046 14.8 0.316 0.324 0.36824 144.22 0.046 14.8 0.348 0.396 0.360

Ra (minimum) 0.236 0.232 0.190

42

2.6.2 AWJ machining

In AWJ machining, the experiment condition material of machined

workpiece is Al 7075-T6 wrought alloy (AlZnMgCul.5). The chemical composition

of Al 7075-T6 wrought alloy includes Al 91.02%, Cu 1.65%, Mg 2.0%, Cr 0.23%,

Zn 5% and Mn 0.1%.

2.6.2.1 AWJ experimental design

The coded level form for the machining is based on DOE for the five process

parameters is defined in Table 2.9. During the experiments, a distance of 5mm from

the top of the cutting surface was taken for the measurements. A handy device named

SJ-201 was used to measure the average Ra. In order to examine the machined

surface another device named LEO 32 scanning electron microscope (SEM) was

used.

Table 2.9: Levels of process parameters and coding identification

Level in coded form

Independent Variables Units 1 2 3

Traverse speed, V mm/min 50 1 0 0 150

Waterjet pressure, P MPa 125 175 250

Standoff distance, h Mm 1 2.5 4

Abrasive grit size, d lm 60 90 1 2 0

Abrasive flow rate, m g/s 0.5 2 3.5

43

2.6.2.2 AWJ experimental results

A total of 27 experiments has been performed based on L27 Taguchi’s

orthogonal array to find the minimum and average value of Ra in AWJ machining

The lowest Ra values is 2.124 which was obtained by the following process

parameters V = 50, P = 125, h =1, d = 60, m = 0.5. The values for each

experimental AWJ process parameters and optimal Ra are shown in Table 2.10.

Table 2.10: Ra values for real machining

No Setting values of experimental process parameters Ra (nm)

V (m/min) P (MPa) h (mm) d (jam) m (g/s)

1 50 125 1 60 0.5 2.1242 50 125 1 60 2 2.7533 50 125 1 60 3.5 3.3524 50 175 2.5 90 0.5 4.3115 50 175 2.5 90 2 4.5416 50 175 2.5 90 3.5 5.1237 50 250 4 1 2 0 0.5 6.7898 50 250 4 1 2 0 2 7.5249 50 250 4 1 2 0 3.5 9.123

1 0 1 0 0 125 2.5 1 2 0 0.5 3.5751 1 1 0 0 125 2.5 1 2 0 2 4.4571 2 1 0 0 125 2.5 1 2 0 3.5 5.62813 1 0 0 175 4 60 0.5 7.01014 1 0 0 175 4 60 2 7.53515 1 0 0 175 4 60 3.5 7.89316 1 0 0 250 1 90 0.5 8 . 1 2 1

17 1 0 0 250 1 90 2 8.31218 1 0 0 250 1 90 3.5 9.16319 150 125 4 90 0.5 4.3282 0 150 125 4 90 2 5.1202 1 150 125 4 90 3.5 5.8522 2 150 175 1 1 2 0 0.5 6.14323 150 175 1 1 2 0 2 6.72124 150 175 1 1 2 0 3.5 7.78025 150 250 2.5 60 0.5 8.89026 150 250 2.5 60 2 9.12027 150 250 2.5 60 3.5 10.035

Ra (minimum) 2.124

44

2.7 Summary

This chapter has presented a literature review on optimization of both end

milling and AWJ machining operations. The efficiency of ABC algorithm was

shown in a various research of related domain and problems. Experiment designs for

Ra measurement based on Mohruni (2008) and Caydas and Hascalik, (2008) effort

have been discussed. In the next chapter, the methodology of ABC optimization for

finding the Ra values is presented.

CHAPTER 3

METHODOLOGY

3.1 Introduction

The primary focus of this section is to discuss and investigate the

methodology that is accomplished in this research. This includes discussing the

process flow that is required for the implementation of this research. This chapter

also explained each step involved in developing ABC algorithm to minimize Ra of

machining performance measurement.

Two types of machining operations are used in this research which is end

milling (traditional machining) and AWJ (modem machining). The experimental

data set was based on effort by Mohruni (2008) for end milling operation and Caydas

and Hascalik (2008) for AWJ operation. Subsequently, for each machining operation,

the regression model is developed and the Ra value is calculated. The most minimum

Ra value of predicted equation in each machining is used as the fitness function of

ABC. Consequently, ABC optimization is performed to find the optimal process

parameters for both machining operations. Finally, the results are evaluated with the

experimental, regression modeling, GA optimization and SA optimization.

46

Figure 3.1 Flow of searching for optimum process parameters

47

3.2 Research flow

In this part, the flow of the process for searching the optimal process

parameters that lead to Ra value is explained. There are four phases that is

implemented in this research, which are:

i. Assessment of real experimental data

ii. Regression modeling development

iii. ABC algorithm for optimization of process parameters

iv. Validation and evaluation of results

These phases and process steps for searching the optimal process parameters

are illustrated in the Figure 3.1.

3.3 Assessment of real experimental data

The evaluation and results of real experimental data for both machining

operations are discussed in Section 2.6. This experimental evaluation is based on

effort attempted by Mohruni (2008) and also Caydas and Hascalik (2008).

3.4 Regression modeling development

Regression modeling is concerned in predicting of one variable from one or

more variables and grants the scientist with a great tool and provides the information.

The information afterward allows the scientist to decide what action that needs to be

taken. The regression modeling is timeless and less costly to gather the information

to make the predictions (Stockburger, 1996).

3.4.1 Regression modeling in end milling

48

For end miling machining, three types of cutting tools which is uncoated

carbide (WC-Co) and two TiAIN coated carbide tools which comprise of PVD-

TiAlN coated carbide tool and PVD with enriched Al-content TiAIN coated carbide

tools or Supemitride coating (SNTr) will be assessed for the experiments.

The regular equation is defined precisely as (3.1) to discover the value of Ra

in end milling:

Ra = cv f l y m £' (3.1)

In equation (3.1), Ra is the calculated surface roughness in jam, v is the

cutting speed in m /m in,/is the feed in mm/tooth, y is radial rake angle in ° and c, k,

I, m are the model parameters approximated through experiments.

The equation (3.1) subsequently is linearized by executing a logic

transformation in (3.2) to develop regression model.

In Ra = In c + k In v + / ln /+ m In y + In £’ (3.2)

Equation (3.2) can be written as:

y = box o + b\X\ + biXi + 6 3 X3 + £ (3.3)

In equation (3.3), y is the logarithmic value of the experimental Ra, xq = 1 is an

artificial variable, x\, x2 and x3 are referring to the cutting condition values

(logarithmic transformations) of cutting speed (v), feed rate if) and radial rake angle

(y) correspondingly, £ is the logarithmic transformation of experimental error £’ and

bo, b\, hi and Z>3 are the model parameters to be estimated using the experimental

data.

Equation (3.3) can also be written as follows:

p — y - £ = Z>oXo + 6 1 X1 + biXi + 6 3 X3 (3.4)

49

In equation (3.4) y is the logarithmic value of the predictive (estimated) Ra. Then,

this equation will be proposed as the fitness function of the optimization solution.

3.4.1.1 Regression Model for Each Cutting Tool

The values of coefficients for each cutting tool are demonstrated in

Table 3.1, 3.2 and 3.3. Each of this value is reassigned in equation (3.4) and written

as follows:

y \ = /Tuncoated = 0.451 - 0.00267*1 + 5.671*2 + 0.0046*3 (3.5a)

y l = /tTiAIN = 0.292 - 0.000855*1 + 5.383*2 - 0.00553*3 (3.5b)

v3 = /?SNtr = 0.237 - 0.00175*1 + 8.693*2 + 0.00159*3 (3.5c)

Table 3.1: Uncoated Tool coeffients value

Unstandardizec coefficients Standardized coeffientsIndependent variable B Std.error Beta t Sig

1 (Constant) 0.451 0.175 2.582 0.018SPEED -2.67^-03 0.001 -0.277 -2.407 0.026FEED 5.671 0.811 0.805 6.994 0

RAKE ANGLE 4.60E-03 0.005 0.097 0.842 0.412 (Constant) 0.386 0.025 15.627 0

Table 3.2: TiAIN coated Tool coeffients value


1 (Constant) 0.292 0.158 1.85 0.079SPEED -8.55E-04 0.001 -0.098 -0.854 0.403FEED 5.383 0.731 0.843 7.36 0

RAKE ANGLE -5.53E-03 0.005 -0.129 -1.122 0.2752 (Constant) 0.375 0.022 16.771 0

50

Table 3.3: SNTr coated Tool coeffients value


1 (Constant) 0.237 0.116 2.042 0.055SPEED -1.75E-03 0.001 -0.14 -2.368 0.028FEED 8.693 0.539 0.954 16.143 0

RAKE ANGLE -1.59E-03 0.004 -0.026 -0.437 0.6672 (Constant) 0.392 0.032 12.261 0

Equations (3.5a) to (3.5c) are then used to compute the predicted Ra values,

and the results are potted in Table 3.4. To confirm the best regression model as the

fitness function in ABC algorithm, paired-sample t -test was performed, and the

results are summarized in Tables 3.5 and 3.6.

Table 3.4: Ra predicted values of regression modelling (Zain et al, 2010a)

Setting values of experimental cutting condition

Ra predicted values (jam)

No Datasource

v (m/min) /(mm/tooth)

Y (°) /?uncoated /?TiAlN /?SNtr

1 130 0.03 7 0.306 0.304 0.2592 160 0.03 7 0.226 0.278 0.2073 130 0.07 7 0.533 0.519 0.6074 DOE 160 0.07 7 0.453 0.493 0.5545 2k 130 0.03 13 0.334 0.270 0.2506 160 0.03 13 0.254 0.245 0.1977 130 0.07 13 0.561 0.486 0.5978 160 0.07 13 0.481 0.460 0.5459 144.22 0.046 9.5 0.370 0.364 0.36910 144.22 0.046 9.5 0.370 0.364 0.36911 144.22 0.046 9.5 0.370 0.364 0.36912 Centre 144.22 0.046 9.5 0.370 0.364 0.36913 124.53 0.046 9.5 0.423 0.381 0.40414 124.53 0.046 9.5 0.423 0.381 0.40415 167.03 0.046 9.5 0.310 0.344 0.32916 167.03 0.046 9.5 0.310 0.344 0.32917 144.22 0.025 9.5 0.251 0.251 0.18718 144.22 0.025 9.5 0.251 0.251 0.18719

Axial144.22 0.083 9.5 0.580 0.563 0.691

20 144.22 0.083 9.5 0.580 0.563 0.69121 144.22 0.046 6.2 0.355 0.382 0.37422 144.22 0.046 6.2 0.355 0.382 0.37423 144.22 0.046 14.8 0.395 0.334 0.36124 144.22 0.046 14.8 0.395 0.334 0.361

Ra (minimum) 0.226 0.245 0.187

52

Table 3.5: Statistics and correlations for paired samples

Pair Variable Mean N

Std.

deviation

Std.error

mean

Correlation

(Pearson)

Sig

Pair 1 EXP UNCO

REG UNCO

0.38558

0.38567

24

24

0.12088

0.10363

2.47E-02

2.12E-02

0.857 0.000

Pair 2 EXP_TiAlN

REG_TiAlN

0.37533

0.37587

24

24

0.10964

9.42E-02

2.24E-02

1.92E-02

0.859 0.000

Pair 3 EXP_SNTr

REG_ SNtr

0.39167

0.39100

24

24

0.1565

0.1509

3.19E-02

3.08E-02

0.965 0.000

Table 3.5 indicates that for each pair of regression modeling data are

positively correlated. With r (N= 24), pair 1 correlation is 0.857, pair 2 correlation is

0.859, and pair 3 correlation is 0.965. Whereas results in Table 3.6 signify that the

mean Ra value for pair 1 enhanced from the experimental result to the uncoated

regression model by 0.0000833, t{23)= -0.007, p = 0.995. The 95% confidence

interval ranges from -0.0264 to 0.0263 (including zero).

For that reason, the two means of experimental result and regression model

results are not drastically different from each other. The mean Ra value for pair 2 also

improved from the experimental result to the TiAIN regression model by 0.000542,

t{23)= -0.047, p = 0.963. The 95% confidence interval ranges from -0.0243 to

0.0232 (including zero), which also proves that the two means are not drastically

different from each other.

53

Table 3.6: Paired samples test

Paired differences

95% Confidence Interval of the difference

Pair Mean Std.

Deviation

Std.

error

Mean

Lower Upper T Df Sig.

(2

tailed)

Pair

1

-8.33E-05 6.24E-02 1.27E-02 -2.64E-02 2.63E-02 0.007 23 0.995

Pair

2

-5.42E-04 5.62E-02 1.15E-02 -2.43E-02 2.32E-02 -0.047 23 0.963

Pair

3

6.67E-04 4.13E-02 8.43E-03 -1.68E-02 1.81E-02 0.079 23 0.938

From Table 3.6, it can be seen that the mean Ra value for pair 3 however

reduced from the experimental result to the S N tr regression model by 0.000667,

?(23)=0.079, p = 0.938. The 95% confidence interval ranges from -0.0168 to 0.0181

(including zero). Thus, the two means too are not significantly different from each

other. As a conclusion, it could be summarized that the S N tr coated cutting tool has

given the highest positive correlation and is the only pair that indicated a reduction in

the mean Ra value from the experimental result.

As a result, it can be recommended that the predicted Ra equation of S N tr

coated tools as given in Equation (5c) is the best regression model and it is proposed

to be the fitness function of the ABC optimization.

3.4.2 Regression modeling in abrasive waterjet

54

To calculate the value of Ra in abrasive waterjet machining, it is defined

mathematically in (3.6):

Ra = cVqFf hs cf mu (3.6)

where Ra is the experimental (measured) in jam, V is the traverse cutting speed in

mm/min, P is the waterjet pressure in MPa, h is the standoff distance in mm, d is

abrasive grit size in jam, m is the abrasive flow rate in g/s, £' is experimental error,

and c, q, r, s, t, and u are the model parameters to be estimated using the

experimental data.

To develop the Regression model for estimating the Ra value, the

mathematical model given in (3.6) is linearized by performing a logarithmic

transformation as follows:

In Ra = In c + q In V+ r In P + s In h + t In d + u In m + In £' (3.7)

Subsequently, (3.9) can be written as:

y = boXo + b\X\ + bjXj + 6 3 X3 + 6 4X4 + 6 5 X5+ £ (3.8)

where y is the logarithmic value of the experimental Ra, x0 = 1 is a dummy variable,

xi, X2 , X3 , X4 and X5 are the process parameter values (logarithmic transformations) of

V, P, h, d and m, respectively, £ is the logarithmic transformation of experimental

error £' and bo, bi, b3 , b4 and bs are the model parameters to be estimated using the

experimental data.

Next, (3.8) can also be written as follows:

y = y - £ = Z>oXo + 6 1 X1 + bjXj + 6 3 X3 + 6 4 X4 + 6 5 X5 (3.9)

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

(V), waterjet pressure (P), standoff distance (h), abrasive grit size (d), abrasive flow

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:

Ra= 0.237 - 0.00175 jq+ 8.693 x2 + 0.00159 x3 (4.1)

where x\ is the cutting speed (v) in m/min, xn is the feed (f) in mm/tooth and X3 is the radial rake angle (y) in

For AWJ machining, the objective function is:

Ra = -5.07976 + 0.08169 xi + 0.07912 x2 - 0.34221 x3- 0.08661 x4- 0.34866 x5-

0.00031 x i2 - 0.00012 x2 2 + 0.10575 x3 2 + 0.00041 x4 2 + 0.07590 x5 2 - 0.00008 xi x5

- 0.00009 x2 X5 + 0.03089 X3 X5 + 0.00513 X4 X5 (4.2)

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 >

Min Value, Fitnes & Mean of Fitness/Cycle

1 r

0.9 -

0.8 -

0.7 -

0.6 -

0.5 -

0.4 -

0.3 -

0.2 -

0.1 -

0---------- 1---------- 1---------- 1---------- 1---------- 10 0.2 0.4 0.6 0.8 1

Function for: End Milling

Colony S ize :

Number of Run:

Max Cycles per Run :

Limit (abandoned food):

i— Parameters Range—

X1 X2 X3 X4 X5

Uppest Threshold:

Jl jE T 110

Lowest Threshold:

130 0.000375

All best valuesA'un

Num.Cycles MinValue X I

Ready

l° i Ii -I

Figure 4.1 ABC Matlab program interface

To find the optimal process parameters and minimum Ra values, both end

milling and AWJ have similar steps to be performed. The only difference is the

number of parameters to be optimized and the range of the process parameters. The

process parameters are referred to the threshold value for lower and upper

parameters. The upper threshold (UT) and lower threshold (LT) value for parameters

usually depends on the technical specification of the machining. The threshold range

value was taken from available reference and also based on previous experiments.

According to Zain et al. (2010a), there is no guideline yet given by the researchers

which could be followed in recommending the best combination for setting the value

of process parameters for the best optimal result.

69

In the experiments of both end milling and AWJ, ABC employed control parameters

are as follows:

i. Colony size refers to the number of bees in the colony (employed bees plus

onlooker bees).

ii. Limit where it controls of the number of trials to improve certain food source.

If a food source could not be improved within defined number of trial, it is

abandoned by its employed bee. In the ABC, the parameter limit is calculated

using the formula SN*D, where SN is the number of solutions and D is the

number of variables of the problem.

iii. Maximum Cycle per run defines the number of cycles for foraging. This is a

stopping criterion.

The problem specific parameters are:

i. Number of run defines the number of times to run the algorithm.

ii. Lower bound where it is the lower threshold (LT) value of problem

parameters.

iii. Upper bound where it is the upper threshold value (UT) of problem

parameters.

Each of the experiments has been repeated by 10 runs. It is important to note that

each run complete maximum cycle number. In the experiment, the values of

maximum cycle number and colony size tested were 10, 20, 50 and 100.

The UT and LT threshold value used for end milling in the experiments is as follows:

124.53m/min < x\ <167.03m/min (4.3)

0.025mm/tooth < x2< 0.083mm/tooth (4.4)

6.2 ° < x 3< 14.8° (4.5)

The UT and LT threshold value used for AWJ in the experiments is as follows:

50mm/min <x\ < 150 mm/m in (4.6)

125Mpa < x2 < 250Mpa (4.7)

1mm < X3 < 4mm (4.8)

60(j,m < X4 < 120(j,m (4.9)

0.5g/s < X5 < 3.5g/s (4.10)

The threshold value (upper and lower) for parameters which is set at initial (before

the program run) is affecting the result of ABC algorithm and the number of iteration

to be processed

71

The general pseudocode of ABC in optimizing process parameters of Ra in end

milling and AWJ machining:

Do Initial Step

{Define limit

Do initiate trial array = 0.

Do generate food matrix randomly which each value is within range UT and

LT.

Do calculate and get minimum objective value for food matrix.

Do calculate and get the best fitness value.

Do store first minimum value, best parameters pair value and fitness value.

}Iteration = 0.

While Iteration < maxCycle

Do Employed-bee Phase

{For i = 1 to number of food source

Determine randomly index of parameters ip) to be changed.

Determine randomly index of the value (z) to be changed.

Perform mutation for parameter P(i,z) and assign to new Solution

S (i,z).

Calculate S(/,z) = = S(/,z) + { (S(/,z)- S(/;,z))*random }.

Perform shift value in S(/',z) into between UT and LT.

Evaluate new Parameter S(/',z):

If it’s fitness value is better than P (i,z) then replace P (i,z) with

S (i,z) with greedy selection.

Reset trial (/) = 0.

Else increment trial (/).

End For

72

Do calculate probability.

}Do Onlooker-bee Phase

{Initiate control variable t = 0, iteration i = 0.

While t < number of food source

Generate random value rand.

If probability(7) > rand then: increment t and perform employed-bee

phase again.

Increment i

End While

Store the best parameters and minimum objective value to matrix Global

Parameters (GP) and Global Value (GV) respectively.

Do Scout-bee Phase

{For i = 1 to number of value in trial array

If trial (i) equal to limit then generate new parameters value randomly

and replace the old parameters value with the new one.

Calculate objective value and fitness value for current parameters.

EndFor

Find minimum value inside GV.

Find the best parameter inside GP, based on the minimum value inside GV.

Increment Iteration value.

End While

73

The details for each phases is given as the following four sections:

4.3 Initial phase

The initial phase is the first step before ABC algorithm is executed. The

purpose of this step is to initiate parameters and control variables. In this step, the

initial values of Food matrix (D x N matrix) is also generated, where D is the number

of parameters to be optimized and N is the number of food source, that is equal to

the number of employed or onlooker-bee, or equal to colony size. The food matrix is

a matrix of candidate of the best parameters. Each value in food matrix is in range

between LT and UT.

For example, assume that the food source is 10 then the food matrix for end

milling (three parameters) and AWJ (five parameters) are:

End Milling AWJ

X (l,l) X( 1,2) X(l,3) X (l,l) X(l,2) X(l,3) X(l,4) X(l,5) } Parameters pair

X(2,l) X(2,2) X(2,3) X(2,l) X(2,2) X(2,3) X(2,4) X(2,5)

X(3,l) X(3,2) X(3,3) X(3,l) X(3,2) X(3,3) X(3,4) X(3,5)

X(9,l) X(9,2) X(9,3) X(9,l) X(9,2) X(9,3) X(9,4) X(9,5)

X(10,l) X(10,2)X(10,3) X(10,l) X(10,2)X(10,3)X(10,4)X(10,5)

Where each row of the matrix is a parameters pair.

After the program initiates the food matrix, then it will begin to evaluate the

food matrix for the first time. The program calculates the objective value and the

fitness value for each pair (each row) of parameter in food matrix. Subsequently the

program “memorizes” the best one by storing the minimum objective value and the

74

best parameters value respectively in a matrix GV and GP. The program also initiates

values in trial array to 0. Trial array is an array that contains values to store how

many times unfit conditions is met during execution of ABC algorithm (if the food

source or the parameters pair cannot be optimized anymore, the program will

increment the corresponding trial value). The trial value next will be compared to a

local control variable called limit. And a variable called maxCycle is defined as a

global control variable, which determines maximum iteration that three ABC phases

(Employed-bee Phase, Onlooker-bee Phase and Scout-bee Phase) should run.

Hence, in this initial step, the program gets the first best parameters value

(that give the minimum objective value), the first minimum objective value and the

best fitness value.

4.4 Employed-bee Phase

In this phase, the program performs a mutation on each value in the food

matrix. If a pair of parameters (in which mutated value occurred) is giving the better

fitness value than the previous fitness value (before any value inside that parameters

pair is changed), then related value in this pair of parameter was changed by applying

a greedy algorithm.

The parameters pair which the value inside is being changed is called

solution. The new value is determined by using equation 5.3:

X(i,j) = X(i,j) + { (X(i,j) - X(p,j))*random } (5.3)

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


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.



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:


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


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


fitness

Mean

fitness

1 0.2232 167.0300 0.0307 7.5555 0.8175 0.68642 0.2230 167.0300 0.0307 7.4056 0.8177 0.70053 0.2230 167.0300 0.0307 7.4056 0.8177 0.70184 0.1738 167.0300 0.0250 7.4056 0.8519 0.70985 0.1738 167.0300 0.0250 7.4056 0.8519 0.71136 0.1719 167.0300 0.0250 6.2000 0.8533 0.71497 0.1719 167.0300 0.0250 6.2000 0.8533 0.74098 0.1719 167.0300 0.0250 6.2000 0.8533 0.74159 0.1719 167.0300 0.0250 6.2000 0.8533 0.748010 0.1719 167.0300 0.0250 6.2000 0.8533 0.750611 0.1719 167.0300 0.0250 6.2000 0.8533 0.764212 0.1719 167.0300 0.0250 6.2000 0.8533 0.767813 0.1719 167.0300 0.0250 6.2000 0.8533 0.768814 0.1719 167.0300 0.0250 6.2000 0.8533 0.784615 0.1719 167.0300 0.0250 6.2000 0.8533 0.803216 0.1719 167.0300 0.0250 6.2000 0.8533 0.813017 0.1719 167.0300 0.0250 6.2000 0.8533 0.813018 0.1719 167.0300 0.0250 6.2000 0.8533 0.818419 0.1719 167.0300 0.0250 6.2000 0.8533 0.819320 0.1719 167.0300 0.0250 6.2000 0.8527 0.7895

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


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


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


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



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



fitness

Mean

fitness

1 0.2232 167.0300 0.0307 7.5555 0.8175 0.68642 0.2230 167.0300 0.0307 7.4056 0.8177 0.70053 0.2230 167.0300 0.0307 7.4056 0.8177 0.70184 0.1738 167.0300 0.0250 7.4056 0.8519 0.70985 0.1738 167.0300 0.0250 7.4056 0.8519 0.71136 0.1719 167.0300 0.0250 6.2000 0.8533 0.71497 0.1719 167.0300 0.0250 6.2000 0.8533 0.74098 0.1719 167.0300 0.0250 6.2000 0.8533 0.74159 0.1719 167.0300 0.0250 6.2000 0.8533 0.748010 0.1719 167.0300 0.0250 6.2000 0.8533 0.750611 0.1719 167.0300 0.0250 6.2000 0.8533 0.764212 0.1719 167.0300 0.0250 6.2000 0.8533 0.767813 0.1719 167.0300 0.0250 6.2000 0.8533 0.768814 0.1719 167.0300 0.0250 6.2000 0.8533 0.784615 0.1719 167.0300 0.0250 6.2000 0.8533 0.803216 0.1719 167.0300 0.0250 6.2000 0.8533 0.813017 0.1719 167.0300 0.0250 6.2000 0.8533 0.813018 0.1719 167.0300 0.0250 6.2000 0.8533 0.818419 0.1719 167.0300 0.0250 6.2000 0.8533 0.819320 0.1719 167.0300 0.0250 6.2000 0.8527 0.789521 0.1719 167.0300 0.0250 6.2000 0.8527 0.792822 0.1719 167.0300 0.0250 6.2000 0.8527 0.793023 0.1719 167.0300 0.0250 6.2000 0.8527 0.798324 0.1719 167.0300 0.0250 6.2000 0.8527 0.802625 0.1719 167.0300 0.0250 6.2000 0.8527 0.813726 0.1719 167.0300 0.0250 6.2000 0.8529 0.815427 0.1719 167.0300 0.0250 6.2000 0.8533 0.821228 0.1719 167.0300 0.0250 6.2000 0.8533 0.821529 0.1719 167.0300 0.0250 6.2000 0.8533 0.8215

84

30 0.1719 167.0300 0.0250 6.2000 0.8533 0.822131 0.1719 167.0300 0.0250 6.2000 0.8533 0.822532 0.1719 167.0300 0.0250 6.2000 0.8533 0.826033 0.1719 167.0300 0.0250 6.2000 0.8533 0.829034 0.1719 167.0300 0.0250 6.2000 0.8533 0.829235 0.1719 167.0300 0.0250 6.2000 0.8533 0.829236 0.1719 167.0300 0.0250 6.2000 0.8533 0.833137 0.1719 167.0300 0.0250 6.2000 0.8533 0.833238 0.1719 167.0300 0.0250 6.2000 0.8533 0.835939 0.1719 167.0300 0.0250 6.2000 0.8533 0.839540 0.1719 167.0300 0.0250 6.2000 0.8533 0.839641 0.1719 167.0300 0.0250 6.2000 0.8533 0.841742 0.1719 167.0300 0.0250 6.2000 0.8533 0.842243 0.1719 167.0300 0.0250 6.2000 0.8533 0.803544 0.1719 167.0300 0.0250 6.2000 0.8533 0.804045 0.1719 167.0300 0.0250 6.2000 0.8533 0.809446 0.1719 167.0300 0.0250 6.2000 0.8533 0.812147 0.1719 167.0300 0.0250 6.2000 0.8533 0.812148 0.1719 167.0300 0.0250 6.2000 0.8533 0.820149 0.1719 167.0300 0.0250 6.2000 0.8533 0.822750 0.1719 167.0300 0.0250 6.2000 0.8533 0.8228

85

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


R a = 0.237 — (0.00175 x tc 1} -4- (3 693 x x2) •+■ (0.00159 x x3>

10


Colony S ize :

Number of Run:

Max Cycles per Run:



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


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


Cycle


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



fitness

Mean

fitness

1 0.2232 167.0300 0.0307 7.5555 0.8175 0.68642 0.2230 167.0300 0.0307 7.4056 0.8177 0.70053 0.2230 167.0300 0.0307 7.4056 0.8177 0.70184 0.1738 167.0300 0.0250 7.4056 0.8519 0.70985 0.1738 167.0300 0.0250 7.4056 0.8519 0.71136 0.1719 167.0300 0.0250 6.2000 0.8533 0.71497 0.1719 167.0300 0.0250 6.2000 0.8533 0.74098 0.1719 167.0300 0.0250 6.2000 0.8533 0.74159 0.1719 167.0300 0.0250 6.2000 0.8533 0.748010 0.1719 167.0300 0.0250 6.2000 0.8533 0.750611 0.1719 167.0300 0.0250 6.2000 0.8533 0.764212 0.1719 167.0300 0.0250 6.2000 0.8533 0.767813 0.1719 167.0300 0.0250 6.2000 0.8533 0.768814 0.1719 167.0300 0.0250 6.2000 0.8533 0.784615 0.1719 167.0300 0.0250 6.2000 0.8533 0.803216 0.1719 167.0300 0.0250 6.2000 0.8533 0.813017 0.1719 167.0300 0.0250 6.2000 0.8533 0.813018 0.1719 167.0300 0.0250 6.2000 0.8533 0.818419 0.1719 167.0300 0.0250 6.2000 0.8533 0.819320 0.1719 167.0300 0.0250 6.2000 0.8527 0.789521 0.1719 167.0300 0.0250 6.2000 0.8527 0.792822 0.1719 167.0300 0.0250 6.2000 0.8527 0.793023 0.1719 167.0300 0.0250 6.2000 0.8527 0.798324 0.1719 167.0300 0.0250 6.2000 0.8527 0.802625 0.1719 167.0300 0.0250 6.2000 0.8527 0.813726 0.1719 167.0300 0.0250 6.2000 0.8529 0.815427 0.1719 167.0300 0.0250 6.2000 0.8533 0.821228 0.1719 167.0300 0.0250 6.2000 0.8533 0.821529 0.1719 167.0300 0.0250 6.2000 0.8533 0.8215

87

30 0.1719 167.0300 0.0250 6.2000 0.8533 0.822131 0.1719 167.0300 0.0250 6.2000 0.8533 0.822532 0.1719 167.0300 0.0250 6.2000 0.8533 0.826033 0.1719 167.0300 0.0250 6.2000 0.8533 0.829034 0.1719 167.0300 0.0250 6.2000 0.8533 0.829235 0.1719 167.0300 0.0250 6.2000 0.8533 0.829236 0.1719 167.0300 0.0250 6.2000 0.8533 0.833137 0.1719 167.0300 0.0250 6.2000 0.8533 0.833238 0.1719 167.0300 0.0250 6.2000 0.8533 0.835939 0.1719 167.0300 0.0250 6.2000 0.8533 0.839540 0.1719 167.0300 0.0250 6.2000 0.8533 0.839641 0.1719 167.0300 0.0250 6.2000 0.8533 0.841742 0.1719 167.0300 0.0250 6.2000 0.8533 0.842243 0.1719 167.0300 0.0250 6.2000 0.8533 0.803544 0.1719 167.0300 0.0250 6.2000 0.8533 0.804045 0.1719 167.0300 0.0250 6.2000 0.8533 0.809446 0.1719 167.0300 0.0250 6.2000 0.8533 0.812147 0.1719 167.0300 0.0250 6.2000 0.8533 0.812148 0.1719 167.0300 0.0250 6.2000 0.8533 0.820149 0.1719 167.0300 0.0250 6.2000 0.8533 0.822750 0.1719 167.0300 0.0250 6.2000 0.8533 0.822851 0.1719 167.0300 0.0250 6.2000 0.8533 0.824252 0.1719 167.0300 0.0250 6.2000 0.8533 0.824353 0.1719 167.0300 0.0250 6.2000 0.8533 0.824354 0.1719 167.0300 0.0250 6.2000 0.8533 0.829755 0.1719 167.0300 0.0250 6.2000 0.8533 0.830356 0.1719 167.0300 0.0250 6.2000 0.8533 0.830357 0.1719 167.0300 0.0250 6.2000 0.8533 0.809658 0.1719 167.0300 0.0250 6.2000 0.8533 0.810259 0.1719 167.0300 0.0250 6.2000 0.8533 0.810260 0.1719 167.0300 0.0250 6.2000 0.8533 0.810761 0.1719 167.0300 0.0250 6.2000 0.8533 0.780862 0.1719 167.0300 0.0250 6.2000 0.8533 0.7533

88

63 0.1719 167.0300 0.0250 6.2000 0.8533 0.756364 0.1719 167.0300 0.0250 6.2000 0.8533 0.765965 0.1719 167.0300 0.0250 6.2000 0.8533 0.767366 0.1719 167.0300 0.0250 6.2000 0.8533 0.769067 0.1719 167.0300 0.0250 6.2000 0.8533 0.769668 0.1719 167.0300 0.0250 6.2000 0.8533 0.780169 0.1719 167.0300 0.0250 6.2000 0.8533 0.789670 0.1719 167.0300 0.0250 6.2000 0.8113 0.769871 0.1719 167.0300 0.0250 6.2000 0.8186 0.761172 0.1719 167.0300 0.0250 6.2000 0.8288 0.768673 0.1719 167.0300 0.0250 6.2000 0.8288 0.774374 0.1719 167.0300 0.0250 6.2000 0.8460 0.782675 0.1719 167.0300 0.0250 6.2000 0.8481 0.783076 0.1719 167.0300 0.0250 6.2000 0.8481 0.797377 0.1719 167.0300 0.0250 6.2000 0.8483 0.805978 0.1719 167.0300 0.0250 6.2000 0.8488 0.813279 0.1719 167.0300 0.0250 6.2000 0.8488 0.813880 0.1719 167.0300 0.0250 6.2000 0.8490 0.816481 0.1719 167.0300 0.0250 6.2000 0.8511 0.817082 0.1719 167.0300 0.0250 6.2000 0.8528 0.819483 0.1719 167.0300 0.0250 6.2000 0.8528 0.820584 0.1719 167.0300 0.0250 6.2000 0.8530 0.821485 0.1719 167.0300 0.0250 6.2000 0.8530 0.825386 0.1719 167.0300 0.0250 6.2000 0.8532 0.827387 0.1719 167.0300 0.0250 6.2000 0.8533 0.827888 0.1719 167.0300 0.0250 6.2000 0.8533 0.831189 0.1719 167.0300 0.0250 6.2000 0.8533 0.834190 0.1719 167.0300 0.0250 6.2000 0.8533 0.836891 0.1719 167.0300 0.0250 6.2000 0.8533 0.838592 0.1719 167.0300 0.0250 6.2000 0.8533 0.839293 0.1719 167.0300 0.0250 6.2000 0.8533 0.839594 0.1719 167.0300 0.0250 6.2000 0.8533 0.842395 0.1719 167.0300 0.0250 6.2000 0.8533 0.8432

89

96 0.1719 167.0300 0.0250 6.2000 0.8533 0.843297 0.1719 167.0300 0.0250 6.2000 0.8533 0.845098 0.1719 167.0300 0.0250 6.2000 0.8533 0.845399 0.1719 167.0300 0.0250 6.2000 0.8533 0.8453100 0.1719 167.0300 0.0250 6.2000 0.8533 0.8455

90


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.


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



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


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


Cycle


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



fitness

Mean

fitness

1 0.2132 161.4920 0.0286 6.5213 0.8242 0.75052 0.2072 153.2815 0.0250 13.2790 0.8284 0.75653 0.2011 167.0178 0.0284 6.2000 0.8326 0.76064 0.1746 167.0300 0.0250 7.9207 0.8513 0.77225 0.1746 167.0300 0.0250 7.9207 0.8513 0.77316 0.1746 167.0300 0.0250 7.9207 0.8513 0.78177 0.1745 167.0300 0.0250 7.8760 0.8514 0.78288 0.1745 167.0300 0.0250 7.8760 0.8514 0.78409 0.1739 167.0300 0.0250 7.4603 0.8519 0.785810 0.1725 167.0300 0.0250 6.5963 0.8529 0.7914

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;



R a = 0 237 — (0.00 175 x x l ) -+- (3 693 x x2) -+- (0.00 159 x x3>

20


Colony S ize :

Number of Run:

Max Cycles per Run:


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


C yc le


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


fitness

Mean

fitness

1 0.2298 137.1148 0.0250 9.6827 0.8132 0.71652 0.2298 137.1148 0.0250 9.6827 0.8132 0.72293 0.2057 150.8473 0.0250 9.6827 0.8294 0.73114 0.1806 165.2712 0.0250 9.7294 0.8470 0.74805 0.1805 165.2712 0.0250 9.7159 0.8471 0.74916 0.1805 165.2712 0.0250 9.7159 0.8471 0.75277 0.1805 165.2712 0.0250 9.7159 0.8471 0.75818 0.1781 165.2712 0.0250 8.1505 0.8489 0.76649 0.1778 165.2712 0.0250 7.9602 0.8491 0.773310 0.1775 165.2712 0.0250 7.8255 0.8492 0.775811 0.1719 167.0300 0.0250 6.2000 0.8533 0.778312 0.1719 167.0300 0.0250 6.2000 0.8533 0.782613 0.1719 167.0300 0.0250 6.2000 0.8533 0.788414 0.1719 167.0300 0.0250 6.2000 0.8533 0.795715 0.1719 167.0300 0.0250 6.2000 0.8533 0.797116 0.1719 167.0300 0.0250 6.2000 0.8533 0.798817 0.1719 167.0300 0.0250 6.2000 0.8533 0.799118 0.1719 167.0300 0.0250 6.2000 0.8533 0.800019 0.1719 167.0300 0.0250 6.2000 0.8533 0.800320 0.1719 167.0300 0.0250 6.2000 0.8533 0.8016

95

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



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:



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



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



96



fitness

Mean

fitness

1 0.1865 163.5834 0.0250 11.5787 0.8428 0.71902 0.1860 163.8355 0.0250 11.5787 0.8432 0.72143 0.1761 167.0300 0.0253 7.1985 0.8502 0.73624 0.1761 167.0300 0.0253 7.1985 0.8502 0.74155 0.1754 167.0300 0.0253 6.7027 0.8508 0.75006 0.1746 167.0300 0.0253 6.2000 0.8514 0.75627 0.1746 167.0300 0.0253 6.2000 0.8514 0.75698 0.1746 167.0300 0.0253 6.2000 0.8514 0.75909 0.1746 167.0300 0.0253 6.2000 0.8514 0.760810 0.1719 167.0300 0.0250 6.2000 0.8533 0.769711 0.1719 167.0300 0.0250 6.2000 0.8533 0.774212 0.1719 167.0300 0.0250 6.2000 0.8533 0.778413 0.1719 167.0300 0.0250 6.2000 0.8533 0.779014 0.1719 167.0300 0.0250 6.2000 0.8533 0.787115 0.1719 167.0300 0.0250 6.2000 0.8533 0.788816 0.1719 167.0300 0.0250 6.2000 0.8533 0.791917 0.1719 167.0300 0.0250 6.2000 0.8533 0.796418 0.1719 167.0300 0.0250 6.2000 0.8533 0.798619 0.1719 167.0300 0.0250 6.2000 0.8533 0.804420 0.1719 167.0300 0.0250 6.2000 0.8533 0.805221 0.1719 167.0300 0.0250 6.2000 0.8533 0.808822 0.1719 167.0300 0.0250 6.2000 0.8533 0.810623 0.1719 167.0300 0.0250 6.2000 0.8533 0.812824 0.1719 167.0300 0.0250 6.2000 0.8533 0.813025 0.1719 167.0300 0.0250 6.2000 0.8533 0.815926 0.1719 167.0300 0.0250 6.2000 0.8533 0.818927 0.1719 167.0300 0.0250 6.2000 0.8533 0.819928 0.1719 167.0300 0.0250 6.2000 0.8533 0.821629 0.1719 167.0300 0.0250 6.2000 0.8533 0.8217

97

30 0.1719 167.0300 0.0250 6.2000 0.8533 0.828131 0.1719 167.0300 0.0250 6.2000 0.8533 0.830332 0.1719 167.0300 0.0250 6.2000 0.8533 0.830633 0.1719 167.0300 0.0250 6.2000 0.8533 0.831634 0.1719 167.0300 0.0250 6.2000 0.8533 0.834335 0.1719 167.0300 0.0250 6.2000 0.8533 0.834436 0.1719 167.0300 0.0250 6.2000 0.8533 0.836237 0.1719 167.0300 0.0250 6.2000 0.8533 0.837838 0.1719 167.0300 0.0250 6.2000 0.8533 0.837839 0.1719 167.0300 0.0250 6.2000 0.8533 0.839240 0.1719 167.0300 0.0250 6.2000 0.8533 0.839741 0.1719 167.0300 0.0250 6.2000 0.8533 0.840442 0.1719 167.0300 0.0250 6.2000 0.8533 0.840643 0.1719 167.0300 0.0250 6.2000 0.8533 0.815144 0.1719 167.0300 0.0250 6.2000 0.8533 0.815845 0.1719 167.0300 0.0250 6.2000 0.8533 0.816446 0.1719 167.0300 0.0250 6.2000 0.8533 0.817847 0.1719 167.0300 0.0250 6.2000 0.8533 0.819848 0.1719 167.0300 0.0250 6.2000 0.8533 0.822649 0.1719 167.0300 0.0250 6.2000 0.8533 0.822950 0.1719 167.0300 0.0250 6.2000 0.8533 0.8313

98

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<



Ra = 0.237 — (0.00175 x x l) -4- (3 693 x x2) + (0.00159 x tc3>

10


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



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



fitness

Mean

fitness

1 0.2436 167.0300 0.0331 6.7848 0.8041 0.68902 0.1721 167.0300 0.0250 6.3459 0.8532 0.70093 0.1721 167.0300 0.0250 6.3459 0.8532 0.70564 0.1719 167.0300 0.0250 6.2000 0.8533 0.71555 0.1719 167.0300 0.0250 6.2000 0.8533 0.71876 0.1719 167.0300 0.0250 6.2000 0.8533 0.72657 0.1719 167.0300 0.0250 6.2000 0.8533 0.72818 0.1719 167.0300 0.0250 6.2000 0.8533 0.73449 0.1719 167.0300 0.0250 6.2000 0.8533 0.735310 0.1719 167.0300 0.0250 6.2000 0.8533 0.738411 0.1719 167.0300 0.0250 6.2000 0.8533 0.747512 0.1719 167.0300 0.0250 6.2000 0.8533 0.749513 0.1719 167.0300 0.0250 6.2000 0.8533 0.750714 0.1719 167.0300 0.0250 6.2000 0.8533 0.752215 0.1719 167.0300 0.0250 6.2000 0.8533 0.759316 0.1719 167.0300 0.0250 6.2000 0.8533 0.766217 0.1719 167.0300 0.0250 6.2000 0.8533 0.772418 0.1719 167.0300 0.0250 6.2000 0.8533 0.774419 0.1719 167.0300 0.0250 6.2000 0.8533 0.775220 0.1719 167.0300 0.0250 6.2000 0.8533 0.783221 0.1719 167.0300 0.0250 6.2000 0.8533 0.783722 0.1719 167.0300 0.0250 6.2000 0.8533 0.785823 0.1719 167.0300 0.0250 6.2000 0.8533 0.785824 0.1719 167.0300 0.0250 6.2000 0.8533 0.788625 0.1719 167.0300 0.0250 6.2000 0.8533 0.792426 0.1719 167.0300 0.0250 6.2000 0.8533 0.797027 0.1719 167.0300 0.0250 6.2000 0.8533 0.797628 0.1719 167.0300 0.0250 6.2000 0.8533 0.801429 0.1719 167.0300 0.0250 6.2000 0.8533 0.8040

10 0

30 0.1719 167.0300 0.0250 6.2000 0.8533 0.804231 0.1719 167.0300 0.0250 6.2000 0.8533 0.808432 0.1719 167.0300 0.0250 6.2000 0.8533 0.808833 0.1719 167.0300 0.0250 6.2000 0.8533 0.811334 0.1719 167.0300 0.0250 6.2000 0.8533 0.813435 0.1719 167.0300 0.0250 6.2000 0.8533 0.814436 0.1719 167.0300 0.0250 6.2000 0.8533 0.821337 0.1719 167.0300 0.0250 6.2000 0.8533 0.822838 0.1719 167.0300 0.0250 6.2000 0.8533 0.823639 0.1719 167.0300 0.0250 6.2000 0.8533 0.826140 0.1719 167.0300 0.0250 6.2000 0.8533 0.826941 0.1719 167.0300 0.0250 6.2000 0.8533 0.829842 0.1719 167.0300 0.0250 6.2000 0.8533 0.830143 0.1719 167.0300 0.0250 6.2000 0.8533 0.830344 0.1719 167.0300 0.0250 6.2000 0.8533 0.831145 0.1719 167.0300 0.0250 6.2000 0.8533 0.831346 0.1719 167.0300 0.0250 6.2000 0.8533 0.833147 0.1719 167.0300 0.0250 6.2000 0.8533 0.833148 0.1719 167.0300 0.0250 6.2000 0.8533 0.834649 0.1719 167.0300 0.0250 6.2000 0.8533 0.835750 0.1719 167.0300 0.0250 6.2000 0.8533 0.835851 0.1719 167.0300 0.0250 6.2000 0.8533 0.836052 0.1719 167.0300 0.0250 6.2000 0.8533 0.840353 0.1719 167.0300 0.0250 6.2000 0.8533 0.824354 0.1719 167.0300 0.0250 6.2000 0.8533 0.826755 0.1719 167.0300 0.0250 6.2000 0.8533 0.826856 0.1719 167.0300 0.0250 6.2000 0.8533 0.827357 0.1719 167.0300 0.0250 6.2000 0.8533 0.828258 0.1719 167.0300 0.0250 6.2000 0.8533 0.829959 0.1719 167.0300 0.0250 6.2000 0.8533 0.831360 0.1719 167.0300 0.0250 6.2000 0.8533 0.833961 0.1719 167.0300 0.0250 6.2000 0.8533 0.834862 0.1719 167.0300 0.0250 6.2000 0.8533 0.8350

101

63 0.1719 167.0300 0.0250 6.2000 0.8533 0.835664 0.1719 167.0300 0.0250 6.2000 0.8533 0.841065 0.1719 167.0300 0.0250 6.2000 0.8533 0.841466 0.1719 167.0300 0.0250 6.2000 0.8533 0.841567 0.1719 167.0300 0.0250 6.2000 0.8533 0.841768 0.1719 167.0300 0.0250 6.2000 0.8533 0.841869 0.1719 167.0300 0.0250 6.2000 0.8533 0.841970 0.1719 167.0300 0.0250 6.2000 0.8533 0.842171 0.1719 167.0300 0.0250 6.2000 0.8533 0.844872 0.1719 167.0300 0.0250 6.2000 0.8533 0.845173 0.1719 167.0300 0.0250 6.2000 0.8533 0.848174 0.1719 167.0300 0.0250 6.2000 0.8533 0.848475 0.1719 167.0300 0.0250 6.2000 0.8533 0.848476 0.1719 167.0300 0.0250 6.2000 0.8533 0.848677 0.1719 167.0300 0.0250 6.2000 0.8533 0.848878 0.1719 167.0300 0.0250 6.2000 0.8533 0.823379 0.1719 167.0300 0.0250 6.2000 0.8533 0.831580 0.1719 167.0300 0.0250 6.2000 0.8533 0.845881 0.1719 167.0300 0.0250 6.2000 0.8533 0.833182 0.1719 167.0300 0.0250 6.2000 0.8533 0.833683 0.1719 167.0300 0.0250 6.2000 0.8533 0.829484 0.1719 167.0300 0.0250 6.2000 0.8533 0.830185 0.1719 167.0300 0.0250 6.2000 0.8533 0.831186 0.1719 167.0300 0.0250 6.2000 0.8533 0.832187 0.1719 167.0300 0.0250 6.2000 0.8533 0.834088 0.1719 167.0300 0.0250 6.2000 0.8533 0.837389 0.1719 167.0300 0.0250 6.2000 0.8533 0.839190 0.1719 167.0300 0.0250 6.2000 0.8533 0.840191 0.1719 167.0300 0.0250 6.2000 0.8533 0.844392 0.1719 167.0300 0.0250 6.2000 0.8533 0.828793 0.1719 167.0300 0.0250 6.2000 0.8533 0.833994 0.1719 167.0300 0.0250 6.2000 0.8533 0.833995 0.1719 167.0300 0.0250 6.2000 0.8533 0.8352

10 2

96 0.1719 167.0300 0.0250 6.2000 0.8533 0.835997 0.1719 167.0300 0.0250 6.2000 0.8533 0.811098 0.1719 167.0300 0.0250 6.2000 0.8533 0.811199 0.1719 167.0300 0.0250 6.2000 0.8533 0.8128100 0.1719 167.0300 0.0250 6.2000 0.8533 0.8155

103

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




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



Ra = 0.237 — (0.00 175 x x l) -»- (3.693 x x 2 ) ■+• (0.00 159 x x3)


Colony S iz e :

Number of R un:



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


_l_________l_

Best fitness

Mean fitness

Min R„ value

5 6 Cycle

0


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



fitness

Mean

fitness

1 0.1730 167.0110 0.0250 6.8994 0.8525 0.73942 0.1729 167.0110 0.0250 6.8391 0.8526 0.74973 0.1729 167.0179 0.0250 6.8391 0.8526 0.75354 0.1729 167.0179 0.0250 6.8391 0.8526 0.75965 0.1728 167.0179 0.0250 6.7489 0.8527 0.76496 0.1728 167.0179 0.0250 6.7489 0.8527 0.77277 0.1723 167.0300 0.0250 6.4891 0.8530 0.77608 0.1723 167.0300 0.0250 6.4891 0.8530 0.78419 0.1719 167.0300 0.0250 6.2000 0.8533 0.788510 0.1719 167.0300 0.0250 6.2000 0.8533 0.7914

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;



Ra = 0 237 — (0.00 175 X icl) + (3 693 x x2) ■+■ (0.00 159 X tc3>


Colony S iz e :

Number of R un:



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



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



fitness

Mean

fitness

1 0.2074 148.1252 0.0250 7.7552 0.8282 0.68952 0.2074 148.1252 0.0250 7.7552 0.8282 0.70113 0.2011 167.0300 0.0279 8.7554 0.8326 0.70824 0.2011 167.0300 0.0279 8.7554 0.8326 0.71355 0.1946 154.0561 0.0250 6.2000 0.8371 0.71866 0.1946 154.0561 0.0250 6.2000 0.8371 0.72097 0.1919 155.6038 0.0250 6.2000 0.8390 0.72518 0.1919 155.6038 0.0250 6.2000 0.8390 0.72809 0.1719 167.0300 0.0250 6.2000 0.8533 0.731410 0.1719 167.0300 0.0250 6.2000 0.8533 0.735111 0.1719 167.0300 0.0250 6.2000 0.8533 0.741412 0.1719 167.0300 0.0250 6.2000 0.8533 0.745813 0.1719 167.0300 0.0250 6.2000 0.8533 0.753114 0.1719 167.0300 0.0250 6.2000 0.8533 0.761915 0.1719 167.0300 0.0250 6.2000 0.8533 0.766616 0.1719 167.0300 0.0250 6.2000 0.8533 0.771117 0.1719 167.0300 0.0250 6.2000 0.8533 0.774818 0.1719 167.0300 0.0250 6.2000 0.8533 0.777719 0.1719 167.0300 0.0250 6.2000 0.8533 0.781920 0.1719 167.0300 0.0250 6.2000 0.8533 0.7852

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<



Ra = 0.237 — (0.00 175 X i l ) + (3 693 x + (0.00159 X x3>


Colony S iz e :

Number of R un:




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



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



fitness

Mean

fitness

1 0.2145 162.8207 0.0291 6.2000 0.8234 0.68752 0.1792 162.8207 0.0250 6.2000 0.8480 0.69273 0.1719 167.0300 0.0250 6.2000 0.8533 0.69904 0.1719 167.0300 0.0250 6.2000 0.8533 0.70435 0.1719 167.0300 0.0250 6.2000 0.8533 0.71686 0.1719 167.0300 0.0250 6.2000 0.8533 0.72247 0.1719 167.0300 0.0250 6.2000 0.8533 0.72948 0.1719 167.0300 0.0250 6.2000 0.8533 0.73529 0.1719 167.0300 0.0250 6.2000 0.8533 0.744010 0.1719 167.0300 0.0250 6.2000 0.8533 0.746211 0.1719 167.0300 0.0250 6.2000 0.8533 0.753412 0.1719 167.0300 0.0250 6.2000 0.8533 0.756513 0.1719 167.0300 0.0250 6.2000 0.8533 0.761314 0.1719 167.0300 0.0250 6.2000 0.8533 0.763815 0.1719 167.0300 0.0250 6.2000 0.8533 0.768816 0.1719 167.0300 0.0250 6.2000 0.8533 0.775417 0.1719 167.0300 0.0250 6.2000 0.8533 0.776518 0.1719 167.0300 0.0250 6.2000 0.8533 0.777419 0.1719 167.0300 0.0250 6.2000 0.8533 0.782320 0.1719 167.0300 0.0250 6.2000 0.8533 0.787921 0.1719 167.0300 0.0250 6.2000 0.8533 0.793322 0.1719 167.0300 0.0250 6.2000 0.8533 0.794923 0.1719 167.0300 0.0250 6.2000 0.8533 0.796224 0.1719 167.0300 0.0250 6.2000 0.8533 0.796725 0.1719 167.0300 0.0250 6.2000 0.8533 0.801126 0.1719 167.0300 0.0250 6.2000 0.8533 0.802827 0.1719 167.0300 0.0250 6.2000 0.8533 0.803728 0.1719 167.0300 0.0250 6.2000 0.8533 0.806929 0.1719 167.0300 0.0250 6.2000 0.8533 0.8099

11 0

30 0.1719 167.0300 0.0250 6.2000 0.8533 0.812831 0.1719 167.0300 0.0250 6.2000 0.8533 0.814632 0.1719 167.0300 0.0250 6.2000 0.8533 0.816533 0.1719 167.0300 0.0250 6.2000 0.8533 0.817034 0.1719 167.0300 0.0250 6.2000 0.8533 0.817835 0.1719 167.0300 0.0250 6.2000 0.8533 0.818836 0.1719 167.0300 0.0250 6.2000 0.8533 0.823537 0.1719 167.0300 0.0250 6.2000 0.8533 0.823938 0.1719 167.0300 0.0250 6.2000 0.8533 0.825039 0.1719 167.0300 0.0250 6.2000 0.8533 0.826940 0.1719 167.0300 0.0250 6.2000 0.8533 0.827241 0.1719 167.0300 0.0250 6.2000 0.8533 0.828442 0.1719 167.0300 0.0250 6.2000 0.8533 0.828843 0.1719 167.0300 0.0250 6.2000 0.8533 0.829144 0.1719 167.0300 0.0250 6.2000 0.8533 0.829345 0.1719 167.0300 0.0250 6.2000 0.8533 0.832946 0.1719 167.0300 0.0250 6.2000 0.8533 0.833947 0.1719 167.0300 0.0250 6.2000 0.8533 0.835048 0.1719 167.0300 0.0250 6.2000 0.8533 0.836549 0.1719 167.0300 0.0250 6.2000 0.8533 0.838250 0.1719 167.0300 0.0250 6.2000 0.8533 0.8390

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;



Ra = 0.237 — (0.00 175 X icl) + (3 693 x ■+■ (0.00 159 x tc3>


Colony S iz e :

Number of R un:




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


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



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



fitness

Mean

fitness

1 0.1865 158.6923 0.0250 6.2000 0.8428 0.69652 0.1719 167.0300 0.0250 6.2000 0.8533 0.70263 0.1719 167.0300 0.0250 6.2000 0.8533 0.70824 0.1719 167.0300 0.0250 6.2000 0.8533 0.71135 0.1719 167.0300 0.0250 6.2000 0.8533 0.72186 0.1719 167.0300 0.0250 6.2000 0.8533 0.72727 0.1719 167.0300 0.0250 6.2000 0.8533 0.73338 0.1719 167.0300 0.0250 6.2000 0.8533 0.73879 0.1719 167.0300 0.0250 6.2000 0.8533 0.748610 0.1719 167.0300 0.0250 6.2000 0.8533 0.756011 0.1719 167.0300 0.0250 6.2000 0.8533 0.762412 0.1719 167.0300 0.0250 6.2000 0.8533 0.766713 0.1719 167.0300 0.0250 6.2000 0.8533 0.769914 0.1719 167.0300 0.0250 6.2000 0.8533 0.776215 0.1719 167.0300 0.0250 6.2000 0.8533 0.782316 0.1719 167.0300 0.0250 6.2000 0.8533 0.785617 0.1719 167.0300 0.0250 6.2000 0.8533 0.787618 0.1719 167.0300 0.0250 6.2000 0.8533 0.790519 0.1719 167.0300 0.0250 6.2000 0.8533 0.794220 0.1719 167.0300 0.0250 6.2000 0.8533 0.797721 0.1719 167.0300 0.0250 6.2000 0.8533 0.804222 0.1719 167.0300 0.0250 6.2000 0.8533 0.806223 0.1719 167.0300 0.0250 6.2000 0.8533 0.808824 0.1719 167.0300 0.0250 6.2000 0.8533 0.812425 0.1719 167.0300 0.0250 6.2000 0.8533 0.815026 0.1719 167.0300 0.0250 6.2000 0.8533 0.815527 0.1719 167.0300 0.0250 6.2000 0.8533 0.818228 0.1719 167.0300 0.0250 6.2000 0.8533 0.8202

113

29 0.1719 167.0300 0.0250 6.2000 0.8533 0.822030 0.1719 167.0300 0.0250 6.2000 0.8533 0.822631 0.1719 167.0300 0.0250 6.2000 0.8533 0.823932 0.1719 167.0300 0.0250 6.2000 0.8533 0.826133 0.1719 167.0300 0.0250 6.2000 0.8533 0.826934 0.1719 167.0300 0.0250 6.2000 0.8533 0.827535 0.1719 167.0300 0.0250 6.2000 0.8533 0.829836 0.1719 167.0300 0.0250 6.2000 0.8533 0.832137 0.1719 167.0300 0.0250 6.2000 0.8533 0.832738 0.1719 167.0300 0.0250 6.2000 0.8533 0.833339 0.1719 167.0300 0.0250 6.2000 0.8533 0.836140 0.1719 167.0300 0.0250 6.2000 0.8533 0.838141 0.1719 167.0300 0.0250 6.2000 0.8533 0.839242 0.1719 167.0300 0.0250 6.2000 0.8533 0.839943 0.1719 167.0300 0.0250 6.2000 0.8533 0.839944 0.1719 167.0300 0.0250 6.2000 0.8533 0.841445 0.1719 167.0300 0.0250 6.2000 0.8533 0.841546 0.1719 167.0300 0.0250 6.2000 0.8533 0.842847 0.1719 167.0300 0.0250 6.2000 0.8533 0.843348 0.1719 167.0300 0.0250 6.2000 0.8533 0.844749 0.1719 167.0300 0.0250 6.2000 0.8533 0.845350 0.1719 167.0300 0.0250 6.2000 0.8533 0.846151 0.1719 167.0300 0.0250 6.2000 0.8533 0.846552 0.1719 167.0300 0.0250 6.2000 0.8533 0.847253 0.1719 167.0300 0.0250 6.2000 0.8533 0.847554 0.1719 167.0300 0.0250 6.2000 0.8533 0.847955 0.1719 167.0300 0.0250 6.2000 0.8533 0.847956 0.1719 167.0300 0.0250 6.2000 0.8533 0.848057 0.1719 167.0300 0.0250 6.2000 0.8533 0.848258 0.1719 167.0300 0.0250 6.2000 0.8533 0.848859 0.1719 167.0300 0.0250 6.2000 0.8533 0.848960 0.1719 167.0300 0.0250 6.2000 0.8533 0.849761 0.1719 167.0300 0.0250 6.2000 0.8533 0.8499

114

62 0.1719 167.0300 0.0250 6.2000 0.8533 0.850163 0.1719 167.0300 0.0250 6.2000 0.8533 0.850364 0.1719 167.0300 0.0250 6.2000 0.8533 0.850565 0.1719 167.0300 0.0250 6.2000 0.8533 0.850666 0.1719 167.0300 0.0250 6.2000 0.8533 0.850767 0.1719 167.0300 0.0250 6.2000 0.8533 0.851168 0.1719 167.0300 0.0250 6.2000 0.8533 0.851569 0.1719 167.0300 0.0250 6.2000 0.8533 0.851570 0.1719 167.0300 0.0250 6.2000 0.8533 0.851771 0.1719 167.0300 0.0250 6.2000 0.8533 0.851872 0.1719 167.0300 0.0250 6.2000 0.8533 0.851973 0.1719 167.0300 0.0250 6.2000 0.8533 0.851974 0.1719 167.0300 0.0250 6.2000 0.8533 0.852175 0.1719 167.0300 0.0250 6.2000 0.8533 0.852176 0.1719 167.0300 0.0250 6.2000 0.8533 0.852177 0.1719 167.0300 0.0250 6.2000 0.8533 0.852278 0.1719 167.0300 0.0250 6.2000 0.8533 0.852479 0.1719 167.0300 0.0250 6.2000 0.8533 0.852580 0.1719 167.0300 0.0250 6.2000 0.8533 0.845781 0.1719 167.0300 0.0250 6.2000 0.8533 0.845882 0.1719 167.0300 0.0250 6.2000 0.8533 0.846083 0.1719 167.0300 0.0250 6.2000 0.8533 0.837084 0.1719 167.0300 0.0250 6.2000 0.8533 0.835985 0.1719 167.0300 0.0250 6.2000 0.8533 0.836686 0.1719 167.0300 0.0250 6.2000 0.8533 0.838487 0.1719 167.0300 0.0250 6.2000 0.8533 0.838588 0.1719 167.0300 0.0250 6.2000 0.8533 0.831689 0.1719 167.0300 0.0250 6.2000 0.8533 0.831690 0.1719 167.0300 0.0250 6.2000 0.8533 0.832491 0.1719 167.0300 0.0250 6.2000 0.8533 0.832692 0.1719 167.0300 0.0250 6.2000 0.8533 0.832293 0.1719 167.0300 0.0250 6.2000 0.8533 0.837794 0.1719 167.0300 0.0250 6.2000 0.8533 0.8384

115

95 0.1719 167.0300 0.0250 6.2000 0.8533 0.837096 0.1719 167.0300 0.0250 6.2000 0.8533 0.839597 0.1719 167.0300 0.0250 6.2000 0.8533 0.840298 0.1719 167.0300 0.0250 6.2000 0.8533 0.830699 0.1719 167.0300 0.0250 6.2000 0.8533 0.8345100 0.1719 167.0300 0.0250 6.2000 0.8533 0.8350

116

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.




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<



Ra = 0 237 — (0.00 175 X icl) + (3 693 x ■+■ (0.00 159 x x3>


Colony S iz e :

Number of R un:




X1 X2 X3 X4 X5

Uppest Threshold

167.03 0.083 3.5

Lowest Threshold

124.53 0.025 6.2

All best valuesAun


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


Cycle


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



fitness

Mean

fitness

1 0.2212 144.5240 0.0261 6.2000 0.8189 0.69432 0.2113 144.5240 0.0250 6.2000 0.8256 0.70003 0.1884 159.2385 0.0250 7.9867 0.8415 0.70624 0.1863 160.4344 0.0250 7.9867 0.8430 0.71295 0.1841 161.1510 0.0250 7.3935 0.8445 0.71686 0.1748 166.4708 0.0250 7.3935 0.8512 0.72247 0.1719 167.0300 0.0250 6.2000 0.8533 0.73088 0.1719 167.0300 0.0250 6.2000 0.8533 0.73859 0.1719 167.0300 0.0250 6.2000 0.8533 0.742710 0.1719 167.0300 0.0250 6.2000 0.8533 0.7450

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


Ra = 0 237 — (0.00 175 X i l ) + (3 693 x x 2 ) + (0.00159 x x3>

100


Colony S iz e :

Number of R un:




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


Mean fitness

/Mill Ra value

10Cycle

15 20


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



12 0



fitness

Mean

fitness

1 0.1891 165.9984 0.0267 6.4028 0.8410 0.67812 0.1875 165.9984 0.0266 6.4028 0.8421 0.68303 0.1872 165.9984 0.0266 6.2000 0.8423 0.69104 0.1854 167.0300 0.0266 6.2000 0.8436 0.69925 0.1719 167.0300 0.0250 6.2000 0.8533 0.70566 0.1719 167.0300 0.0250 6.2000 0.8533 0.71187 0.1719 167.0300 0.0250 6.2000 0.8533 0.71598 0.1719 167.0300 0.0250 6.2000 0.8533 0.72149 0.1719 167.0300 0.0250 6.2000 0.8533 0.727410 0.1719 167.0300 0.0250 6.2000 0.8533 0.735611 0.1719 167.0300 0.0250 6.2000 0.8533 0.741412 0.1719 167.0300 0.0250 6.2000 0.8533 0.747213 0.1719 167.0300 0.0250 6.2000 0.8533 0.751014 0.1719 167.0300 0.0250 6.2000 0.8533 0.756815 0.1719 167.0300 0.0250 6.2000 0.8533 0.764916 0.1719 167.0300 0.0250 6.2000 0.8533 0.771317 0.1719 167.0300 0.0250 6.2000 0.8533 0.776018 0.1719 167.0300 0.0250 6.2000 0.8533 0.780219 0.1719 167.0300 0.0250 6.2000 0.8533 0.785520 0.1719 167.0300 0.0250 6.2000 0.8533 0.7884

121

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--------



Ra = 0.237 — (0.00 175 x i l ) -1- (3 693 x ■+• (0.00159 x x3>


Colony S iz e :

Number of R un:



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



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



fitness

Mean

fitness

1 0.1755 165.1503 0.0250 6.4014 0.8507 0.68962 0.1719 167.0300 0.0250 6.2000 0.8533 0.69823 0.1719 167.0300 0.0250 6.2000 0.8533 0.70394 0.1719 167.0300 0.0250 6.2000 0.8533 0.70925 0.1719 167.0300 0.0250 6.2000 0.8533 0.71746 0.1719 167.0300 0.0250 6.2000 0.8533 0.72227 0.1719 167.0300 0.0250 6.2000 0.8533 0.72568 0.1719 167.0300 0.0250 6.2000 0.8533 0.73409 0.1719 167.0300 0.0250 6.2000 0.8533 0.740810 0.1719 167.0300 0.0250 6.2000 0.8533 0.743911 0.1719 167.0300 0.0250 6.2000 0.8533 0.748112 0.1719 167.0300 0.0250 6.2000 0.8533 0.756713 0.1719 167.0300 0.0250 6.2000 0.8533 0.759714 0.1719 167.0300 0.0250 6.2000 0.8533 0.765515 0.1719 167.0300 0.0250 6.2000 0.8533 0.770016 0.1719 167.0300 0.0250 6.2000 0.8533 0.774417 0.1719 167.0300 0.0250 6.2000 0.8533 0.779318 0.1719 167.0300 0.0250 6.2000 0.8533 0.782219 0.1719 167.0300 0.0250 6.2000 0.8533 0.786620 0.1719 167.0300 0.0250 6.2000 0.8533 0.789121 0.1719 167.0300 0.0250 6.2000 0.8533 0.793022 0.1719 167.0300 0.0250 6.2000 0.8533 0.796023 0.1719 167.0300 0.0250 6.2000 0.8533 0.800324 0.1719 167.0300 0.0250 6.2000 0.8533 0.804625 0.1719 167.0300 0.0250 6.2000 0.8533 0.807526 0.1719 167.0300 0.0250 6.2000 0.8533 0.809827 0.1719 167.0300 0.0250 6.2000 0.8533 0.812028 0.1719 167.0300 0.0250 6.2000 0.8533 0.814329 0.1719 167.0300 0.0250 6.2000 0.8533 0.8154

123

30 0.1719 167.0300 0.0250 6.2000 0.8533 0.816231 0.1719 167.0300 0.0250 6.2000 0.8533 0.817332 0.1719 167.0300 0.0250 6.2000 0.8533 0.818433 0.1719 167.0300 0.0250 6.2000 0.8533 0.820834 0.1719 167.0300 0.0250 6.2000 0.8533 0.823635 0.1719 167.0300 0.0250 6.2000 0.8533 0.824836 0.1719 167.0300 0.0250 6.2000 0.8533 0.827137 0.1719 167.0300 0.0250 6.2000 0.8533 0.827838 0.1719 167.0300 0.0250 6.2000 0.8533 0.829039 0.1719 167.0300 0.0250 6.2000 0.8533 0.830340 0.1719 167.0300 0.0250 6.2000 0.8533 0.831741 0.1719 167.0300 0.0250 6.2000 0.8533 0.832442 0.1719 167.0300 0.0250 6.2000 0.8533 0.834443 0.1719 167.0300 0.0250 6.2000 0.8533 0.835244 0.1719 167.0300 0.0250 6.2000 0.8533 0.836245 0.1719 167.0300 0.0250 6.2000 0.8533 0.837246 0.1719 167.0300 0.0250 6.2000 0.8533 0.838547 0.1719 167.0300 0.0250 6.2000 0.8533 0.838948 0.1719 167.0300 0.0250 6.2000 0.8533 0.839349 0.1719 167.0300 0.0250 6.2000 0.8533 0.840550 0.1719 167.0300 0.0250 6.2000 0.8533 0.8424

124

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.



Ra = 0 237 — (0.00 175 x i l ) -4- (S.693 x x2) + (0.00159 x x3>

10


Colony S iz e :

Number of R un:




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


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



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



fitness

Mean

fitness

1 0.1964 158.5504 0.0250 12.3068 0.8358 0.70662 0.1964 158.5504 0.0250 12.2979 0.8358 0.71143 0.1842 165.0309 0.0250 11.7750 0.8444 0.71984 0.1807 167.0300 0.0250 11.7750 0.8469 0.72695 0.1807 167.0300 0.0250 11.7750 0.8469 0.73176 0.1740 166.7493 0.0250 7.2084 0.8518 0.73557 0.1738 166.7493 0.0250 7.1150 0.8519 0.73888 0.1719 167.0300 0.0250 6.2000 0.8533 0.74489 0.1719 167.0300 0.0250 6.2000 0.8533 0.748110 0.1719 167.0300 0.0250 6.2000 0.8533 0.754211 0.1719 167.0300 0.0250 6.2000 0.8533 0.756812 0.1719 167.0300 0.0250 6.2000 0.8533 0.762013 0.1719 167.0300 0.0250 6.2000 0.8533 0.765614 0.1719 167.0300 0.0250 6.2000 0.8533 0.770415 0.1719 167.0300 0.0250 6.2000 0.8533 0.775116 0.1719 167.0300 0.0250 6.2000 0.8533 0.780817 0.1719 167.0300 0.0250 6.2000 0.8533 0.785518 0.1719 167.0300 0.0250 6.2000 0.8533 0.789619 0.1719 167.0300 0.0250 6.2000 0.8533 0.791620 0.1719 167.0300 0.0250 6.2000 0.8533 0.795021 0.1719 167.0300 0.0250 6.2000 0.8533 0.799122 0.1719 167.0300 0.0250 6.2000 0.8533 0.801123 0.1719 167.0300 0.0250 6.2000 0.8533 0.803624 0.1719 167.0300 0.0250 6.2000 0.8533 0.807225 0.1719 167.0300 0.0250 6.2000 0.8533 0.809426 0.1719 167.0300 0.0250 6.2000 0.8533 0.811627 0.1719 167.0300 0.0250 6.2000 0.8533 0.815928 0.1719 167.0300 0.0250 6.2000 0.8533 0.8176

126

29 0.1719 167.0300 0.0250 6.2000 0.8533 0.819330 0.1719 167.0300 0.0250 6.2000 0.8533 0.821131 0.1719 167.0300 0.0250 6.2000 0.8533 0.823832 0.1719 167.0300 0.0250 6.2000 0.8533 0.825833 0.1719 167.0300 0.0250 6.2000 0.8533 0.826834 0.1719 167.0300 0.0250 6.2000 0.8533 0.827835 0.1719 167.0300 0.0250 6.2000 0.8533 0.829436 0.1719 167.0300 0.0250 6.2000 0.8533 0.831437 0.1719 167.0300 0.0250 6.2000 0.8533 0.832638 0.1719 167.0300 0.0250 6.2000 0.8533 0.833939 0.1719 167.0300 0.0250 6.2000 0.8533 0.834840 0.1719 167.0300 0.0250 6.2000 0.8533 0.835341 0.1719 167.0300 0.0250 6.2000 0.8533 0.837342 0.1719 167.0300 0.0250 6.2000 0.8533 0.838543 0.1719 167.0300 0.0250 6.2000 0.8533 0.838944 0.1719 167.0300 0.0250 6.2000 0.8533 0.840245 0.1719 167.0300 0.0250 6.2000 0.8533 0.840846 0.1719 167.0300 0.0250 6.2000 0.8533 0.842147 0.1719 167.0300 0.0250 6.2000 0.8533 0.842448 0.1719 167.0300 0.0250 6.2000 0.8533 0.843149 0.1719 167.0300 0.0250 6.2000 0.8533 0.844850 0.1719 167.0300 0.0250 6.2000 0.8533 0.845251 0.1719 167.0300 0.0250 6.2000 0.8533 0.846052 0.1719 167.0300 0.0250 6.2000 0.8533 0.846553 0.1719 167.0300 0.0250 6.2000 0.8533 0.847354 0.1719 167.0300 0.0250 6.2000 0.8533 0.847855 0.1719 167.0300 0.0250 6.2000 0.8533 0.848656 0.1719 167.0300 0.0250 6.2000 0.8533 0.849057 0.1719 167.0300 0.0250 6.2000 0.8533 0.849258 0.1719 167.0300 0.0250 6.2000 0.8533 0.849459 0.1719 167.0300 0.0250 6.2000 0.8533 0.849560 0.1719 167.0300 0.0250 6.2000 0.8533 0.849661 0.1719 167.0300 0.0250 6.2000 0.8533 0.8501

127

62 0.1719 167.0300 0.0250 6.2000 0.8533 0.850463 0.1719 167.0300 0.0250 6.2000 0.8533 0.850664 0.1719 167.0300 0.0250 6.2000 0.8533 0.850965 0.1719 167.0300 0.0250 6.2000 0.8533 0.851266 0.1719 167.0300 0.0250 6.2000 0.8533 0.851467 0.1719 167.0300 0.0250 6.2000 0.8533 0.851668 0.1719 167.0300 0.0250 6.2000 0.8533 0.851769 0.1719 167.0300 0.0250 6.2000 0.8533 0.851970 0.1719 167.0300 0.0250 6.2000 0.8533 0.852071 0.1719 167.0300 0.0250 6.2000 0.8533 0.852172 0.1719 167.0300 0.0250 6.2000 0.8533 0.852273 0.1719 167.0300 0.0250 6.2000 0.8533 0.852274 0.1719 167.0300 0.0250 6.2000 0.8533 0.852375 0.1719 167.0300 0.0250 6.2000 0.8533 0.852376 0.1719 167.0300 0.0250 6.2000 0.8533 0.852477 0.1719 167.0300 0.0250 6.2000 0.8533 0.852478 0.1719 167.0300 0.0250 6.2000 0.8533 0.852579 0.1719 167.0300 0.0250 6.2000 0.8533 0.852580 0.1719 167.0300 0.0250 6.2000 0.8533 0.852581 0.1719 167.0300 0.0250 6.2000 0.8533 0.852682 0.1719 167.0300 0.0250 6.2000 0.8533 0.852783 0.1719 167.0300 0.0250 6.2000 0.8533 0.852784 0.1719 167.0300 0.0250 6.2000 0.8533 0.852885 0.1719 167.0300 0.0250 6.2000 0.8533 0.852886 0.1719 167.0300 0.0250 6.2000 0.8533 0.852887 0.1719 167.0300 0.0250 6.2000 0.8533 0.852988 0.1719 167.0300 0.0250 6.2000 0.8533 0.852989 0.1719 167.0300 0.0250 6.2000 0.8533 0.853090 0.1719 167.0300 0.0250 6.2000 0.8533 0.853091 0.1719 167.0300 0.0250 6.2000 0.8533 0.853092 0.1719 167.0300 0.0250 6.2000 0.8533 0.853193 0.1719 167.0300 0.0250 6.2000 0.8533 0.853194 0.1719 167.0300 0.0250 6.2000 0.8533 0.8531

128

95 0.1719 167.0300 0.0250 6.2000 0.8533 0.853196 0.1719 167.0300 0.0250 6.2000 0.8533 0.853197 0.1719 167.0300 0.0250 6.2000 0.8533 0.853198 0.1719 167.0300 0.0250 6.2000 0.8533 0.853199 0.1719 167.0300 0.0250 6.2000 0.8533 0.8531100 0.1719 167.0300 0.0250 6.2000 0.8533 0.8532

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.


4.8 Experiment 2 - ABC optimization parameters for AWJ


food)

10 10 50

10 20 50

10 50 50

10 100 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:



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


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

''


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

Cy

cle

Min Ra XI (V) X2 (P) X3 (h) X4 (a) X5

(m)

Best

fitness

Mean

fitness

1 3.5322 62.2021 154.0466 2.1971 93.6909 0.6386 0.2206 0.18272 2.8448 76.8439 125 1.2769 100.7081 1.0733 0.2601 0.19423 2.8435 76.8439 125 1.2769 98.7292 1.0733 0.2602 0.20054 2.8425 76.8439 125 1.3059 98.7292 1.0733 0.2602 0.20285 2.8130 75.9811 125 1.3059 98.7292 1.0733 0.2623 0.20336 2.8130 75.9811 125 1.3059 98.7292 1.0733 0.2623 0.20557 2.7113 73.1095 125 1.3059 98.7292 1.0733 0.2694 0.20738 2.7090 73.1095 125 1.4156 98.9371 1.0733 0.2696 0.20889 2.7090 73.1095 125 1.4156 98.9371 1.0733 0.2696 0.209710 2.7090 73.1095 125 1.4156 98.9371 1.0733 0.2696 0.2099

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



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:



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


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

speed, 125Mpa waterjet pressure, 2.4197mm standoff distance, 102.2916[am abrasive

gritsize and 0.5000g/s abrasive flowrate.

133

Table 4.23: The best value returned from 20 max cycle per run with limit of 50

Cycle Min Ra XI (V) X2 (P) X3 (h) X4 (a) X5

(m)

Best

fitness

Mean

fitness

1 3.2539 68.9046 125.7593 3.5708 109.3744 1.3790 0.2351 3.2539

2 3.2539 68.9046 125.7593 3.5708 109.3744 1.3790 0.2351 3.2539

3 3.1513 68.3609 125.7593 3.5708 97.0500 1.3377 0.2409 3.1513

4 3.1395 68.0617 125.7593 3.5708 97.0500 1.3377 0.2416 3.1395

5 2.9808 68.0617 125.7593 3.1873 97.0500 1.3377 0.2512 2.9808

6 2.9808 68.0617 125.7593 3.1873 97.0500 1.3377 0.2512 2.9808

7 2.8698 66.4615 125.7593 3.1873 97.0500 1.2269 0.2584 2.8698

8 2.8695 66.4615 125.7593 3.1873 98.1111 1.2269 0.2584 2.8695

9 2.7784 66.4615 125.7593 3.1873 98.1111 1.0024 0.2647 2.7784

10 2.6159 66.4615 125.7593 2.9679 98.1111 0.7601 0.2766 2.6159

11 2.5787 66.4615 125 2.9679 98.1111 0.7601 0.2794 2.5787

12 2.5787 66.4615 125 2.9679 98.1111 0.7601 0.2794 2.5787

13 2.5783 66.4615 125 2.9679 98.2622 0.7601 0.2795 2.5783

14 2.4862 66.4615 125 2.9679 102.2774 0.5000 0.2868 2.4862

15 2.2043 59.8291 125 2.9679 102.2774 0.5000 0.3121 2.2043

16 1.7364 50 125 2.9679 102.2774 0.5000 0.3654 1.7364

17 1.7364 50 125 2.9679 102.2916 0.5000 0.3654 1.7364

18 1.7364 50 125 2.9679 102.2916 0.5000 0.3654 1.7364

19 1.7364 50 125 2.9679 102.2916 0.5000 0.3654 1.7364

20 1.6032 50 125 2.4197 102.2916 0.5000 0.3841 1.6032

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*



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);


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


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


Cycle


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


Cycle Min Ra XI (V) X2 (P) X3 (h) X4 (d) X5

(m)

Best

fitness

Mean

fitness

1 2.6148 56.9891 139.8145 1.5643 99.9421 0.6767 0.2766 0.16192 2.2761 50 139.8145 1.5643 99.9421 0.6767 0.3052 0.16953 2.2249 50 139.8145 1.5643 100.3379 0.5000 0.3101 0.17164 2.2249 50 139.8145 1.5643 100.3379 0.5000 0.3101 0.17495 1.5242 50 125 1.5643 100.3379 0.5000 0.3962 0.19296 1.5226 50 125 1.5643 101.6083 0.5000 0.3964 0.19367 1.5226 50 125 1.5630 101.6083 0.5000 0.3964 0.19368 1.5226 50 125 1.5630 101.6083 0.5000 0.3964 0.19389 1.5226 50 125 1.5630 101.6083 0.5000 0.3964 0.197810 1.5226 50 125 1.5630 101.6083 0.5000 0.3964 0.199811 1.5226 50 125 1.5630 101.6083 0.5000 0.3964 0.201912 1.5226 50 125 1.5630 101.6083 0.5000 0.3964 0.203813 1.5226 50 125 1.5630 101.6083 0.5000 0.3964 0.205014 1.5226 50 125 1.5630 101.6083 0.5000 0.3964 0.207615 1.5226 50 125 1.5630 101.6083 0.5000 0.3964 0.209716 1.5226 50 125 1.5630 101.6083 0.5000 0.3964 0.212517 1.5223 50 125 1.5630 102.2855 0.5000 0.3965 0.212518 1.5223 50 125 1.5376 102.2855 0.5000 0.3965 0.215419 1.5223 50 125 1.5376 102.2855 0.5000 0.3965 0.218520 1.5223 50 125 1.5376 102.2855 0.5000 0.3965 0.218821 1.5223 50 125 1.5376 102.2855 0.5000 0.3965 0.219122 1.5223 50 125 1.5376 102.2855 0.5000 0.3965 0.219123 1.5223 50 125 1.5376 102.2855 0.5000 0.3965 0.220024 1.5223 50 125 1.5376 102.2855 0.5000 0.3965 0.220125 1.5223 50 125 1.5376 102.2855 0.5000 0.3965 0.220926 1.5223 50 125 1.5376 102.2855 0.5000 0.3965 0.226227 1.5223 50 125 1.5376 102.4426 0.5000 0.3965 0.227228 1.5223 50 125 1.5376 102.4426 0.5000 0.3965 0.227229 1.5223 50 125 1.5376 102.4426 0.5000 0.3965 0.2317

136

30 1.5223 50 125 1.5376 102.4426 0.5000 0.3965 0.233931 1.5223 50 125 1.5376 102.4426 0.5000 0.3965 0.249032 1.5223 50 125 1.5376 102.4426 0.5000 0.3965 0.249033 1.5223 50 125 1.5405 102.4790 0.5000 0.3965 0.250234 1.5223 50 125 1.5405 102.4790 0.5000 0.3965 0.250435 1.5223 50 125 1.5405 102.4790 0.5000 0.3965 0.251536 1.5223 50 125 1.5405 102.4790 0.5000 0.3965 0.252237 1.5223 50 125 1.5405 102.4790 0.5000 0.3965 0.253938 1.5223 50 125 1.5405 102.4790 0.5000 0.3965 0.258839 1.5223 50 125 1.5405 102.4790 0.5000 0.3965 0.258840 1.5223 50 125 1.5405 102.4790 0.5000 0.3965 0.258841 1.5223 50 125 1.5405 102.4790 0.5000 0.3965 0.260942 1.5223 50 125 1.5405 102.4790 0.5000 0.3965 0.261043 1.5223 50 125 1.5405 102.4790 0.5000 0.3965 0.261344 1.5223 50 125 1.5405 102.4790 0.5000 0.3965 0.261345 1.5223 50 125 1.5405 102.4790 0.5000 0.3965 0.261346 1.5223 50 125 1.5405 102.4790 0.5000 0.3965 0.262347 1.5223 50 125 1.5405 102.4790 0.5000 0.3965 0.262348 1.5223 50 125 1.5405 102.4790 0.5000 0.3965 0.266649 1.5223 50 125 1.5405 102.4790 0.5000 0.3965 0.269850 1.5223 50 125 1.5405 102.4790 0.5000 0.3965 0.2698

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



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:



— Parameters Range---------

X1 X2 X3

Abrasive Waterjet

100

Uppest Threshold

120 T 3.5

Lowest Threshold

50 125

All best valuesfrun


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


5


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

50/min traverse speed, 125Mpa waterjet pressure, 1.5648mm standoff distance,

102.4940|am abrasive gritsize and 0.5000g/s abrasive flowrate.

138



(m)

Best

fitness

Mean

fitness

1 3.5188 63.6171 150.7416 1.1125 102.1060 1.0243 0.2213 0.15952 3.5188 63.6171 150.7416 1.1125 102.1060 1.0243 0.2213 0.16003 3.5188 63.6171 150.7416 1.1125 102.1060 1.0243 0.2213 0.16354 3.5188 63.6171 150.7416 1.1125 102.1060 1.0243 0.2213 0.16595 3.2269 57.5342 150.7416 1.1125 102.1060 0.9540 0.2366 0.17066 3.1124 57.5342 148.3256 1.1125 99.4207 0.9297 0.2432 0.17307 2.7307 52.5931 144.9701 1.1125 99.4207 0.9297 0.2680 0.17968 1.8802 52.5931 127.1120 1.5159 99.4207 0.9062 0.3472 0.19599 1.7771 52.5931 125 1.5159 99.4207 0.9062 0.3601 0.199410 1.6755 52.5931 125 1.5159 101.2018 0.5816 0.3738 0.202311 1.5265 50 125 1.5159 101.2018 0.5122 0.3958 0.207512 1.5265 50 125 1.5159 101.2018 0.5122 0.3958 0.211413 1.5231 50 125 1.5159 101.2018 0.5000 0.3963 0.211714 1.5231 50 125 1.5159 101.2018 0.5000 0.3963 0.214615 1.5231 50 125 1.5159 101.2018 0.5000 0.3963 0.215116 1.5231 50 125 1.5159 101.2018 0.5000 0.3963 0.218217 1.5231 50 125 1.5159 101.2018 0.5000 0.3963 0.219118 1.5231 50 125 1.5159 101.2018 0.5000 0.3963 0.221119 1.5231 50 125 1.5159 101.2018 0.5000 0.3963 0.223320 1.5231 50 125 1.5159 101.2018 0.5000 0.3963 0.223721 1.5231 50 125 1.5159 101.2018 0.5000 0.3963 0.226222 1.5231 50 125 1.5159 101.2018 0.5000 0.3963 0.233123 1.5231 50 125 1.5159 101.2018 0.5000 0.3963 0.238724 1.5231 50 125 1.5159 101.2018 0.5000 0.3963 0.241225 1.5231 50 125 1.5159 101.2018 0.5000 0.3963 0.241526 1.5224 50 125 1.5159 102.4300 0.5000 0.3965 0.246727 1.5224 50 125 1.5718 102.4300 0.5000 0.3965 0.251928 1.5224 50 125 1.5718 102.4300 0.5000 0.3965 0.252929 1.5224 50 125 1.5718 102.4300 0.5000 0.3965 0.2585

139

30 1.5224 50 125 1.5718 102.4300 0.5000 0.3965 0.268431 1.5224 50 125 1.5718 102.4300 0.5000 0.3965 0.270132 1.5224 50 125 1.5718 102.4300 0.5000 0.3965 0.272133 1.5224 50 125 1.5718 102.4300 0.5000 0.3965 0.279434 1.5224 50 125 1.5718 102.4300 0.5000 0.3965 0.290735 1.5224 50 125 1.5718 102.4300 0.5000 0.3965 0.294836 1.5224 50 125 1.5718 102.4300 0.5000 0.3965 0.299437 1.5224 50 125 1.5718 102.4300 0.5000 0.3965 0.303938 1.5224 50 125 1.5718 102.4300 0.5000 0.3965 0.304039 1.5224 50 125 1.5718 102.4300 0.5000 0.3965 0.304840 1.5224 50 125 1.5718 102.4300 0.5000 0.3965 0.309341 1.5223 50 125 1.5648 102.4940 0.5000 0.3965 0.309542 1.5223 50 125 1.5648 102.4940 0.5000 0.3965 0.324043 1.5223 50 125 1.5648 102.4940 0.5000 0.3965 0.327244 1.5223 50 125 1.5648 102.4940 0.5000 0.3965 0.328945 1.5223 50 125 1.5648 102.4940 0.5000 0.3965 0.332546 1.5223 50 125 1.5648 102.4940 0.5000 0.3965 0.332547 1.5223 50 125 1.5648 102.4940 0.5000 0.3965 0.332848 1.5223 50 125 1.5648 102.4940 0.5000 0.3965 0.333349 1.5223 50 125 1.5648 102.4940 0.5000 0.3965 0.335750 1.5223 50 125 1.5648 102.4940 0.5000 0.3965 0.335751 1.5223 50 125 1.5648 102.4940 0.5000 0.3965 0.336752 1.5223 50 125 1.5648 102.4940 0.5000 0.3965 0.337353 1.5223 50 125 1.5648 102.4940 0.5000 0.3965 0.344354 1.5223 50 125 1.5648 102.4940 0.5000 0.3965 0.348155 1.5223 50 125 1.5648 102.4940 0.5000 0.3965 0.351156 1.5223 50 125 1.5648 102.4940 0.5000 0.3965 0.352957 1.5223 50 125 1.5648 102.4940 0.5000 0.3965 0.353758 1.5223 50 125 1.5648 102.4940 0.5000 0.3965 0.353759 1.5223 50 125 1.5648 102.4940 0.5000 0.3965 0.356260 1.5223 50 125 1.5648 102.4940 0.5000 0.3965 0.356261 1.5223 50 125 1.5648 102.4940 0.5000 0.3965 0.356262 1.5223 50 125 1.5648 102.4940 0.5000 0.3965 0.3569

140

63 1.5223 50 125 1.5648 102.4940 0.5000 0.3965 0.357164 1.5223 50 125 1.5648 102.4940 0.5000 0.3965 0.357365 1.5223 50 125 1.5648 102.4940 0.5000 0.3965 0.357966 1.5223 50 125 1.5648 102.4940 0.5000 0.3964 0.312567 1.5223 50 125 1.5648 102.4940 0.5000 0.3964 0.312868 1.5223 50 125 1.5648 102.4940 0.5000 0.3964 0.315369 1.5223 50 125 1.5545 102.4443 0.5000 0.3965 0.315570 1.5223 50 125 1.5545 102.4443 0.5000 0.3965 0.318871 1.5223 50 125 1.5545 102.4443 0.5000 0.3965 0.319072 1.5223 50 125 1.5545 102.4443 0.5000 0.3965 0.319073 1.5223 50 125 1.5545 102.4443 0.5000 0.3965 0.323574 1.5223 50 125 1.5545 102.4443 0.5000 0.3965 0.326275 1.5223 50 125 1.5545 102.4443 0.5000 0.3965 0.327176 1.5223 50 125 1.5545 102.4443 0.5000 0.3965 0.327277 1.5223 50 125 1.5545 102.4443 0.5000 0.3965 0.330978 1.5223 50 125 1.5545 102.4443 0.5000 0.3965 0.332079 1.5223 50 125 1.5545 102.4443 0.5000 0.3965 0.334780 1.5223 50 125 1.5545 102.4443 0.5000 0.3965 0.335781 1.5223 50 125 1.5545 102.4443 0.5000 0.3965 0.336482 1.5223 50 125 1.5545 102.4443 0.5000 0.3965 0.337083 1.5223 50 125 1.5545 102.4443 0.5000 0.3965 0.337484 1.5223 50 125 1.5545 102.4443 0.5000 0.3965 0.338385 1.5223 50 125 1.5545 102.4443 0.5000 0.3965 0.341286 1.5223 50 125 1.5545 102.4443 0.5000 0.3965 0.341787 1.5223 50 125 1.5545 102.4443 0.5000 0.3965 0.350388 1.5223 50 125 1.5545 102.4443 0.5000 0.3965 0.351389 1.5223 50 125 1.5545 102.4443 0.5000 0.3965 0.351990 1.5223 50 125 1.5545 102.4443 0.5000 0.3965 0.352791 1.5223 50 125 1.5545 102.4443 0.5000 0.3965 0.356092 1.5223 50 125 1.5545 102.4443 0.5000 0.3965 0.304293 1.5223 50 125 1.5507 102.5797 0.5000 0.3965 0.308694 1.5223 50 125 1.5507 102.5797 0.5000 0.3965 0.308695 1.5223 50 125 1.5507 102.5797 0.5000 0.3965 0.3124

141

96 1.5223 50 125 1.5507 102.5797 0.5000 0.3965 0.312997 1.5223 50 125 1.5507 102.5797 0.5000 0.3965 0.313598 1.5223 50 125 1.5507 102.5797 0.5000 0.3965 0.313899 1.5223 50 125 1.5507 102.5797 0.5000 0.3965 0.3143100 1.5223 50 125 1.5507 102.5797 0.5000 0.3965 0.3148

142


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.



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



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


i— Parameters Range---------

X1 X2 X3

Abrasive W ate r#

X4 X5

Uppest Threshold:

120 3.5

Lowest Threshold:

125 60

All best valuesAun


• • . <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



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

traverse speed, 125Mpa waterjet pressure, 1.8195mm standoff distance, 87.3173[am

abrasive gritsize and 0.5000g/s abrasive flowrate.

144



(m)

Best

fitness

Mean

fitness

1 2.3284 61.0663 126.4985 2.0314 85.4320 0.7824 0.3004 0.17602 2.3154 61.0663 126.4985 1.8985 85.4320 0.7824 0.3016 0.17923 2.2507 61.0663 126.4985 1.8985 85.4320 0.5000 0.3076 0.18134 2.2293 61.0663 126.4985 1.8985 87.0375 0.5000 0.3097 0.18255 1.7067 50 126.4985 1.8985 87.0375 0.5000 0.3695 0.19356 1.7039 50 126.4985 1.8579 87.0375 0.5000 0.3698 0.19477 1.7039 50 126.4985 1.8579 87.0375 0.5000 0.3698 0.19598 1.6271 50 125 1.8579 87.3173 0.5000 0.3807 0.19879 1.6271 50 125 1.8579 87.3173 0.5000 0.3807 0.199810 1.6247 50 125 1.8195 87.3173 0.5000 0.3810 0.2027

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*



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:



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



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



(m)

Best

fitness

Mean

fitness

1 3.0108 57.2225 143.1136 1.8934 119.0669 0.9003 0.2493 0.14182 2.9986 57.2225 143.1136 1.8322 118.5863 0.9003 0.2501 0.14833 2.9986 57.2225 143.1136 1.8322 118.5863 0.9003 0.2501 0.14874 2.9129 57.2225 143.1136 1.8322 111.6937 0.9003 0.2556 0.15105 2.4408 50 140.3886 1.8322 111.6937 0.9003 0.2906 0.16106 1.7020 50 125 1.4852 111.6937 0.9003 0.3701 0.17107 1.7020 50 125 1.4852 111.6937 0.9003 0.3701 0.17658 1.5574 50 125 1.4852 111.6937 0.5000 0.3910 0.17999 1.5364 50 125 1.4852 96.7044 0.5000 0.3943 0.181410 1.5364 50 125 1.4852 96.7044 0.5000 0.3943 0.181811 1.5234 50 125 1.4852 103.8398 0.5000 0.3963 0.183112 1.5234 50 125 1.4852 103.8398 0.5000 0.3963 0.186613 1.5234 50 125 1.4852 103.8398 0.5000 0.3963 0.194114 1.5233 50 125 1.4852 103.7480 0.5000 0.3963 0.198515 1.5229 50 125 1.5563 103.7480 0.5000 0.3964 0.201416 1.5229 50 125 1.5563 103.7480 0.5000 0.3964 0.201417 1.5229 50 125 1.5563 103.7480 0.5000 0.3964 0.203518 1.5229 50 125 1.5563 103.7480 0.5000 0.3964 0.204719 1.5229 50 125 1.5563 103.7480 0.5000 0.3964 0.206020 1.5229 50 125 1.5563 103.7480 0.5000 0.3964 0.2112

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


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:



— Parameters Range---------

X1 X2 X3

Abrasive Waterjet

20

T »

X4 X5

Uppest Threshold

120 3.5

Lowest Threshold

SO 125 1

All best valuesAun


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


10 20 30 40 50Cycle

5


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



(m)

Best

fitness

Mean

fitness

1 2.8625 57.9995 140.0170 1.3421 80.6551 0.7452 0.2589 0.17012 2.7050 57.9995 137.3707 1.3421 80.6551 0.5520 0.2699 0.17503 2.6773 57.9995 137.3707 1.3421 82.2914 0.5520 0.2719 0.17724 1.9199 50.2000 125.3663 1.3332 89.5340 1.5207 0.3425 0.19175 1.6765 50.2000 125.3663 1.3534 89.5340 0.7313 0.3736 0.19626 1.6585 50.2000 125 1.3534 89.5340 0.7313 0.3762 0.19957 1.6585 50.2000 125 1.3534 89.5340 0.7313 0.3762 0.20298 1.6480 50 125 1.6559 89.5340 0.7313 0.3776 0.20529 1.6480 50 125 1.6559 89.5340 0.7313 0.3776 0.208010 1.6480 50 125 1.6559 89.5340 0.7313 0.3776 0.214211 1.6285 50 125 1.6559 91.8201 0.7313 0.3804 0.218912 1.6281 50 125 1.6411 91.8201 0.7313 0.3805 0.223713 1.6231 50 125 1.6411 91.8201 0.7127 0.3812 0.228314 1.6001 50 125 1.6411 91.8201 0.6239 0.3846 0.231615 1.5699 50 125 1.6357 91.8201 0.5000 0.3891 0.232916 1.5699 50 125 1.6357 91.8201 0.5000 0.3891 0.237717 1.5699 50 125 1.6357 91.8201 0.5000 0.3891 0.243418 1.5683 50 125 1.6098 91.9539 0.5000 0.3894 0.245419 1.5683 50 125 1.6098 91.9539 0.5000 0.3894 0.248920 1.5683 50 125 1.6098 91.9539 0.5000 0.3894 0.254921 1.5561 50 125 1.6098 93.4747 0.5000 0.3912 0.261422 1.5561 50 125 1.6098 93.4747 0.5000 0.3912 0.263523 1.5561 50 125 1.6098 93.4747 0.5000 0.3912 0.264224 1.5446 50 125 1.6098 95.1844 0.5000 0.3930 0.266125 1.5446 50 125 1.6098 95.1844 0.5000 0.3930 0.266426 1.5255 50 125 1.6098 99.9104 0.5000 0.3960 0.268527 1.5251 50 125 1.5679 99.9104 0.5000 0.3960 0.276128 1.5251 50 125 1.5679 99.9104 0.5000 0.3960 0.277229 1.5251 50 125 1.5679 99.9104 0.5000 0.3960 0.2808

149

30 1.5250 50 125 1.5679 99.9460 0.5000 0.3960 0.282831 1.5245 50 125 1.5679 100.2020 0.5000 0.3961 0.284332 1.5245 50 125 1.5679 100.2020 0.5000 0.3961 0.287333 1.5245 50 125 1.5295 100.2020 0.5000 0.3961 0.289634 1.5245 50 125 1.5295 100.2020 0.5000 0.3961 0.290135 1.5223 50 125 1.5295 102.3062 0.5000 0.3965 0.295736 1.5223 50 125 1.5295 102.3062 0.5000 0.3965 0.296037 1.5223 50 125 1.5295 102.3062 0.5000 0.3965 0.296838 1.5223 50 125 1.5295 102.3062 0.5000 0.3965 0.307439 1.5223 50 125 1.5295 102.3062 0.5000 0.3965 0.310740 1.5223 50 125 1.5295 102.3062 0.5000 0.3965 0.313841 1.5223 50 125 1.5295 102.3062 0.5000 0.3965 0.316442 1.5223 50 125 1.5295 102.3830 0.5000 0.3965 0.318643 1.5223 50 125 1.5295 102.3830 0.5000 0.3965 0.321044 1.5223 50 125 1.5295 102.3830 0.5000 0.3965 0.321445 1.5223 50 125 1.5295 102.3830 0.5000 0.3965 0.322846 1.5223 50 125 1.5295 102.3830 0.5000 0.3965 0.323747 1.5223 50 125 1.5295 102.6003 0.5000 0.3965 0.324248 1.5223 50 125 1.5295 102.4046 0.5000 0.3965 0.325249 1.5223 50 125 1.5295 102.4046 0.5000 0.3965 0.327150 1.5223 50 125 1.5295 102.4046 0.5000 0.3965 0.3284

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



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:



p— Parameters Range —

X1 X2

Abrasive Waterjet

X3 X4 X5

Uppest Threshold:

3.5

Lowest Threshold

125 60

All best valuesAun


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


1.5


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



(m)

Best

fitness

Mean

fitness

1 3.3086 50.9788 128.0358 3.3277 118.1032 2.5124 0.2321 0.14332 3.2595 50 128.0358 3.3277 118.1032 2.5124 0.2348 0.14703 3.0972 50 128.0358 3.3277 109.8899 2.5124 0.2441 0.14874 3.0972 50 128.0358 3.3277 109.8899 2.5124 0.2441 0.14915 2.9499 50 125 3.3277 109.8899 2.5124 0.2532 0.15206 2.6661 50 125 2.5274 109.8899 2.5124 0.2728 0.15627 2.6661 50 125 2.5274 109.8899 2.5124 0.2728 0.15818 2.5968 50 125 2.5274 109.8899 2.4060 0.2780 0.16099 2.5968 50 125 2.5274 109.8899 2.4060 0.2780 0.163310 2.5968 50 125 2.5274 109.8899 2.4060 0.2780 0.165711 2.5968 50 125 2.5274 109.8899 2.4060 0.2780 0.170112 2.5968 50 125 2.5274 109.8899 2.4060 0.2780 0.171613 2.5968 50 125 2.5274 109.8899 2.4060 0.2780 0.174914 2.5968 50 125 2.5274 109.8899 2.4060 0.2780 0.177015 2.5627 50 125 2.4296 109.8899 2.3917 0.2807 0.178016 2.5627 50 125 2.4296 109.8899 2.3917 0.2807 0.179917 2.0880 50 125 2.3857 109.8899 1.5851 0.3238 0.191918 1.9841 50 125 2.3857 106.8684 1.4365 0.3351 0.201819 1.9841 50 125 2.3857 106.8684 1.4365 0.3351 0.212720 1.9757 50 125 2.3442 106.8684 1.4365 0.3361 0.213521 1.9338 50 125 2.3442 95.0809 1.4365 0.3409 0.218222 1.9338 50 125 2.3442 95.0809 1.4365 0.3409 0.219523 1.7823 50 125 2.3442 95.0809 1.0425 0.3594 0.223324 1.7698 50 125 2.3442 98.2695 1.0257 0.3610 0.226525 1.7659 50 125 2.3231 98.2695 1.0257 0.3615 0.233826 1.7659 50 125 2.3231 98.2695 1.0257 0.3615 0.234927 1.7659 50 125 2.3231 98.2695 1.0257 0.3615 0.239828 1.7659 50 125 2.3231 98.2695 1.0257 0.3615 0.239929 1.7531 50 125 2.3231 98.2695 0.9905 0.3632 0.2404

152

30 1.7490 50 125 1.9125 91.1636 1.0671 0.3638 0.250231 1.7442 50 125 2.3231 100.5453 0.9667 0.3644 0.257132 1.5974 50 125 1.4825 94.6507 0.6920 0.3850 0.264833 1.5814 50 125 1.4825 99.0751 0.6920 0.3874 0.266434 1.5720 50 125 1.4825 99.0751 0.6599 0.3888 0.267835 1.5720 50 125 1.4825 99.0751 0.6599 0.3888 0.270936 1.5720 50 125 1.4825 99.0751 0.6599 0.3888 0.272937 1.5702 50 125 1.4825 100.2715 0.6599 0.3891 0.273738 1.5702 50 125 1.4825 100.2715 0.6599 0.3891 0.279339 1.5702 50 125 1.4825 100.2715 0.6599 0.3891 0.279540 1.5702 50 125 1.4825 100.2715 0.6599 0.3891 0.280141 1.5702 50 125 1.4879 100.2715 0.6599 0.3891 0.280642 1.5241 50 125 1.4879 104.3914 0.5000 0.3962 0.281543 1.5241 50 125 1.4899 104.3914 0.5000 0.3962 0.282144 1.5241 50 125 1.4899 104.3914 0.5000 0.3962 0.282845 1.5241 50 125 1.4899 104.3914 0.5000 0.3962 0.286846 1.5241 50 125 1.4899 104.3914 0.5000 0.3962 0.291347 1.5241 50 125 1.4899 104.3914 0.5000 0.3962 0.302848 1.5241 50 125 1.4899 104.3914 0.5000 0.3962 0.302949 1.5241 50 125 1.4899 104.3914 0.5000 0.3962 0.305050 1.5241 50 125 1.4899 104.3914 0.5000 0.3962 0.306051 1.5241 50 125 1.4899 104.3914 0.5000 0.3962 0.306252 1.5241 50 125 1.4899 104.3914 0.5000 0.3962 0.306853 1.5238 50 125 1.5333 104.3914 0.5000 0.3962 0.308654 1.5236 50 125 1.5333 104.2812 0.5000 0.3963 0.309755 1.5236 50 125 1.5333 104.2812 0.5000 0.3963 0.310556 1.5236 50 125 1.5333 104.2812 0.5000 0.3963 0.311357 1.5236 50 125 1.5333 104.2812 0.5000 0.3963 0.311958 1.5223 50 125 1.5333 102.7407 0.5000 0.3965 0.312259 1.5223 50 125 1.5333 102.6660 0.5000 0.3965 0.315960 1.5223 50 125 1.5333 102.6660 0.5000 0.3965 0.318361 1.5223 50 125 1.5333 102.6660 0.5000 0.3965 0.319062 1.5223 50 125 1.5333 102.6660 0.5000 0.3965 0.3208

153

63 1.5223 50 125 1.5333 102.6660 0.5000 0.3965 0.321664 1.5223 50 125 1.5333 102.3463 0.5000 0.3965 0.323265 1.5223 50 125 1.5333 102.3463 0.5000 0.3965 0.327966 1.5223 50 125 1.5371 102.3463 0.5000 0.3965 0.334167 1.5223 50 125 1.5371 102.3463 0.5000 0.3965 0.337168 1.5223 50 125 1.5380 102.3463 0.5000 0.3965 0.337369 1.5223 50 125 1.5380 102.4036 0.5000 0.3965 0.338170 1.5223 50 125 1.5383 102.4036 0.5000 0.3965 0.341271 1.5223 50 125 1.5383 102.4036 0.5000 0.3965 0.341772 1.5223 50 125 1.5383 102.4036 0.5000 0.3965 0.341973 1.5223 50 125 1.5383 102.4036 0.5000 0.3965 0.347574 1.5223 50 125 1.5383 102.4036 0.5000 0.3965 0.354275 1.5223 50 125 1.5383 102.4036 0.5000 0.3965 0.355676 1.5223 50 125 1.5383 102.4036 0.5000 0.3965 0.358077 1.5223 50 125 1.5383 102.4036 0.5000 0.3965 0.360278 1.5223 50 125 1.5383 102.4036 0.5000 0.3965 0.361979 1.5223 50 125 1.5383 102.4036 0.5000 0.3965 0.362880 1.5223 50 125 1.5383 102.4036 0.5000 0.3965 0.362981 1.5223 50 125 1.5429 102.4036 0.5000 0.3965 0.365382 1.5223 50 125 1.5429 102.4036 0.5000 0.3965 0.365883 1.5223 50 125 1.5429 102.4036 0.5000 0.3965 0.366684 1.5223 50 125 1.5429 102.4036 0.5000 0.3965 0.366785 1.5223 50 125 1.5429 102.4036 0.5000 0.3965 0.367286 1.5223 50 125 1.5429 102.4175 0.5000 0.3965 0.3674

87 1.5223 50 125 1.5429 102.4175 0.5000 0.3965 0.370088 1.5223 50 125 1.5429 102.4175 0.5000 0.3965 0.370989 1.5223 50 125 1.5429 102.4175 0.5000 0.3965 0.371190 1.5223 50 125 1.5429 102.4175 0.5000 0.3965 0.371691 1.5223 50 125 1.5429 102.4175 0.5000 0.3965 0.373392 1.5223 50 125 1.5429 102.4175 0.5000 0.3965 0.373393 1.5223 50 125 1.5429 102.4175 0.5000 0.3965 0.374394 1.5223 50 125 1.5429 102.4175 0.5000 0.3965 0.374395 1.5223 50 125 1.5429 102.4712 0.5000 0.3965 0.3764

154

96 1.5223 50 125 1.5433 102.4712 0.5000 0.3965 0.378397 1.5223 50 125 1.5433 102.4712 0.5000 0.3965 0.378398 1.5223 50 125 1.5433 102.4712 0.5000 0.3965 0.380399 1.5223 50 125 1.5433 102.4712 0.5000 0.3965 0.3803100 1.5223 50 125 1.5433 102.4712 0.5000 0.3965 0.3806

155


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.



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


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

50/min traverse speed, 125Mpa waterjet pressure, 1.5515mm standoff distance,

92.0639pm abrasive gritsize and 0.5421g/s abrasive flowrate.

157



(m)

Best

fitness

Mean

fitness

1 2.7684 50.0163 147.1365 1.6606 80.1993 0.5703 0.2654 0.14102 2.7676 50 147.1365 1.6606 80.1993 0.5703 0.2654 0.14273 1.7402 50 125 1.6606 80.1993 0.5703 0.3649 0.15084 1.7402 50 125 1.6606 80.1993 0.5703 0.3649 0.15375 1.6202 50 125 1.6606 87.9062 0.5424 0.3817 0.15676 1.6202 50 125 1.6606 87.9062 0.5424 0.3817 0.1593

7 1.6202 50 125 1.6606 87.9062 0.5424 0.3817 0.16238 1.6202 50 125 1.6606 87.9062 0.5424 0.3817 0.16359 1.6180 50 125 1.6606 88.0939 0.5424 0.3820 0.1666

10 1.5769 50 125 1.5515 92.0639 0.5424 0.3881 0.1712

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


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 :



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


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,

1.5283mm standoff distance, 98.7731 pm abrasive gritsize and 0.5000 g/s abrasive

flowrate.

159



(m)

Best

fitness

Mean

fitness

1 3.7331 77.8498 128.9791 3.6607 109.8497 1.2889 0.2113 0.14002 3.7331 77.8498 128.9791 3.6607 109.8497 1.2889 0.2113 0.14153 3.6606 77.8498 128.9791 3.5012 109.8497 1.2889 0.2146 0.14624 2.7072 54.3676 128.9791 3.5012 109.8497 1.2889 0.2697 0.15085 2.7072 54.3676 128.9791 3.5012 109.8497 1.2889 0.2697 0.15426 2.7072 54.3676 128.9791 3.5012 109.8497 1.2889 0.2697 0.15597 2.2724 54.3676 125 2.8457 109.8497 1.2889 0.3056 0.16218 2.0573 50 125 2.8457 109.8497 1.2889 0.3271 0.16499 2.0134 50 125 2.8457 104.1823 1.2889 0.3319 0.172610 2.0124 50 125 2.8457 104.1823 1.2867 0.3320 0.176311 1.7578 50 125 2.4134 98.5039 0.9571 0.3626 0.182312 1.6988 50 125 2.4134 98.5039 0.7878 0.3705 0.185513 1.6974 50 125 2.4134 99.6131 0.7878 0.3707 0.188914 1.6974 50 125 2.4134 99.6131 0.7878 0.3707 0.190415 1.5328 50 125 1.5031 97.4698 0.5000 0.3948 0.198916 1.5328 50 125 1.5031 97.4698 0.5000 0.3948 0.2003

17 1.5327 50 125 1.5283 97.4698 0.5000 0.3948 0.207018 1.5327 50 125 1.5283 97.4698 0.5000 0.3948 0.210119 1.5327 50 125 1.5283 97.4698 0.5000 0.3948 0.2133

20 1.5280 50 125 1.5283 98.7731 0.5000 0.3956 0.2169


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:


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


Cycle


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


speed, 125Mpa waterjet pressure, 1.5428 mm standoff distance, 102.5184pm


f

161



(m)

Best

fitness

Mean

fitness

1 2.4406 58.4597 129.1298 1.4424 94.9639 1.4188 0.2906 0.15412 2.4406 58.4597 129.1298 1.4424 94.9639 1.4188 0.2906 0.15793 2.4348 58.4597 129.0094 1.4424 94.9639 1.4188 0.2911 0.16164 1.9686 53.4644 128.9087 2.4313 100.5644 0.5000 0.3369 0.17105 1.7108 53.4644 125 1.9248 100.5644 0.5000 0.3689 0.17486 1.7099 53.4644 125 1.9248 103.7482 0.5000 0.3690 0.17977 1.7099 53.4644 125 1.9248 103.7482 0.5000 0.3690 0.18208 1.7099 53.4644 125 1.9248 103.7482 0.5000 0.3690 0.18509 1.7099 53.4644 125 1.9248 103.7482 0.5000 0.3690 0.189110 1.7099 53.4644 125 1.9248 103.7482 0.5000 0.3690 0.193311 1.5324 50 125 1.8446 103.7482 0.5000 0.3949 0.198412 1.5324 50 125 1.8446 103.7482 0.5000 0.3949 0.201913 1.5323 50 125 1.8446 103.6489 0.5000 0.3949 0.204614 1.5323 50 125 1.8446 103.6489 0.5000 0.3949 0.206315 1.5318 50 125 1.8446 102.9040 0.5000 0.3950 0.213416 1.5267 50 125 1.7477 102.9040 0.5000 0.3958 0.2148

17 1.5267 50 125 1.7477 102.9040 0.5000 0.3958 0.216618 1.5225 50 125 1.5879 102.9040 0.5000 0.3964 0.219119 1.5225 50 125 1.5879 102.9040 0.5000 0.3964 0.221420 1.5225 50 125 1.5879 102.9040 0.5000 0.3964 0.226221 1.5225 50 125 1.5879 102.9040 0.5000 0.3964 0.228022 1.5225 50 125 1.5879 102.9040 0.5000 0.3964 0.232923 1.5225 50 125 1.5879 102.9040 0.5000 0.3964 0.234624 1.5225 50 125 1.5879 102.2331 0.5000 0.3964 0.236825 1.5225 50 125 1.5879 102.2331 0.5000 0.3964 0.2393

26 1.5223 50 125 1.5490 102.2331 0.5000 0.3965 0.241827 1.5223 50 125 1.5490 102.2331 0.5000 0.3965 0.243628 1.5223 50 125 1.5490 102.2331 0.5000 0.3965 0.245229 1.5223 50 125 1.5490 102.2331 0.5000 0.3965 0.2456

162

30 1.5223 50 125 1.5490 102.3732 0.5000 0.3965 0.247431 1.5223 50 125 1.5490 102.3732 0.5000 0.3965 0.250832 1.5223 50 125 1.5490 102.4474 0.5000 0.3965 0.253033 1.5223 50 125 1.5490 102.4474 0.5000 0.3965 0.255434 1.5223 50 125 1.5490 102.4474 0.5000 0.3965 0.257835 1.5223 50 125 1.5490 102.4474 0.5000 0.3965 0.261236 1.5223 50 125 1.5422 102.4474 0.5000 0.3965 0.262237 1.5223 50 125 1.5422 102.4474 0.5000 0.3965 0.264038 1.5223 50 125 1.5422 102.4474 0.5000 0.3965 0.2660

39 1.5223 50 125 1.5422 102.4474 0.5000 0.3965 0.267240 1.5223 50 125 1.5422 102.4474 0.5000 0.3965 0.270141 1.5223 50 125 1.5422 102.4474 0.5000 0.3965 0.273042 1.5223 50 125 1.5428 102.4474 0.5000 0.3965 0.276643 1.5223 50 125 1.5428 102.4474 0.5000 0.3965 0.278644 1.5223 50 125 1.5428 102.5184 0.5000 0.3965 0.279445 1.5223 50 125 1.5428 102.5184 0.5000 0.3965 0.284446 1.5223 50 125 1.5428 102.5184 0.5000 0.3965 0.285347 1.5223 50 125 1.5428 102.5184 0.5000 0.3965 0.286248 1.5223 50 125 1.5428 102.5184 0.5000 0.3965 0.2904

49 1.5223 50 125 1.5428 102.5184 0.5000 0.3965 0.290850 1.5223 50 125 1.5428 102.5184 0.5000 0.3965 0.2926

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;



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 :


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


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



(m)

Best

fitness

Mean

fitness

1 3.7331 77.8498 128.9791 3.6607 109.8497 1.2889 0.2113 0.14002 3.7331 77.8498 128.9791 3.6607 109.8497 1.2889 0.2113 0.14153 3.6606 77.8498 128.9791 3.5012 109.8497 1.2889 0.2146 0.14624 2.7072 54.3676 128.9791 3.5012 109.8497 1.2889 0.2697 0.15085 2.7072 54.3676 128.9791 3.5012 109.8497 1.2889 0.2697 0.15426 2.7072 54.3676 128.9791 3.5012 109.8497 1.2889 0.2697 0.15597 2.2724 54.3676 125 2.8457 109.8497 1.2889 0.3056 0.16218 2.0573 50 125 2.8457 109.8497 1.2889 0.3271 0.16499 2.0134 50 125 2.8457 104.1823 1.2889 0.3319 0.172610 2.0124 50 125 2.8457 104.1823 1.2867 0.3320 0.176311 1.7578 50 125 2.4134 98.5039 0.9571 0.3626 0.182312 1.6988 50 125 2.4134 98.5039 0.7878 0.3705 0.185513 1.6974 50 125 2.4134 99.6131 0.7878 0.3707 0.188914 1.6974 50 125 2.4134 99.6131 0.7878 0.3707 0.190415 1.5328 50 125 1.5031 97.4698 0.5000 0.3948 0.198916 1.5328 50 125 1.5031 97.4698 0.5000 0.3948 0.2003

17 1.5327 50 125 1.5283 97.4698 0.5000 0.3948 0.207018 1.5327 50 125 1.5283 97.4698 0.5000 0.3948 0.210119 1.5327 50 125 1.5283 97.4698 0.5000 0.3948 0.213320 1.5280 50 125 1.5283 98.7731 0.5000 0.3956 0.216921 1.5280 50 125 1.5283 98.7731 0.5000 0.3956 0.219422 1.5280 50 125 1.5283 98.7731 0.5000 0.3956 0.220623 1.5280 50 125 1.5522 98.7731 0.5000 0.3956 0.223424 1.5280 50 125 1.5522 98.7731 0.5000 0.3956 0.229125 1.5273 50 125 1.5522 99.0059 0.5000 0.3957 0.2308

26 1.5223 50 125 1.5522 102.4524 0.5000 0.3965 0.233527 1.5223 50 125 1.5522 102.4524 0.5000 0.3965 0.235028 1.5223 50 125 1.5522 102.4524 0.5000 0.3965 0.237229 1.5223 50 125 1.5522 102.4524 0.5000 0.3965 0.2390

165

30 1.5223 50 125 1.5522 102.4524 0.5000 0.3965 0.243831 1.5223 50 125 1.5522 102.4524 0.5000 0.3965 0.245232 1.5223 50 125 1.5522 102.4524 0.5000 0.3965 0.246233 1.5223 50 125 1.5446 102.4524 0.5000 0.3965 0.250534 1.5223 50 125 1.5446 102.4524 0.5000 0.3965 0.251935 1.5223 50 125 1.5446 102.4524 0.5000 0.3965 0.255536 1.5223 50 125 1.5446 102.4524 0.5000 0.3965 0.257137 1.5223 50 125 1.5446 102.4524 0.5000 0.3965 0.262538 1.5223 50 125 1.5446 102.4524 0.5000 0.3965 0.2665

39 1.5223 50 125 1.5446 102.4524 0.5000 0.3965 0.270140 1.5223 50 125 1.5446 102.4524 0.5000 0.3965 0.271241 1.5223 50 125 1.5446 102.4524 0.5000 0.3965 0.272542 1.5223 50 125 1.5446 102.4524 0.5000 0.3965 0.276043 1.5223 50 125 1.5446 102.4524 0.5000 0.3965 0.280744 1.5223 50 125 1.5446 102.4524 0.5000 0.3965 0.285045 1.5223 50 125 1.5446 102.4524 0.5000 0.3965 0.287046 1.5223 50 125 1.5446 102.4524 0.5000 0.3965 0.288847 1.5223 50 125 1.5446 102.4649 0.5000 0.3965 0.291248 1.5223 50 125 1.5446 102.4649 0.5000 0.3965 0.291949 1.5223 50 125 1.5446 102.4649 0.5000 0.3965 0.295050 1.5223 50 125 1.5446 102.4649 0.5000 0.3965 0.297951 1.5223 50 125 1.5446 102.4649 0.5000 0.3965 0.300652 1.5223 50 125 1.5446 102.4649 0.5000 0.3965 0.301553 1.5223 50 125 1.5446 102.4649 0.5000 0.3965 0.303754 1.5223 50 125 1.5446 102.4649 0.5000 0.3965 0.305055 1.5223 50 125 1.5446 102.4649 0.5000 0.3965 0.306156 1.5223 50 125 1.5446 102.4649 0.5000 0.3965 0.3090

57 1.5223 50 125 1.5446 102.4649 0.5000 0.3965 0.312758 1.5223 50 125 1.5446 102.4649 0.5000 0.3965 0.3133

59 1.5223 50 125 1.5446 102.4649 0.5000 0.3965 0.315260 1.5223 50 125 1.5436 102.4880 0.5000 0.3965 0.318861 1.5223 50 125 1.5436 102.4880 0.5000 0.3965 0.322262 1.5223 50 125 1.5436 102.4880 0.5000 0.3965 0.3232

166

63 1.5223 50 125 1.5446 102.4770 0.5000 0.3965 0.324864 1.5223 50 125 1.5446 102.4770 0.5000 0.3965 0.325665 1.5223 50 125 1.5446 102.4770 0.5000 0.3965 0.327066 1.5223 50 125 1.5453 102.4770 0.5000 0.3965 0.328267 1.5223 50 125 1.5453 102.4770 0.5000 0.3965 0.329568 1.5223 50 125 1.5453 102.4770 0.5000 0.3965 0.330469 1.5223 50 125 1.5453 102.4770 0.5000 0.3965 0.332970 1.5223 50 125 1.5453 102.4825 0.5000 0.3965 0.334371 1.5223 50 125 1.5453 102.4825 0.5000 0.3965 0.336072 1.5223 50 125 1.5453 102.4825 0.5000 0.3965 0.338873 1.5223 50 125 1.5453 102.4825 0.5000 0.3965 0.340374 1.5223 50 125 1.5453 102.4825 0.5000 0.3965 0.342975 1.5223 50 125 1.5453 102.4835 0.5000 0.3965 0.344076 1.5223 50 125 1.5453 102.4835 0.5000 0.3965 0.346277 1.5223 50 125 1.5453 102.4835 0.5000 0.3965 0.349578 1.5223 50 125 1.5453 102.4835 0.5000 0.3965 0.3505

79 1.5223 50 125 1.5453 102.4835 0.5000 0.3965 0.350780 1.5223 50 125 1.5453 102.4835 0.5000 0.3965 0.352781 1.5223 50 125 1.5453 102.4835 0.5000 0.3965 0.355782 1.5223 50 125 1.5453 102.4835 0.5000 0.3965 0.357983 1.5223 50 125 1.5453 102.4835 0.5000 0.3965 0.358884 1.5223 50 125 1.5448 102.4835 0.5000 0.3965 0.358985 1.5223 50 125 1.5448 102.4835 0.5000 0.3965 0.359386 1.5223 50 125 1.5448 102.4835 0.5000 0.3965 0.3605

87 1.5223 50 125 1.5448 102.4835 0.5000 0.3965 0.361288 1.5223 50 125 1.5448 102.4835 0.5000 0.3965 0.3622

89 1.5223 50 125 1.5448 102.4835 0.5000 0.3965 0.363790 1.5223 50 125 1.5448 102.4835 0.5000 0.3965 0.364391 1.5223 50 125 1.5448 102.4835 0.5000 0.3965 0.365592 1.5223 50 125 1.5448 102.4835 0.5000 0.3965 0.366093 1.5223 50 125 1.5448 102.4835 0.5000 0.3965 0.366694 1.5223 50 125 1.5448 102.4835 0.5000 0.3965 0.368895 1.5223 50 125 1.5448 102.4835 0.5000 0.3965 0.3696

167

96 1.5223 50 125 1.5448 102.4835 0.5000 0.3965 0.370197 1.5223 50 125 1.5448 102.4835 0.5000 0.3965 0.371998 1.5223 50 125 1.5448 102.4835 0.5000 0.3965 0.372599 1.5223 50 125 1.5448 102.4835 0.5000 0.3965 0.3734100 1.5223 50 125 1.5448 102.4868 0.5000 0.3965 0.3745

168

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.




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—



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 :



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


Cycle

5


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



(m)

Best

fitness

Mean

fitness

1 3.0485 52.3725 125 2.4067 92.6455 3.2450 0.2470 3.04852 3.0273 52.3725 125 2.4067 86.6599 3.2450 0.2483 3.02733 2.9094 50 125 2.4067 86.6599 3.2450 0.2558 2.90944 2.8429 50 125 2.1266 86.6599 3.2450 0.2602 2.84295 2.7381 50 141.2298 3.0432 113.3087 0.8982 0.2675 2.73816 2.4477 50.7560 125 2.8223 91.0909 2.1794 0.2901 2.44777 1.9679 50 125 3.0432 113.3087 0.8849 0.3369 1.96798 1.8787 50 125 2.7427 113.3087 0.8849 0.3474 0.16649 1.8768 50 125 2.7424 113.1437 0.8849 0.3476 0.1694

10 1.7025 50 125 2.1894 105.0051 0.8849 0.3700 0.1733

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


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 :



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


50 0.5


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


speed, 125Mpa waterjet pressure, 1.5359 mm standoff distance, 102.3683|am


172



(m)

Best

fitness

Mean

fitness

1 2.6782 57.2655 125 2.7471 67.8716 1.2845 0.2719 0.14812 2.6782 57.2655 125 2.7471 67.8716 1.2845 0.2719 0.15073 2.6013 57.2655 125 2.4336 67.8716 1.2845 0.2777 0.15464 2.6013 57.2655 125 2.4336 67.8716 1.2845 0.2777 0.15855 2.5975 57.2655 125 2.4154 67.8716 1.2845 0.2780 0.16086 2.5415 57.2655 125 2.0943 67.8716 1.2845 0.2824 0.1632

7 2.0984 50 125 2.0943 67.8716 0.8484 0.3227 0.16708 2.0096 50 125 2.0943 70.0319 0.6581 0.3323 0.16949 2.0096 50 125 2.0943 70.0319 0.6581 0.3323 0.174310 2.0096 50 125 2.0943 70.0319 0.6581 0.3323 0.176411 2.0096 50 125 2.0943 70.0319 0.6581 0.3323 0.178312 2.0096 50 125 2.0943 70.0319 0.6581 0.3323 0.180613 1.9585 57.7059 125 1.9942 100.7599 0.6390 0.3380 0.183314 1.9557 57.7059 125 1.9942 100.7599 0.6298 0.3383 0.185315 1.7787 50 125 2.0943 79.0936 0.5000 0.3599 0.187516 1.7787 50 125 2.0943 79.0936 0.5000 0.3599 0.1902

17 1.7431 50 125 2.0943 81.0289 0.5000 0.3646 0.192918 1.5436 50 125 1.9942 102.3683 0.5000 0.3931 0.1966

19 1.5223 50 125 1.5359 102.3683 0.5000 0.3965 0.199920 1.5223 50 125 1.5359 102.3895 0.5000 0.3965 0.2027


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


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 :




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


Cycle


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


1.5479 mm standoff distance, 102.521 ljam abrasive gritsize and 0.5000g/s abrasive

flowrate.

5

174


Cycle Min Ra XI (V) X 2(P ) X3 (h) X4 (d) X5

(m)

Best

fitness

Mean

fitness

1 2.8657 58.0213 145.3158 1.3389 100.4561 0.5129 0.2587 0.14372 2.8657 58.0213 145.3158 1.3389 100.4561 0.5129 0.2587 0.14713 2.7811 50 139.0474 1.3128 71.4895 1.4976 0.2645 0.15044 2.7811 50 139.0474 1.3128 71.4895 1.4976 0.2645 0.15415 2.7811 50 139.0474 1.3128 71.4895 1.4976 0.2645 0.15566 2.5200 58.0213 137.7459 1.6673 102.1511 0.5129 0.2841 0.15777 2.3723 58.0213 134.5636 1.6673 102.1511 0.5129 0.2965 0.15998 1.9129 58.0213 125 1.6186 102.1511 0.5129 0.3433 0.16279 1.5266 50 125 1.6186 102.1511 0.5129 0.3958 0.165610 1.5266 50 125 1.6186 102.1511 0.5129 0.3958 0.168611 1.5266 50 125 1.6186 102.1511 0.5129 0.3958 0.171912 1.5229 50 125 1.6186 102.1511 0.5000 0.3964 0.176313 1.5229 50 125 1.6186 102.1511 0.5000 0.3964 0.178714 1.5229 50 125 1.6186 102.1511 0.5000 0.3964 0.1813

15 1.5223 50 125 1.5479 102.1511 0.5000 0.3965 0.184316 1.5223 50 125 1.5479 102.6075 0.5000 0.3965 0.186917 1.5223 50 125 1.5479 102.4509 0.5000 0.3965 0.190918 1.5223 50 125 1.5479 102.4509 0.5000 0.3965 0.192819 1.5223 50 125 1.5479 102.4509 0.5000 0.3965 0.195120 1.5223 50 125 1.5479 102.4509 0.5000 0.3965 0.198221 1.5223 50 125 1.5479 102.4509 0.5000 0.3965 0.200522 1.5223 50 125 1.5479 102.4509 0.5000 0.3965 0.204223 1.5223 50 125 1.5479 102.4509 0.5000 0.3965 0.206724 1.5223 50 125 1.5479 102.4509 0.5000 0.3965 0.209125 1.5223 50 125 1.5479 102.4509 0.5000 0.3965 0.213226 1.5223 50 125 1.5479 102.4509 0.5000 0.3965 0.214727 1.5223 50 125 1.5479 102.4509 0.5000 0.3965 0.217128 1.5223 50 125 1.5450 102.5492 0.5000 0.3965 0.219329 1.5223 50 125 1.5450 102.5492 0.5000 0.3965 0.2243

175

30 1.5223 50 125 1.5450 102.5492 0.5000 0.3965 0.227531 1.5223 50 125 1.5450 102.5492 0.5000 0.3965 0.231032 1.5223 50 125 1.5450 102.5492 0.5000 0.3965 0.233233 1.5223 50 125 1.5450 102.5492 0.5000 0.3965 0.235334 1.5223 50 125 1.5450 102.5492 0.5000 0.3965 0.240435 1.5223 50 125 1.5450 102.5492 0.5000 0.3965 0.241836 1.5223 50 125 1.5450 102.5492 0.5000 0.3965 0.244837 1.5223 50 125 1.5450 102.5492 0.5000 0.3965 0.249838 1.5223 50 125 1.5450 102.5492 0.5000 0.3965 0.2540

39 1.5223 50 125 1.5450 102.5492 0.5000 0.3965 0.258240 1.5223 50 125 1.5450 102.5342 0.5000 0.3965 0.261641 1.5223 50 125 1.5450 102.5342 0.5000 0.3965 0.264242 1.5223 50 125 1.5450 102.5342 0.5000 0.3965 0.267643 1.5223 50 125 1.5450 102.5331 0.5000 0.3965 0.269844 1.5223 50 125 1.5450 102.4594 0.5000 0.3965 0.272745 1.5223 50 125 1.5450 102.4594 0.5000 0.3965 0.273746 1.5223 50 125 1.5450 102.4594 0.5000 0.3965 0.277247 1.5223 50 125 1.5450 102.4594 0.5000 0.3965 0.278448 1.5223 50 125 1.5454 102.5045 0.5000 0.3965 0.2823

49 1.5223 50 125 1.5454 102.5045 0.5000 0.3965 0.286050 1.5223 50 125 1.5454 102.5045 0.5000 0.3965 0.2904

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;



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 :




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


5


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


1.5504 mm standoff distance, 102.5213[am abrasive gritsize and 0.5000g/s abrasive

flowrate.

177



(m)

Best

fitness

Mean

fitness

1 2.2441 61.6679 125 1.1142 105.8174 0.9604 0.3083 0.13982 2.2441 61.6679 125 1.1142 105.8174 0.9604 0.3083 0.14193 2.2131 61.6679 125 1.3407 105.8174 0.9078 0.3112 0.14404 1.6647 50 125 1.3407 105.8174 0.9078 0.3753 0.15025 1.6647 50 125 1.3407 105.8174 0.9078 0.3753 0.15216 1.6629 50 125 1.5504 105.8174 0.9078 0.3755 0.1576

7 1.5695 50 125 1.6020 93.3007 0.5501 0.3892 0.1601

8 1.5223 50 125 1.5504 102.5213 0.5000 0.3965 0.16389 1.5223 50 125 1.5504 102.5213 0.5000 0.3965 0.166110 1.5223 50 125 1.5504 102.5213 0.5000 0.3965 0.169011 1.5223 50 125 1.5504 102.5213 0.5000 0.3965 0.171812 1.5223 50 125 1.5504 102.5213 0.5000 0.3965 0.174713 1.5223 50 125 1.5504 102.5213 0.5000 0.3965 0.178714 1.5223 50 125 1.5504 102.5213 0.5000 0.3965 0.180815 1.5223 50 125 1.5504 102.5213 0.5000 0.3965 0.187016 1.5223 50 125 1.5450 102.5213 0.5000 0.3965 0.1915

17 1.5223 50 125 1.5450 102.5213 0.5000 0.3965 0.192718 1.5223 50 125 1.5450 102.5213 0.5000 0.3965 0.197819 1.5223 50 125 1.5450 102.5213 0.5000 0.3965 0.201020 1.5223 50 125 1.5450 102.5213 0.5000 0.3965 0.204221 1.5223 50 125 1.5450 102.5213 0.5000 0.3965 0.207322 1.5223 50 125 1.5450 102.5213 0.5000 0.3965 0.210323 1.5223 50 125 1.5450 102.5213 0.5000 0.3965 0.213724 1.5223 50 125 1.5450 102.5050 0.5000 0.3965 0.217725 1.5223 50 125 1.5450 102.5050 0.5000 0.3965 0.220126 1.5223 50 125 1.5450 102.5050 0.5000 0.3965 0.2226

27 1.5223 50 125 1.5450 102.5050 0.5000 0.3965 0.226528 1.5223 50 125 1.5450 102.5050 0.5000 0.3965 0.229629 1.5223 50 125 1.5450 102.5050 0.5000 0.3965 0.2319

178

30 1.5223 50 125 1.5450 102.5050 0.5000 0.3965 0.234231 1.5223 50 125 1.5450 102.5050 0.5000 0.3965 0.239732 1.5223 50 125 1.5450 102.5050 0.5000 0.3965 0.241833 1.5223 50 125 1.5450 102.5050 0.5000 0.3965 0.245834 1.5223 50 125 1.5450 102.5050 0.5000 0.3965 0.250635 1.5223 50 125 1.5450 102.5050 0.5000 0.3965 0.253136 1.5223 50 125 1.5450 102.5050 0.5000 0.3965 0.255537 1.5223 50 125 1.5450 102.5050 0.5000 0.3965 0.258138 1.5223 50 125 1.5450 102.5050 0.5000 0.3965 0.2651

39 1.5223 50 125 1.5450 102.5050 0.5000 0.3965 0.268940 1.5223 50 125 1.5450 102.5050 0.5000 0.3965 0.270241 1.5223 50 125 1.5450 102.5050 0.5000 0.3965 0.272942 1.5223 50 125 1.5450 102.5050 0.5000 0.3965 0.278443 1.5223 50 125 1.5450 102.5050 0.5000 0.3965 0.282144 1.5223 50 125 1.5450 102.5050 0.5000 0.3965 0.285445 1.5223 50 125 1.5450 102.5050 0.5000 0.3965 0.287246 1.5223 50 125 1.5450 102.5050 0.5000 0.3965 0.290047 1.5223 50 125 1.5450 102.5050 0.5000 0.3965 0.292148 1.5223 50 125 1.5450 102.5050 0.5000 0.3965 0.2946

49 1.5223 50 125 1.5450 102.5050 0.5000 0.3965 0.296650 1.5223 50 125 1.5450 102.5050 0.5000 0.3965 0.298351 1.5223 50 125 1.5450 102.5050 0.5000 0.3965 0.301052 1.5223 50 125 1.5450 102.5050 0.5000 0.3965 0.302753 1.5223 50 125 1.5450 102.5050 0.5000 0.3965 0.306254 1.5223 50 125 1.5450 102.5050 0.5000 0.3965 0.307455 1.5223 50 125 1.5450 102.5050 0.5000 0.3965 0.310456 1.5223 50 125 1.5450 102.5050 0.5000 0.3965 0.3128

57 1.5223 50 125 1.5450 102.5050 0.5000 0.3965 0.314558 1.5223 50 125 1.5450 102.5050 0.5000 0.3965 0.3166

59 1.5223 50 125 1.5450 102.5050 0.5000 0.3965 0.318160 1.5223 50 125 1.5450 102.5050 0.5000 0.3965 0.320661 1.5223 50 125 1.5450 102.5050 0.5000 0.3965 0.322262 1.5223 50 125 1.5450 102.5050 0.5000 0.3965 0.3228

179

63 1.5223 50 125 1.5450 102.5050 0.5000 0.3965 0.324364 1.5223 50 125 1.5450 102.5050 0.5000 0.3965 0.325365 1.5223 50 125 1.5450 102.5050 0.5000 0.3965 0.326666 1.5223 50 125 1.5450 102.5050 0.5000 0.3965 0.327367 1.5223 50 125 1.5450 102.5050 0.5000 0.3965 0.330068 1.5223 50 125 1.5450 102.5050 0.5000 0.3965 0.331769 1.5223 50 125 1.5450 102.5050 0.5000 0.3965 0.332870 1.5223 50 125 1.5450 102.5050 0.5000 0.3965 0.334171 1.5223 50 125 1.5450 102.5050 0.5000 0.3965 0.336572 1.5223 50 125 1.5450 102.5050 0.5000 0.3965 0.338073 1.5223 50 125 1.5450 102.5050 0.5000 0.3965 0.340574 1.5223 50 125 1.5450 102.5050 0.5000 0.3965 0.342275 1.5223 50 125 1.5450 102.5050 0.5000 0.3965 0.344976 1.5223 50 125 1.5450 102.5050 0.5000 0.3965 0.345477 1.5223 50 125 1.5450 102.5050 0.5000 0.3965 0.346278 1.5223 50 125 1.5450 102.5050 0.5000 0.3965 0.347979 1.5223 50 125 1.5450 102.5002 0.5000 0.3965 0.348880 1.5223 50 125 1.5450 102.5002 0.5000 0.3965 0.349581 1.5223 50 125 1.5450 102.5002 0.5000 0.3965 0.353282 1.5223 50 125 1.5450 102.5002 0.5000 0.3965 0.355883 1.5223 50 125 1.5450 102.5002 0.5000 0.3965 0.360584 1.5223 50 125 1.5450 102.5002 0.5000 0.3965 0.362785 1.5223 50 125 1.5450 102.5002 0.5000 0.3965 0.363086 1.5223 50 125 1.5450 102.5002 0.5000 0.3965 0.3645

87 1.5223 50 125 1.5450 102.5002 0.5000 0.3965 0.365888 1.5223 50 125 1.5450 102.5002 0.5000 0.3965 0.3663

89 1.5223 50 125 1.5450 102.5002 0.5000 0.3965 0.366590 1.5223 50 125 1.5450 102.5002 0.5000 0.3965 0.366791 1.5223 50 125 1.5450 102.5002 0.5000 0.3965 0.368692 1.5223 50 125 1.5450 102.4978 0.5000 0.3965 0.369593 1.5223 50 125 1.5450 102.4978 0.5000 0.3965 0.370194 1.5223 50 125 1.5450 102.4978 0.5000 0.3965 0.371295 1.5223 50 125 1.5450 102.4978 0.5000 0.3965 0.3717

180

96 1.5223 50 125 1.5450 102.4978 0.5000 0.3965 0.371797 1.5223 50 125 1.5450 102.4978 0.5000 0.3965 0.372598 1.5223 50 125 1.5450 102.4978 0.5000 0.3965 0.373199 1.5223 50 125 1.5450 102.4978 0.5000 0.3965 0.3736100 1.5223 50 125 1.5450 102.4978 0.5000 0.3965 0.3742

4.9 Summary of end milling experimental results

181

A number of 10, 20, 50 and 100 colony sizes have been tested and the

algorithm has been run 10 times for each of the population size. From the experiment

it can be observed that the lowest value of Ra can be achieved by using the smallest

bee colony size of 10. The bee colony size of 10 gives a minimal Ra value of

0.1719|am even though the value of bee colony size is increased to 100. All control

variables combination with the bee colony size of 10 gives a minimal Ra value of

1.1719(j,m in first runs. In bee colony size of 20, the first control variables

combination gives a minimal Ra value of 0.1725|am. This Ra value is improved by

0.3% when the max cycles per run are increased to 20, 50 and 100.

0.05

20

Colony Size 10

Colony Size 20

Colony Size 50

Colony Size 100

40 60

Cycles

80 100 120

Figure 4.34 Comparison of the effect of colony size in end milling experiment

When the bee colony size is increased to 50 and 100, all control variables

combinations also give good results where the minimal Ra value found is 0.1719|am.

From the experiment, we found out that a minimum of max per cycle 10 with 10 runs

is sufficient to get a minimum value of Ra. Even if we increased the number of runs

182

and max per cycles value, the results did not give any significant differences. The

average minimal Ra value of 0.1719(j,m is achieved on the sixth runs. Figure 4.34

shows the comparison of effect of population size in end milling machining. Table

4.42 shows the summary of ABC optimization results using different colony size and

limit in end milling.

Table 4.41: Summary of ABC optimization results using different colony size

and limit in end milling

Colony Size Max cycles per run Limit Min Ra (|im)

10 10 30

0.1719

10 20 30

10 50 30

10 100 30

20 10 60 0.1725

20 20 60

0.171920 50 60

20 100 60

50 10 150

0.1719

50 20 150

50 50 150

50 100 150

100 10 300

0.1719

100 20 300

100 50 300

100 100 300

4.10 Summary of AWJ experimental results

183

In Experiment 2 of AWJ, the same control parameter setting of end milling

experiment was employed. The experiment shows that a smaller number of bee

colony sizes, 10 also give an optimal Ra value. For bee colony size of 10, the first

control variables combinations give a minimum Ra value of 2.7090. The value of Ra

is improved by 41% when the max cycles per run value increased to 20. The minimal

Ra value found is 1.6032|am.

Next, when the max cycles per run are increased to 50 and 100, the minimal

Ra value found is 1.5223[am. This minimal Ra value is enhanced by 44% and 5%

compared to the first and second control variables combinations respectively. When

the bee colony size is increased to 20, the minimal Ra value achieved is 1.6247|am.

When the max cycle per run is increases to 20, the minimal Ra value achieved is

1,5229|am which is less by 6% compared to the first control variable combinations of

bee colony size 20. The minimal Ra of 1.5223[am is achieved when the max cycle per

run was increased to 50 and 100. This minimal Ra value is less by 6% and 0.04%

compared to the first and second control variable combinations. Subsequently, the

bee colony size is increased to 50. The first control variables combinations give a

minimal Ra value of 1.5769|am. This minimal Ra value is improved further by 3%

where a minimal Ra value of 1.5280 is found in the second control variables

combinations. When the max cycles per run are increased to 50 and 100, the minimal

Ra value achieved is 1.5223(j,m.

184

3.5

2.5OJc

_cdarjocr:O!

DCO

1.5

0.5

t

\

V ' I __

• • ColonySize 10

“ “ ColonySize 20

ColonySize 50

—■ColonySize 100

20 40 60

Cycles

SO 100 120

Figure 4.35 Comparison of the effect of colony size in AWJ experiment

For the last experiments, the bee colony size is increased to 100. The first

control variables combinations give a minimal Ra value of 1.7025(j,m. However this

minimal Ra value was further improved by 10% in the second, third and fourth

control variables combinations where a minimal Ra value of 1.5223[am is found. In

AWJ machining experiment, we found out that to get a minimal Ra value of

1.5223jam, a minimum 50 max cycle per and 10 runs is adequate. A max cycle value

of 10 and 20 did not give a good result in all bee colony sizes. The average minimal

Ra value of 0.15223[am is achieved on the sixth runs. Figure 4.35 shows the

comparison of the effect of colony size in AWJ. Table 4.44 shows the summary of

ABC optimization results using different colony size and limit in AWJ.

and limit in AWJ

Table 4.42: Summary of ABC optimization results using different colony

Colony Size Max cycles per run Limit Min Ra (|im)

10 10 50 2.7090

10 20 50 1.6032

10 50 50 1.5223

10 100 50

20 10 100 1.6247

20 20 100 1.5229

20 50 100

1.522320 100 100

50 10 250 1.5769

50 20 250 1.5280

50 50 250

1.522350 100 250

100 10 500 1.7025

100 20 500

1.5223100 50 500

100 100 500

CHAPTER 5

ANALYSIS OF RESULTS

1.1 Introduction

The objective of this chapter is to validate and evaluate the results of ABC

optimization. Validation is performed to determine whether the results of ABC

optimization technique are acceptable to describe the problem investigated.

Evaluation process is conducted to investigate how significance of results from ABC

optimization technique for the problem investigated. In the previous chapter, the

main phases of ABC optimization was described in details and the experimental

results also have been presented.

187

The validation process of ABC optimization results is given as follows:

i. For end milling and AWJ, the equation 4.1 and 4.2 are used to

validate the results respectively.

The evaluation processes of ABC optimization results are given as follows:

i. Analyse the predicted Ra value estimated by ABC optimization.

ii. Analyse optimal process parameters estimated by ABC optimization.

5.2 Analysis of results

5.2.1 Validation and evaluation of ABC for end milling

The best results of end milling are shown in Figure 5.2 where the set values

of process parameters that lead to the minimum Ra value for ABC are 167.0300

m/min for cutting speed, 0.0250 mm/tooth for feed rate and 6.200° for radial rake

angle. Based on equation 4.1, the calculation for validating the ABC result for end

milling is given as follows:

Ra= 0.237 - 0.00175 (167.0300) + 8.693 (0.0250) + 0.00159 (6.200)

= 0.17185 ~0.1719(am

188

As a result, evaluations of the Ra for ABC optimization results for end milling are

given as follows:

(i) Evaluation of the Ra for ABC in end milling

(a) Experimental data vs. ABC

With Ra = 0.1719|am for ABC and Ra = 0.190[am for experimental data, it can

be stated that ABC has given a lower minimum value of the predicted Ra by

about 0.0181 jam.

(b) Regression vs ABC

With Ra = 0.1719|am for ABC and Ra = 0.187jam for regression, it can be

stated that ABC has given a lower minimum value of the predicted Ra by

about 0.0151 jam.

(c) GA vs ABC

GA performance is much better than ABC by giving a minimal value of the

predicted by about 0.0334|am where Ra = 0.1719|am for ABC and Ra =

0.1385|am for GA.

(d) SA vs. ABC

SA performance is much better than ABC by giving a minimal value of the

predicted by about 0.0334|am where Ra = 0.1719|am for ABC and Ra =

0.1385(j,m for SA.

189

In order to evaluate the optimal process parameters of ABC for end milling,

the values of the process parameters level of the end milling experimental design,

noted as -1.4142, -1, 0, +1 and +1.4142 as given in Table 2.6 are classified as the

lowest, lower, medium, high, highest scales. With xi = optimal cutting conditions of

AWJ, Table 5.1 shows the conditions used to define the scale of the levels for the

three optimal process parameters.

Table 5.1: Conditions to define the scale for optimal process parameters of end

milling

(ii) Evaluation of the optimal process parameters for ABC in end milling

Decision Independent variables

v (m/min) / (mm/tooth) y(°)

Lowest 124.53 < xi < 133.03 0.025 < xi < 0.036 6.20 < xi < 7.92

Low 133.03 < xi < 141.53 0.036 < xi < 0.048 7.92 < xi < 9.64

Medium 141.53 < xi < 150.03 0.048 < xi < 0.059 9.64 < xi < 11.36

High 150.03 < xi < 158.53 0.059 < xi < 0.071 11.36 < xi < 13.08

Highest 158.53 < xi < 167.03 0.071 < xi< 0.083 13.08 < xi < 14.80

The set values of optimal process parameters that lead to the minimum Ra

value are 167.0300 m/mm for cutting speed, 0.0250 mm/tooth for feed rate and

6.200° for radial rake angle. Considering the conditions given in Table 5.2, it could

be stated that optimal process parameters that lead to minimum predicted Ra value

are highest cutting speed, lowest feed rate and lowest radial rake angle. Table 5.3

below shows the comparison of the optimal process parameters in end milling using

three optimization techniques such as GA, SA and ABC.

Table 5.2: Comparison of the optimal process parameters in end milling

Technique Cutting Speed (v) Feed rate if) Radial rake

angle (y)

The best

predicted

value of Ra

GA 167.029 0.025 14.769 0.138

SA 167.03 0.025 14.797 0.1385

ABC 167.0300 0.0250 6.200 0.1719

5.2.2 Validation and evaluation of ABC for AWJ

Figure 5.3 shows the optimal solution of the ABC are 50 mm/min for cutting

speed, 125 Mpa for waterjet pressure, 1.5504 mm for standoff distance, 102.5213(j,m

for abrasive grit size and 0.5 g/s for abrasive flow rate. Considering Equation 4.2, the

calculation for validating the AWJ is given as follows:

Ra = -5.07976 + 0.08169 (50)+ 0.07912 (125) - 0.34221 (1.5504) - 0.08661

(102.5213) - 0.34866 (0.5) - 0.00031 (50)2 - 0.00012 (125)2 + 0.10575 (1.5504)2 +

0.00041 (102.5213)2 + 0.07590 (0.5)2 - 0.00008 (50) (0.5)- 0.00009 (125) (0.5) +

0.03089 (1.5504) (0.5) + 0.00513 (102.5213) (0.5)

= 1.52227 ~ 1.5223(j,m

191

As a result, evaluations of the Ra for ABC optimization results for end milling are

given as follows:

(i) Evaluation of the Ra for ABC in AWJ

(a) Experimental data vs. ABC

With Ra = 1.5223[am for ABC and Ra = 2.124(j,m for experimental data, it can

be stated that ABC has given a lower minimum value of the predicted Ra by

about 0.6017|jm.

(b) Regression vs ABC

With Ra = 1.5223|am for ABC and Ra = 2.62195(j,m for regression, it can be

stated that ABC has given a lower minimum value of the predicted Ra by

about 0.10685|jm.

(c) GA vs ABC

With Ra = 1.5223 [am for ABC and Ra = 1,5549|am for GA, it can be stated

that ABC performance is much better than GA by giving a minimal value of

the predicted by about 0.0326(j,m.

(d) SA vs. ABC

With Ra = 1.5223[am for ABC and Ra = 1,5355|am for ABC, it can be stated

that ABC performance is much better than SA by giving a minimal value of

the predicted by about 0.0132|am.

192

In order to evaluate the optimal process parameters of ABC for AWJ, the

values of the cutting condition level noted as 1, 2 and 3 as given in Table 2.9, are

classified as the lowest, lower, medium, high, highest scales. With xi = optimal

cutting conditions of AWJ, Table 5.3 shows the conditions used to define the scale of

the levels for the five optimal process parameters.

Table 5.3: Conditions to define the scale for optimal process parameters of AWJ

(ii) Evaluation of the optimal process parameters for ABC in AWJ

Decision Independent variables

V (mm/min) P (Mpa) h (mm) d (jam) m (g/s)Lowest 50 < xi< 70 125 <xi< 150 1.0 <xi< 1.6 60 <xi< 72 0.5 <xi< 1.1

Low 70 < xi< 90 150 <xi< 175 1.6 <xi< 2.2 72 <xi< 84 1.1 <xi< 1.7

Medium 90 <xi< 110 175 <xi< 200 2.2 <xi< 2.8 84 <xi< 96 1.7 <xi< 2.3

High 110 <xi < 130 200 <xi < 225 2.8 <xi< 3.4 96 <xi< 108

2.3 < xi< 2.9

Highest 130 <xi \ <

150225 <xi < 250 3.4 <xi< 4.0 108 <xi<

1202.9 <xi< 3.5

The set values of optimal process parameters that lead to the minimum Ra

value are 50 mm/min for traverse speed, 125 MPa for waterjet pressure, 1.5504 mm

for standoff distance, 102.5213 jam for abrasive grit size and 0.500 g/s for abrasive

flow rate. Considering the conditions given in Table 5.3, it could be stated that

optimal process parameters that lead to minimum predicted Ra value lowest cutting

speed, lowest waterjet pressure, lowest standoff distance, high abrasive grit size and

lowest abrasive flow rate. Table 5.4 below shows the comparison of the optimal

process parameters in end milling using three optimization techniques such as GA,

SA and ABC,

193

Table 5.4: Comparison of the optimal process parameters in AWJ

Technique Traverse

cutting

speed (V)

Waterjet

pressure

(P)

Standoff

distance

(h)

Abrasive

grit size

{d)

Abrasive

flow rate

(m)

The best

predicted

value of

Ra

GA 50.024 125.018 1.636 94.73 0.525 1.5549

SA 50.003 125.029 1.486 107.737 0.500 1.5335

ABC 50 125 1.5504 102.5213 0.500 1.5223

In Table 5.5, a minimal Ra of 0.1719(j,m was found using ABC and it is clear

that ABC algorithm outperforms experimental and regression results in optimizing

process parameters of end milling machining. However, compared to GA and SA,

both techniques performed better than ABC where the Ra value achieved was much

lower compared to ABC. There are a few possibilities that can clarify these

outcomes such as:

i. The regression model that was employed in end milling in equation

3.4 was a simple regression model compared to AWJ where the

regression model used in equation 3.10 was developed using second

order polynomial regression.

ii. In end milling, the optimal process parameters setting that lead to

minimum predicted Ra value of 0.1719|am are highest cutting speed,

lowest feed rate and lowest radial rake angle. Compared to GA and

SA optimization, both have the same setting of highest cutting speed

and lowest feed rate. However for the third process parameters, the

setting of radial rake angle is highest in GA and SA.

194

Table 5.5: Comparison of minimum Ra in end milling and AWJ machining

Technique Min Ra in Experiment 1 -

(End milling)

Min Ra in Experiment 2 -(AWJ)

Experimental 0.190 2.124

Regression 0.187 2.62915

GA 0.139 1.5549

SA 0.1385 1.5355

ABC 0.1719 1.5223

In AWJ, a minimum Ra value of 1.5223[am was achieved and when compared

to experimental, regression, GA and SA, it has been found that ABC technique

decrease the Ra value which are about, 28%, 42%, 2% and 0.9% respectively. In

optimizing the process parameters of AWJ, the performance of ABC is superior

compared to experimental, regression, GA and SA.

195

This chapter has discussed the validation and evaluation of results of the

ABC optimization that was proposed in this study. From the results, the proposed

technique was successfully found minimum Ra value in both end milling and AWJ.

In end milling, the ABC performance is better compared to the experimental and

regression but not GA and SA. However the performance of ABC is better in AWJ

where the minimal Ra found was lower compared to experimental, regression, GA

and SA.

5.3 Summary

CHAPTER 6

CONCLUSION AND FUTURE WORK

6.1 Introduction

This chapter discusses the work that has been done or overall conclusion to

complete this study. Basically, the aim of this study is to study the optimal effect of

process parameters of end milling and AWJ machining in influencing the minimum

Ra value. In this study, experiments design for Ra measurement based on the work of

(Mohruni, 2008) for end milling machining and (Caydas and Hascalik, 2008) for

AWJ machining have been referred. The regression modeling was developed and

ABC optimization algorithm was employed to find the minimum Ra value. The

performance of ABC technique was evaluated and has been compared to the results

of experimental, regression, GA and SA techniques.

197

In doing this research, the work had been done according to the steps outlined

in the project methodology. The experiments that have been done and the summary

of work in this research are listed below:

i. Assessment of real experimental data based on effort

attempted by Mohruni (2008) and also (Caydas and Hascalik,

2008).

ii. Regression modeling development

iii. ABC algorithm for optimization of process parameters

a) Formulation of optimization solution

b) Find the combination of the optimal process parameters.

c) Find the minimum Ra value.

iv. Validation and evaluation of results

a) The minimum Ra value of ABC was compared to the result

of experimental sample data, regression modeling, GA and

SA.

6.1 Summary of Work

198

Based on the experiment that has been done on this study, the summary of the

experiments are as follows:

i. From Table 6.1, the minimum Ra value in end milling found was

0.1719|am by using ABC optimization algorithm. When compared to

other techniques such as experimental and regression, the Ra value

using the proposed technique was much lower by 10% and 8%

respectively. However when compared to other optimization

technique such as GA and SA, both techniques give minimum Ra

value compared to ABC. In GA and SA, the minimum Ra value found

was 0.139|am.

Table 6.1: Reduction percentage of minimum surface roughness in end milling

6.2 Research summary and conclusion

Data type Technique % of reduction

End milling ABC vs. experimental 10%

ABC vs. regression 8%

ABC vs. GA -23.6%

ABC vs. SA -23.6%

ii. In optimizing process parameters of AWJ machining, the minimum Ra

value found was 1.5223jj,m. This Ra value was the lowest compared to

other technique like experimental, regression, GA and SA. In

experimental the minimum Ra value was 2.124|am and in regression

the minimum Ra value was 2.62915[am. ABC optimization technique

successfully minimized the Ra value by 28% and 42% from

experimental and regression.

199

When compared to GA and SA, ABC also gives better results where

the Ra value was much lower in GA and SA by 2% and 0.9%

respectively. This is shown in Table 6.2.

Table 6.2: Reduction percentage of minimum surface roughness in AWJ

Data type Technique % of reduction

AWJ ABC vs. experimental 28%

ABC vs. regression 42%

ABC vs. GA 2%

ABC vs. SA 0.9%

iii. Referring to Table 6.3, it can be pointed out that a smaller number of

bee colony sizes were adequate to find the most minimum Ra value in

both end milling and AWJ. In end milling experiments, a bee colony

size of 10 was sufficient to find the minimal Ra value of 0.1719|am

with a maximum number of cycles of 10. When the bee colony size

was increased to 20, 50 and 100, the results remained the same. This

is also happened in AWJ experiments where the minimum Ra value of

1.5223 pm can be found using a smaller number of bee colony size of

10 with a maximum number of cycles of 50. In order to get the best

results, it is mostly determined by the control variable of max cycles

per run. As the value of max cycle per run was increased, the

performance of ABC was also improved. In both end milling and

AWJ experiments, the value 50 and 100 of max cycles per run gives a

better performance. In both machining experiment, an average of sixth

runs is needed to get the best minimal Ra value. When the number of

runs is increased, it does not give any major differences to the result.

200

Table 6.3: Summary of minimum bee colony size and max number of cycles

Data type Bee colony

size

Max number

of cycles

Average

number of

runs

Min Ra (|im)

End milling 10 10 6 0.1719

AWJ 10 50 6 1.5223

iv. By using ABC optimization, the dominant factors that affects for

giving a minimum Ra value in end milling is feed rate if). In ABC, the

minimum Ra value is higher compared to minimum Ra value in GA

and SA. This might be influenced by a lowest level of radial rake

angle (y) as shown in Table 6.4. For AWJ, it was found out that

traverse speed (v) and waterjet pressure ip) are the dominant factors

that influence for giving a minimum Ra value. The level of process

parameters for giving minimum Ra value are the same in SA and GA

approach which are lowest traverse speed ( V), lowest waterjet

pressure (P), lowest standoff distance (h), high abrasive grit size id)

and lowest abrasive flow rate (m). The summary of level of thr

optimal process parameters is shown in Table 6.4.

201

Table 6.4: Summary of level of the optimal process parameters

Technique Level of process parameters

End milling AWJV / y V P h d m

Experimental Hgst Lwst High Lwst Lwst Lwst Lwst Lwst

Regression Med Lwst Low Lwst Lwst Lwst Lwst Med

GA Hgst Lwst Hgst Lwst Lwst Low Med Lwst

SA Hgst Lwst Hgst Lwst Lwst Lwst High Lwst

ABC Hgst Lwst Lwst Lwst Lwst Lwst High Lwst

Indicator of level: Lwst = Lowest, Med = Medium, Hgst = E ighest

6.3 Suggestion for Future Work

In summary, the experimental result have been achieved and evaluated in this

study. However, there are several suggestions for the future works to improve the

performance of this project that can be done later.

i. Currently, the hybrid optimization technique has become a trend

among researchers. By hybridizing the proposed techniques with other

optimization techniques such as GA, SA, PSO or AIS the results

could be improved.

ii. In this study, only a several process parameters have been considered

in order to find a minimum Ra value. In the future, more process

parameters can be considered as well for the machining performances

not just limited to find Ra value. Other machining performances that

can be considered are MRR, production time, production cost, tool

wear, tool geometry and etc.

202

iii. There are two type of machining processes focused in this study

which are end milling (traditional machining) and abrasive waterjet

machining (modem machining). In the future, trial are suggested for

different kind of machining processes especially on other traditional

machining processes such as turning and also modem machining such

as electrical discharge machining (EDM), Wire-cut electro discharge

machining (WEDM).

6.5 Summary

This chapter has discussed and concluded the aim of this study. The results of

the study were presented and evaluated. The three objectives of the study were

achieved and lastly recommendations of future works were suggested.

203

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