Phát triển các phương pháp tối ưu hóa thông minh cho các bài toán cơ học

MINISTRY OF EDUCATION AND TRAINING
HO CHI MINH CITY
UNIVERSITY OF TECHNOLOGY AND EDUCATION

LAM PHAT THUAN

DEVELOPMENT OF META-HEURISTIC OPTIMIZATION
METHODS FOR MECHANICS PROBLEMS

PHD THESIS
MAJOR: ENGINEERING MECHANICS

Ho Chi Minh City, 01/2021


THE WORK IS COMPLETED AT
HCM CITY UNIVERSITY OF TECHNOLOGY AND EDUCATION

LAM PHAT THUAN

DEVELOPMENT OF META-HEURISTIC
OPTIMIZATION METHODS FOR MECHANICS
PROBLEMS
MAJOR: ENGINEERING MECHANICS - 13252010105

Supervisor 1: Assoc. Prof. NGUYEN HOAI SON
Supervisor 2: Assoc. Prof. LE ANH THANG

PhD thesis is protected in front of
EXAMINATION COMMITTEE FOR PROTECTION OF DOCTORAL THESIS

HCM CITY UNIVERSITY OF TECHNOLOGY AND EDUCATION
Date……month……year……

ii


ORIGINALITY STATEMENT
I, Lam Phat Thuan, hereby assure that this dissertation is my own work.
The data and results stated in this dissertation are honest and have not been
published by any works.
Ho Chi Minh City, January 2021

Lam Phat Thuan


ACKNOWLEDGEMENTS
This dissertation has been carried out in the Faculty of Civil Engineering, HCM
City University of Technology and Education, Viet Nam. The process of conducting
this thesis brings excitement but has quite a few challenges and difficulties. And I
can say without hesitation that it has been finished thanks to the encouragement,
support and help of my professors and colleagues.
First of all, I would like to express my deepest gratitude to Assoc. Prof. Dr. Nguyen
Hoai Son and Assoc. Prof. Le Anh Thang, especially Assoc. Prof. Dr. Nguyen Hoai
Son from GACES Group, Ho Chi Minh City University of Technology and
Education, Vietnam for having accepted me as their PhD student and for the
enthusiastic guidance and mobilization during my research.
Secondly, I would like also to acknowledge Msc. Ho Huu Vinh for his
troubleshooting and the cooperation in my study. Furthermore, I am grateful to Civil
Engineering Faculty for their great support to help me have good environment to do
my research.

Thirdly, I take this chance to thank all my nice colleagues at the Faculty of Civil
Engineering, Ho Chi Minh City University of Technology and Education, for their
professional advice and friendly support.
Finally, this dissertation is dedicated to my parents who have always given me
valuable encouragement and assistance.
Lam Phat Thuan

ii


ABSTRACT
Almost all design problems in engineering can be considered as optimization problems
and thus require optimization techniques to solve. During the past few decades, many
optimization techniques have been proposed and applied to solve a wide range of
various optimization problems. Among them, meta-heuristic algorithms have gained
huge popularity in recent years in solving design optimization problems of many types
of structure with different materials. These meta-heuristic algorithms include genetic
algorithms (GA), particle swarm optimization (PSO), bat algorithm (BA), cuckoo
search (CS), differential evolution (DE), firefly algorithm (DA), harmony search (HS),
flower pollination algorithm (FPA), ant colony optimization (ACO), bee algorithms
(BA), Jaya algorithm and many others. Among the methods mentioned above, the
Differential Evolution is one of the most widely used methods. Since it was first
introduced in 1997 by Storn and Price [1], many studies have been carried out to
improve and apply DE in solving structural optimization problems. The DE has
demonstrated excellently performance in solving many different engineering problems.
Besides the Differential Evolution algorithm, the Jaya algorithm recently proposed by
Rao [2] in 2016 is also an effective and efficient methods that has been widely applied
to solve many optimization problems and showed its good performance. It gains
dominate results when being tested with benchmark test functions in comparison with
other meta-heuristic methods. However, like many other population-based optimization

algorithms, one of the disadvantages of DE and Jaya is that the computational time
obtaining optimal solutions is much slower than the gradient-based optimization
methods. This is because DE and Jaya takes a lot of time evaluating the fitness of
individuals in the population. To overcome this disadvantage, Artificial Neuron
Networks (ANN) are studied to combine with the meta-heuristic algorithms, such as
Differential Evolution, to form a new approach which has the ability to solve the design
optimization effectively. Moreover, one of the most important issues in engineering
design is that the optimal designs are often effected by uncertainties which can be
occurred from various sources, such as

iii


manufacturing processes, material properties and operating environments. These
uncertainties may cause structures to improper performance as in the original
design, and hence may result in risks to structures [3]. Therefore, reliability-based
design optimization (RBDO) can be considered as an important and comprehensive
strategy for finding an optimal design.
In this dissertation, an improved version of Differential Evolution has been first
time utilized to solve for optimal fiber angle and thickness of the reinforced
composite. Secondly, the Artificial Neural Network is integrated to the optimization
process of the improved Differential Evolution algorithm to form a new algorithm
call ABDE (ANN-based Differential Evolution) algorithm. This new algorithm is
then applied to solve optimization problems of the reinforced composite plate
structures. Thirdly, an elitist selection technique is utilized to modify the selection
step of the original Jaya algorithm to improve the convergence of the algorithm and
formed a new version of the original Jaya called iJaya algorithm. The improved
Jaya algorithm is then applied to solve for optimization problem of the Timoshenko
composite beam and obtained very good results. Finally, the so-called called
(SLMD-iJaya) algorithm which is the combination of the improved Jaya algorithm

and the Global Single-Loop Deterministic Methods (SLDM) has been proposed as a
new tool set for solving the Reliability-Based Design Optimization problems. This
new method is applied to look for optimal design of Timoshenko composite beam
structures with certain level of reliability.

iv


TĨM TẮT
Hầu như các bài tốn thiết kế trong kỹ thuật có thể được coi là những bài tốn tối ưu và
do đó địi hỏi các kỹ thuật tối ưu hóa để giải quyết. Trong những thập kỷ qua, nhiều kỹ
thuật tối ưu hóa đã được đề xuất và áp dụng để giải quyết một loạt các vấn đề khác
nhau. Trong số đó, các thuật tốn meta-heuristic đã trở nên phổ biến trong những năm
gần đây trong việc giải quyết các vấn đề tối ưu hóa thiết kế của nhiều loại cấu trúc với
các vật liệu khác nhau. Các thuật toán meta-heuristic này bao gồm Genetic Algorithms,
Particle Swarm Optimization, Bat Algorithm, Cuckoo Search, Differential Evolutioin,
Firefly Algorithm, Harmony Search, Flower Pollination Algorithm, Ant Colony
Optimization, Bee Algorithms, Jaya Algorithm và nhiều thuật toán khác. Trong số các
phương pháp được đề cập ở trên, Differential Evolution là một trong những phương
pháp được sử dụng rộng rãi nhất. Kể từ khi được Storn và Price [1] giới thiệu lần đầu
tiên, nhiều nghiên cứu đã được thực hiện để cải thiện và áp dụng DE trong việc giải
quyết các vấn đề tối ưu hóa cấu trúc. DE đã chứng minh hiệu suất tuyệt vời trong việc
giải quyết nhiều vấn đề kỹ thuật khác nhau. Bên cạnh thuật toán Differential Evolution,
thuật toán Jaya được Rao [2] đề xuất gần đây cũng là một phương pháp hiệu quả và đã
được áp dụng rộng rãi để giải quyết nhiều vấn đề tối ưu hóa và cho thấy hiệu suất tốt.
Nó đạt được kết quả vượt trội khi được thử nghiệm với các hàm test benchmark so với
các phương pháp dựa trên dân số khác. Tuy nhiên, giống như nhiều thuật tốn tối ưu
hóa dựa trên dân số khác, một trong những nhược điểm của DE và Jaya là thời gian
tính tốn tối ưu chậm hơn nhiều so với các phương pháp tối ưu hóa dựa trên độ dốc
(gradient-based algorithms). Điều này là do DE và Jaya mất rất nhiều thời gian để đánh

giá hàm mục tiêu của các cá thể trong bộ dân số. Để khắc phục nhược điểm này, các
mạng nơ ron nhân tạo (Artificial Neural Networks) được nghiên cứu để kết hợp với các
thuật toán meta-heuristic, như Differential Evolution, để tạo thành một phương pháp
tiếp cận mới giúp giải quyết

v


các bài tốn tối ưu hóa thiết kế một cách hiệu quả. Bên cạnh đó, một trong những
vấn đề quan trọng nhất trong thiết kế kỹ thuật là các thiết kế tối ưu thường bị ảnh
hưởng bởi những yếu tố ngẫu nhiên. Những yếu tố này có thể xảy ra từ nhiều nguồn
khác nhau, chẳng hạn như quy trình sản xuất, tính chất vật liệu và mơi trường vận
hành và có thể khiến các cấu trúc hoạt động khơng đúng như trong thiết kế ban đầu,
và có thể dẫn đến rủi ro cho các cấu trúc [3]. Do đó, tối ưu hóa thiết kế dựa trên độ
tin cậy (Reliability-Based Design Optimization) có thể được coi là một chiến lược
tồn diện, cần thiết để tìm kiếm một thiết kế tối ưu.
Trong luận án này, lần đầu tiên một phiên bản cải tiến của phương pháp Differential
Evolution đã được sử dụng để tìm góc hướng sợi tối ưu và độ dày của tấm gia
cường vật liệu composite. Thứ hai, Mạng nơ ron nhân tạo (ANN) được tích hợp vào
quy trình tối ưu hóa thuật tốn Differentail Evolution cải tiến để hình thành thuật
toán mới gọi là thuật toán ABDE (Artificial Neural Network-Based Differential
Evolution). Thuật tốn mới này sau đó được áp dụng để giải quyết các bài tốn tối
ưu hóa của các cấu trúc tấm composite gia cường. Thứ ba, một kỹ thuật lựa chọn
tinh hoa (Elitist Selection Technique) được sử dụng để hiệu chỉnh bước lựa chọn
của thuật toán Jaya ban đầu để cải thiện sự hội tụ của thuật toán và hình thành một
phiên bản mới của thuật tốn Jaya được gọi là thuật toán iJaya. Thuật toán Jaya cải
tiến (iJaya) sau đó được áp dụng để giải quyết bài tốn tối ưu hóa dầm Timoshenko
vật liệu composite và thu được kết quả rất tốt. Cuối cùng, thuật toán mới SLMDiJaya được tạo thành từ sự kết hợp giữa thuật tốn Jaya cải tiến và phương pháp
vịng lặp đơn xác định (Single-Loop Deterministic Method) đã được đề xuất như
một công cụ mới để giải quyết các vấn đề Tối ưu hóa thiết kế dựa trên độ tin cậy.

Phương pháp mới này được áp dụng để tìm kiếm thiết kế tối ưu của các cấu trúc
dầm composite Timoshenk và cho kết quả vượt trội.

vi


CONTENTS
ORIGINALITY STATEMENT............................................................................... i
ACKNOWLEDGEMENTS.................................................................................... ii
ABSTRACT...........................................................................................................iii
CONTENTS........................................................................................................... vii
NOMENCLATURE................................................................................................ x
LIST OF TABLES................................................................................................ xiii
LIST OF FIGURES.............................................................................................. xiv
CHAPTER 1............................................................................................................ 1
1.1

An overview on research direction of the thesis....................................... 1

1.2

Motivation of the research......................................................................... 6

1.3

Goals of the dissertation............................................................................. 6

1.4

Research scope of the dissertation............................................................. 7

1.5

Outline......................................................................................................... 7

1.6

Concluding remarks................................................................................... 9

CHAPTER 2.......................................................................................................... 10
2.1

Introduction to Composite Materials...................................................... 10

2.1.1

Basic concepts and applications of Composite Materials...............10

2.1.2

Overview of Composite Material in Design and Optimization......16

2.2

Analysis of Timoshenko composite beam............................................... 18

2.2.1.

Exact analytical displacement and stress...................................... 18

2.2.2.

Boundary-condition types.............................................................. 22

2.3

Analysis of reinforced composite plate................................................... 23

CHAPTER 3.......................................................................................................... 26

vii


3.1

Overview of Metaheuristic Optimization

3.1.1

Meta-h

3.1.2

Meta-h

3.2

Solving Optimization problems using im
41

3.2.1

Brief o

3.2.2

The m

Evolution ..........................................................................................................
3.3

Solving Optimization problems using imp

3.3.1

Jaya A

3.2.2

Improv

3.4

Reliability-based design optimization

deterministic method. .........................................................................................
3.4.1.

Reliab

3.4.2.

A glob

CHAPTER 4 ............................................................................................................
4.1

Fundamental theory of Neural Network .

4.1.1

Basic c

4.1.2

Neural

4.1.3

Neural

4.1.4

Levenb

4.1.5

Over fi

4.2

Artificial Neural Network based meta-h
65

CHAPTER 5 ............................................................................................................

viii


5.1

Verification of iDE algorithm ..................

5.1.1

A 10-b

5.1.2

A 200-

5.1.3

A 72-b

5.1.4

A 120-

5.2

Static analysis of the reinforced composit

5.3

The effective of the improved Differentia

5.4

Optimization of reinforced composite pla

5.4.1

Thickn

5.4.2

Artific

composite plate ................................................................................................
5.5

Deterministic optimization of composite

5.5.1

Optim

5.5.2

Optim

5.6

Reliability-based optimization design of
93

5.6.1

Verific

5.6.2

Reliab

CHAPTER 6 ............................................................................................................
6.1

Conclusions and Remarks ........................

6.2

Recommendations and future works .....

REFERENCES ......................................................................................................
LIST OF PUBLICATIONS ..................................................................................

ix

NOMENCLATURE
Latin Symbols
b
Cij
The width of the composite beam
D
D

Matrix of stiffness
Material matrices of composite plate

E

Material matrices of composite beam

F

Young modulus

G

Loading vector

h,t

Shear modulus

K

The thickness of the composite beam/plate

L

Stiffness matrix of the plate

m

Length of the composite beam

N

Number of constraint satisfactions

NP

Number of layers of composite materials

CR

Size of population

p

Crossover control parameter

Q

Vector of random parameters

S

Matrix of material stiffness coefficients

T

Matrix of compliance

u(x), w(x)

Coordinate transformation matrix

x

Displacement field of the composite beam

X

Vector of design variables

wji

Population set
Vector of weights

Greek Symbols


Poison’s ratio

x








Natural frequency



Mass density
Stress field




yy

xy

Normal stress in y direction

 yz


Normal stress in x direction

Shear stress in xy direction

xz

Shear stress in yz direction



Shear stress in xz direction



Strain field



Normal strain in x direction
yy

Normal strain in y direction



xy



yz



xz



x



j

Shear strain in xy direction
Shear strain in yz direction
Shear strain in xz direction
Mean vector of x
Distance between feasible and infeasible design region

Abbreviations

2D
3D
ANN
MLP
DE
iDE
ABDE

Tow dimension
Three dimension
Artificial Neural Network
Multi-Layer Perceptron
Differential Evolution

improved Differential Evolution
Artificial neural network-Based Differential Evolution

xi


PSO

Particle Swarm Optimization

GA

Genetic Algorithm

FA

Firefly Algorithms

HS

Harmony Search

SLDM

Single Loop Deterministic Method

RBDO

Reliability Based Design Optimization

DOF

Degree Of Freedom

ADO

Approximate Deterministic Optimization

MPP

Most Probable Point

CS-DSG3

Cell-Smoothed Discrete Shear Gap technique using
triangle finite element

xii


LIST OF TABLES
TABLES

PAGE

Table 5. 1. Parameters for 10 bars truss.................................................................. 69
Table 5. 2. The comparison results keep the solution from the improved DE algorithm
with other methods for the 10-bar flattening problem............................................. 70
Table 5. 3. Parameter for 200-bars truss structure................................................... 72
Table 5. 4. Results of the comparison between the solution from the improved DE

algorithm and other methods for the problem of optimizing the 200-bar scaffold
problem................................................................................................................... 73
Table 5. 5. Parameters for 72-bars space truss structure.........................................74
Table 5. 6. Comparison between the solution from iDE algorithm with other methods
for the the 72-bars space truss problem................................................................... 75
Table 5. 7. Parameters for 120-bars arch space truss structure................................76
Table 5. 8. Results of comparison of solutions from the improved DE algorithm with
other methods for the optimization problem of space bar of 120 bars.....................77
Table 5. 9. Comparison of central deflection (mm) of the simply-supported square
reinforced composite plates..................................................................................... 78
Table 5. 10. The optimal results of two problems................................................... 80
Table 5. 11. Optimal thickness results for reinforced composite plate problems....82
Table 5. 12 Sampling and overfitting checking error.............................................. 83
Table 5. 13. Comparison of the accuracy and computational time between DE and
ABDE...................................................................................................................... 84
Table 5. 14. Material properties of lamina.............................................................. 87
Table 5. 15. Comparison of optimal design with continuous design variables........88
Table 5. 16. Comparison of optimal design with discrete design variables.............90
Table 5. 17. Comparison of optimization results of the mathematical problem......94
Table 5. 18. Optimal results of reliability based lightweight design with different
level of reliability.................................................................................................... 96

xiii


LIST OF FIGURES
FIGURES

PAGE

Figure 2. 1. Types of fiber-reinforced composites.................................................. 12
Figure 2. 2. Boeing 787 - first commercial airliner with composite fuselage and
wings. (Courtesy of Boeing Company.).................................................................. 13
Figure 2. 3. Composite mixer drum on concrete transporter truck weighs 2000 lbs
less than conventional steel mixer drum.................................................................. 14
Figure 2. 4. Pultruded fiberglass composite structural elements. (Courtesy of
Strongwell Corporation.)......................................................................................... 15
Figure 2. 5. Composite wind turbine blades. (Courtesy of GE Energy.).................15
Figure 2. 6. Composite laminated beam model...................................................... 19
Figure 2. 7. Free-body diagram.............................................................................. 19
Figure 2. 8. The material and laminate coordinate system...................................... 20
Figure 2. 9. A composite plate reinforced by an r-direction beam..........................24
Figure 3. 1. Source of inspiration in meta-heuristic optimization algorithms.........33
Figure 3. 2. Illustration of the feasible design region............................................. 50
Figure 4. 1. Biological neuron................................................................................ 53
Figure 4. 2. Perceptron neuron of Pitts and McCulloch.......................................... 54
Figure 4. 3. Applying a model based on field data................................................. 55
Figure 4. 4. The relationship between Machine Learning and the neural network.. 56
Figure 4. 5. A Multi-layer perceptron network model............................................ 57
Figure 4. 6. Single node in an MLP network.......................................................... 57
Figure 4. 7. Tanh and Sigmoid function.................................................................. 58
Figure 4. 8. A multi-layer perceptron with one hidden layer. Both layers use the same
activation function g................................................................................................ 59
Figure 4. 9. Diagram for the training process of a neural network with the LevenbergMarquardt algorithm............................................................................................... 63
Figure 4. 10. Dividing the training data for the validation process.........................65
Figure 4. 11. Optimization process using Artificial Neural Network (ANN) based
Differential Evolution (ABDE) optimization algorithm.......................................... 66
Figure 5. 1. A 10-bars truss structure...................................................................... 69
Figure 5. 2. A 200 bars truss structure.................................................................... 71

xiv


Figure 5. 3. A 72-bars space truss structure............................................................ 74
Figure 5. 4. Structure of 120-bars arch space truss................................................. 76
Figure 5. 5. Model of a reinforced composite plate................................................ 77
Figure 5. 6. Models of square and rectangular reinforced composite plates...........79
Figure 5. 7. Model of reinforced composite plate for optimization........................81
Figure 5. 8. Convergence curves of DE, IDE, Jaya and iJaya for the beam with P-P
condition................................................................................................................. 89
Figure 5. 9. Convergence curves of DE, IDE, Jaya and iJaya for the beam with P-P
condition................................................................................................................. 91
Figure 5. 10. Comparison of different design approaches with different boundary
conditions................................................................................................................ 92
Figure 5. 11. Comparison of RBDO optimal results with different levels of reliability
97

xv


CHAPTER 1

LITERATURE REVIEW
1.1 An overview on research direction of the thesis
Almost all design problems in engineering can be considered as optimization problems
and thus require optimization techniques to solve. However, as most real-world
problems are highly non-linear, traditional optimization methods usually do not work
well. The current trend is to use evolutionary algorithms and meta-heuristic
optimization methods to tackle such nonlinear optimization problems. Meta-heuristic
algorithms have gained huge popularity in recent years. These meta-heuristic

algorithms include genetic algorithms, particle swarm optimization, bat algorithm,
cuckoo search, differential evolution, firefly algorithm, harmony search, flower
pollination algorithm, ant colony optimization, bee algorithms, Jaya algorithm and
many others. The popularity of meta-heuristic algorithms can be attributed to their good
characteristics because these algorithms are simple, flexible, efficient, adaptable and
yet easy to implement. Such advantages make them versatile to deal with a wide range
of optimization problems, especially the structural optimization problems [4].
Structural optimization is a potential field and has attracted the attention of many
researchers around the world. During the past decades, many optimization techniques
have been proposed and applied to solve a wide range of various problems. The
algorithms can be classified into two main groups: gradient-based and popular-based
approach. Some of the gradient-based optimization methods can be named here as
sequential linear programming (SLP) [5], [6], sequential quadratic programming (SQP)
[7], [8], Steepest Descent Method, Conjugate Gradient Method, Newton's Method [9].
The gradient-based methods are very fast in reaching the optimal solution, but easy
trapped in local extrema and requires the gradient information to construct the
searching algorithm. Besides, the gradient-based approaches are limited to continuous
design variables and that decreases the productivity of the algorithm. In addition, the
initial solution (or initial design parameters of the structure) also


greatly affects the ability to achieve global or local solutions of gradient-based
algorithms. The population-based techniques, also known as part of meta-heuristic
algorithms, can be listed such as genetic algorithm (GA), differential evolution (DE),
and particle swarm optimization (PSO), Cuckoo Search (CS), Firefly Algorithm (FA),
etc [10]. These methods are used extensively in structural problems because of their
flexibility and efficiency in handling both continuous and discontinuous design
variables. In addition, the solutions obtained from population-based algorithms in most
cases are global ones. Therefore, the optimal result of the problem is not too much
influenced by the initial solution (or initial design of the structure). Among the methods

mentioned above, the Differential Evolution is one of the most widely used methods.
Since it was first introduced by Storn and Price [1], many studies have been carried out
to improve and apply DE in solving structural optimization problems. The DE has
demonstrated excellently performance in solving many different engineering problems.
Wang et al. [11] applied the DE for designing optimal truss structures with continuous
and discrete variables. Wu and Tseng [12] applied a multi-population differential
evolution with a penalty-based, self-adaptive strategy to solve the COP of the truss
structures. Le-Anh et al. [13] using an improved Differential Evolution algorithm and a
smoothed triangular plate element for static and frequency optimization of folded
laminated composite plates. Ho-Huu et al. [14] proposed a new version of the DE to
optimize the shape and size of truss with discrete variables. Besides the Differential
Evolution algorithm, the Jaya algorithm recently proposed by Rao [2] is also an
effective and efficient methods that has been widely applied to solve many optimization
problems and showed its good performance. It gains dominate results when being
tested with benchmark test functions in comparison with other population-based
methods such as homomorphous mapping (HM), adaptive segregational constraint
handling evolutionary algorithm (ASCHEA), simple multi-membered evolution
strategy (SMES), genetic algorithm (GA), particle swarm optimization (PSO),
differential evolution (DE), artificial bee colony (ABC), biogeography based
optimization (BBO). Moreover, it has been also successfully

2


applied in solving many optimal design problem in engineering as presented in
following literature [15]–[17]. However, the performance of the original Jaya
algorithm is not really high. Therefore, there are many variations of the Jaya
algorithm proposed to improve the original one. In this thesis, a new improved
version of the Jaya algorithm will be presented. The new algorithm aims to improve
the population selection technique for the next generation in order to improve the

speed of convergence, while at the same time ensuring the accuracy and the balance
between the exploration and exploitation of Jaya algorithm.
Moreover, like many other population-based optimizations, one of the disadvantages of
DE and Jaya is that the optimal computational time is much slower than the gradientbased optimization methods. This is because DE and Jaya takes a lot of time in
evaluating the fitness of individuals in the population. Specifically, in the structural
optimization problem, the calculation of the objective function or constraint function
values is usually done by using the finite element to analyze the structural response. To
overcome this disadvantage, artificial neuron networks (ANN) are proposed to combine
with the DE algorithm. Based on the idea of imitation of the brain structure, ANN is
capable of approximating an output corresponding to a set of input data quickly after
the network has been trained, also known as a learning process. Thanks to this
remarkable advantage, the computation of objective function or constraint function
values in the DE algorithm will be done quickly. As a result, ANN will help
significantly improve the efficiency of DE calculations. The effectiveness and
applicability of ANN since the early groundwork ideas put forward by Warren
McCulloch and Walter Pitts [18] in 1943 have so far proved to be very convincing
through numerous studies. Application areas include system identification and control,
pattern recognition, sequence recognition (gesture, speech, handwritten text
recognition), data mining, visualization, machine translation, social networking
filtering and email spam filtering, etc. [19]–[24].

The next issue is the development of optimal algorithms integrated ANN with DE
and applying the proposed algorithms to a practical structure to examine the

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effectiveness of the method. At present, the structures made from composite material
are widely used in almost all fields such as construction, mechanical engineering,
marine, aviation, etc. In particular, beams and reinforced plates made of composite

material are an outstanding form and are used increasingly by its superior advantages.
By combining the advantages of composite materials and the reinforced beams
structure, the reinforced composite plates have very high bending strength with very
light weight. Nowadays, reinforced composite plates have been widely used in many
branches of structural engineering such as aircraft, ships, bridges, buildings, etc. For its
advantages in both bending stiffness and the amount of material in comparison with
common bending plate structures, reinforced composite plate usually has higher
economic efficiency in practical applications. Due to its high practical applicability, the
need to optimize the design of the structure to save costs and increase the efficiency of
use is also high. However, because of the complexity of computing the behavior of this
particular type of structure, finding a good algorithm for optimizing design parameters
is essential to ensure computational efficiency. Composite material structures have very
complex behavioral equations, influenced by many geometric and material parameters.
These characteristics of the composite mechanical system also lead to the complexity
of the system of equations to describe the optimal problems, from the objective
functions to the constrained equations. So the use of gradient-based algorithms is not
straightforward. For such types of problems, population-based methodologies are a
superior choice.

Moreover, one of the most important issues in engineering design is that the optimal
designs are often effected by uncertainties which can be occurred from various
sources, such as manufacturing processes, material properties and operating
environments. These uncertainties may cause structures to improper performance as
in the original design, and hence may result in risks to structures [3]. There are two
groups of methods for dealing with uncertainties: reliability-based design and robust
design. Robust design focuses on minimizing variance in design results under
variations of design variables and parameters. Reliability-based design optimization

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(RBDO) ensures that the design is feasible regardless of changes in design variables
and parameters. RBDO can be considered as a comprehensive strategy for finding an
optimal design. RBDO is the focus of this thesis. Although RBDO is more reliable than
static optimization, the biggest drawback of RBDO in practical application is the high
computational cost. To solve this problem, a lot of research has been done to find
effective reliability analysis techniques, such as: sensitivity-based approximation
approaches [25], [26], most probable point (MPP)-based approaches, Monte Carlo
simulations [27]–[29] and response surface model-based approaches [30]. These
techniques focus on nesting the optimization and the reliability assessment in one
process. Another RBDO research focus on exploring the efficient decoupling strategies.
These strategies can be divided into three groups: nested double-loop methods,
decouple-methods, and single-loop methods. Among these three categories, the doubleloop approaches may be the most accurate as it assesses the reliability in every iteration
during the optimization process. However, its limitation is the huge cost of computation
[31]–[33]. The decoupled methods solve the RBDO problem in a different way by
separating the optimization and reliability analysis and solve them sequentially. Hence,
the computational cost can be reduced considerably [31], [33]–
[35]. However, this approach still includes two interrelated loops that result in costly
computation. To overcome this drawback, the single-loop methods have been proposed.
In this approach, the RBDO problem is solved in a single-loop procedure without
reliability analysis. The strategy is to convert an RBDO problem into an approximate
deterministic optimization (ADO) problem by transforming probabilistic constraints
into approximate deterministic constraints. In so doing, the computational cost
significantly decreased [32], [36], [37]. Therefore, these methods would be applicable
to real-world problems. However, studies that deal with the reliability-based design
optimization of laminated composite beams are quite limited. In this thesis, the SingleLoop Deterministic Methods (SLDM), which has been recently proposed by Li et al.
[38], will be studied to integrate with a meta-heuristic

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optimization algorithm to form a new tool set SLDM-iJaya for solving a RBDO
problems of composite structures.
In summary, in this thesis, some modifications will be investigated and propose to
improve the original algorithm of Differential Evolution and Jaya algorithm to
increase the convergence of DE and Jaya algorithm. The modified algorithms are
then combine with ANN and/or SLDM to develop new tools for solving design
optimization problems and the RBDO problems of composite structures, such as
reinforced composite plate, Timoshenko beams, etc.
1.2 Motivation of the research
The motivation to study the topics presented in the thesis comes from the analysis
of published literatures, and from the evaluation of the application potential of
composite material structures and intelligent optimization methods, especially the
reliability-based optimization methods. Therefore, the thesis is motivated by:
- The development / improvement of existing algorithms to improve the efficiency
of solving structural optimization problems with high accuracy and reliability.
- Studying the advantages of Artificial Neural Network (ANN) to combine with
optimal algorithms to improve the speed and the performance of solving structural
optimization problems.
1.3 Goals of the dissertation
Firstly, this thesis focuses on studying and developing meta-heuristic optimization
methods and combines them with the Artificial Neural Network, which has
advantages in approximating data, to build up a new algorithm for solving
composite material structural optimization problems. Particularly, the original
Differential Evolution or Jaya algorithm will be modified to improve the
convergence in solving for global optimal solution and then, the ANN will be
integrated to the improved meta-heuristic algorithms to form a new algorithm,
which is used to look for optimal design of reinforced composite plate structures.
Secondly, the thesis also proposes a new tool set, which is the combination of metaheuristic optimization algorithm and the Single-Loop Deterministic Method to deal

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with Reliability-Based Design Optimization (RBDO) problems. In particular, the
original Jaya algorithm will be modified to improve the convergence in searching
optimal solutions of the optimization problems. Then, this improved version of Jaya
algorithm will be combined with Single-Loop Deterministic Method to solve the
Reliability-Based Design Optimization of composite beam structures.
1.4 Research scope of the dissertation
The thesis focuses on the following main issues:
- Optimize truss, beam and stiffened plate structures using steel and composite
materials.
- Study and improve population-based optimization methods to increase accuracy
and efficiency in solving optimization problems.
- Exploit the ability to create approximate models from data sets of Neural Network
to combine with optimal algorithms to improve the performance and the ability to
solve many different types of problems.
- Combine optimal algorithms with groups of reliability assessment methods to
solve RBDO problems.
- The problems selected for optimization are relatively simple with the main
purpose of evaluating the effectiveness, accuracy and reliability of the proposed
optimization methods. The application of optimal methods proposed in the thesis
for more complex problems will be further studied in the future.
1.5 Outline
The dissertation contains seven chapters and is structured as follows:
 Chapter 1 presents an overview on meta-heuristic algorithms, composite
material structure and especially artificial neural networks and its role and
application in optimization process. This chapter also give out the
organization of the thesis via the outline section and the novelty and goal of
the thesis for quick review of what is studied in this thesis.

 Chapter 2 provides an overview of composite material with basic concepts and
applications in real life. The chapter also introduce theory of Timoshenko

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composite beam and reinforced composite plate which are the main structure
under investigated and studied in optimization problems of this thesis.
 Chapter 3 devotes the presentation of meta-heuristic optimization related to
Differential Evolution and Jaya algorithm and the approach to modify and
improve the original of the algorithm to obtain an improved version of its.
This chapter also gives out an overview and formulation for ReliabilityBased Design Optimization (RBDO) and the proposed methods for solving
RBDO problem.
 Chapter 4 offers the introduction and the historical development of
Artificial Neural Network (ANN). This chapter gives out some basic
concepts related to ANN and introduce the Neural Network Structure which
is used in this thesis to approximate date generated from the Finite Element
Analysis. Moreover, the training algorithm, especially the LevenbergMarquardt and the overfitting phenomenon are also presented in this chapter.
 Chapter 5 illustrate the effectiveness and efficiency of the improve Differential
Evolution and the improve Jaya in solving optimization problems. The
structures investigated in this section includes planar truss structure, space truss
structure, Timoshenko composite beam and reinforced composite plate. In
particular, the improve Differential Evolution (iDE) is applied to solve for
optimal weight of planar truss structures and space truss structures, then it is
used to optimize the fiber angle and the thickness of reinforced composite plates
and show its good effectiveness and performance. The last part of this chapter
devotes to illustration of the improve Jaya algorithm in looking for optimal
design of the Timoshenko composite beam and the results obtained prove its
highly effective performance and accuracy compared with those of others’
author. Moreover, this chapter also presents a new approach called SLDM-iJaya

which is formed by the combination of the improve Jaya algorithm and the
single-loop methods for solving the RBDO problem of the Timoshenko
composite beam. This chapter illustrate the solutions for two

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