Improving evolutionary algorithm for document extractive summarization cải tiến thuật toán trong tóm tắt trích rút văn bản

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HANOI UNIVERSITY OF SCIENCE AND TECHNOLOGY

MASTER’S GRADUATION THESIS
Mang l■i tr■ nghi■m m■i m■ cho ng■■i dùng, công ngh■ hi■n th■ hi■n ■■i, b■n online khơng khác gì so v■i b■n g■c. B■n có th■ phóng to, thu nh■ tùy ý.

Improving Evolutionary Algorithm for
Document Extractive Summarization

NGUYEN THI HOAI

Major: Data Science and Artificial Intelligence

Thesis advisor:

Dr. Nguyen Thi Thu Trang

Institute:

School of Information and Communication Technology

HA NOI, 2021

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luan van hay luan van tot nghiep

HANOI UNIVERSITY OF SCIENCE AND TECHNOLOGY

MASTER’S GRADUATION THESIS
Improving Evolutionary Algorithm for
Document Extractive Summarization

NGUYEN THI HOAI

Major: Data Science and Artificial Intelligence

Thesis advisor:

Dr. Nguyen Thi Thu Trang

Institute:

School of Information and Communication Technology

HA NOI, 2021

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3. Phụ lục: Mô tả rõ hơn nghiên cứu GA-Features và PSO-Harmony
Search.
- Sau khi sửa: Nội dung luận án gồm 5 chương chính là:
• Chương 1: Giới thiệu,
• Chương 2: Lý thuyết tổng quan và các nghiên cứu gần đây,
• Chương 3: Mơ hình lai PSO-GA đề xuất,
• Chương 4: Thực nghiệm,
• Chương 5: Kết luận và nghiên cứu tương lai.
Ngày tháng năm 2021
Tác giả luận văn

Giáo viên hướng dẫn

TS. Nguyễn Thị Thu Trang

Nguyễn Thị Hoài

CHỦ TỊCH HỘI ĐỒNG

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Acknowledgement
It is a genuine pleasure to express my deep sense of thanks and gratitude to
my advisor and guide, Dr. Nguyen Thi Thu Trang. I am highly grateful because
she managed and supported me in completing my thesis. Her unwavering
enthusiasm for science kept me constantly engaged with my research, and her
personal generosity helped make my time at HUST enjoyable. Furthermore, she
has taught me the methodology to carry out the study and present the research
works as clearly as possible. It was a great privilege and honor to work and study
under her guidance.
Also, I would like to thank Dr. Bui Thi Mai Anh for her keen interest in me
in every research. Her prompt inspirations, timely suggestions with kindness,
motivation, and dynamism have enabled me to accomplish this task throughout my
study period.
Most importantly, my sincere thanks and appreciation also go to my family
for their constant source of loving, caring and inspiration. They are such vital parts

of my life that I cannot imagine a life without them.
Last but not least, I gratefully acknowledge my university and the people who
have willingly helped me out with their abilities. I greatly appreciate the support
received through the collaborative work undertaken with them.

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Abstract
The task of text summarization is to generate main ideas that cover the content of
the whole text with the aim of shortening reading time. There are two approaches to
summarizing, extractive and abstractive summarization. Numerous methods have been
researched in this domain, in which using heuristic algorithms is a more effective and
straightforward way than applying machine learning or deep learning. A genetic

algorithm (GA) is a search heuristic that is inspired by Charles Darwin’s theory of natural
evolution. This algorithm reflects the process of natural selection where the fittest
individuals are selected for reproduction in order to produce offspring of the next
generation. However, using traditional GA alone may suffer from a weak local search
capability and slow convergence speed. Another algorithm, Particle Swarm Optimization
(PSO), is a population-based optimization technique inspired by the motion of bird flocks
and schooling fish. The premature convergence of PSO is prevented by applying GA on
a small population. Besides, the local optimum phenomenon of PSO can also be avoided
with GA. The goal of the thesis is to investigate the effectiveness of a hybrid method
combining GA and PSO based attribute selection in improving the performance of
classification algorithms solving the automatic text summarization task. To assess the
effectiveness of the proposed algorithm, I have conducted the experimentation on three
common datasets, DUC2001, DUC2002, which are typically used for extractive
summarization, and CNN/Daily Mail. The experiment results have shown that the hybrid
PSO-GA outperforms all the state-of-the-art works on all three ROUGE point metrics for
these datasets.
The solution presented in this thesis was accepted at The 35th Pacific Asia
Conference on Language, Information and Computation (PACLIC 35) in 2021.

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Chapter 2
2.1

Theoretical Background and Related works .......................................... 4
Text summarization ..................................................................................... 4
2.1.1 Abstractive summarization .................................................................5
2.1.2 Extractive summarization ...................................................................6

2.2

Genetic Algorithm ........................................................................................ 6
2.2.1 Initialization ........................................................................................9
2.2.2 Crossover ............................................................................................9

a)

N-Point Crossover .......................................................................................9

b)

Uniform Crossover: ...................................................................................10
2.2.3 Mutation ............................................................................................11

2.3

Particle swarm optimization...................................................................... 11
2.3.1 Particle and swarm ...........................................................................12
2.3.2 Objective function .............................................................................12

2.4

Term Frequency– Inverse Document Frequency .................................... 13
2.4.1 Term Frequency ................................................................................14
2.4.2 Inverse Document Frequency ...........................................................14

2.5

Cosine Similarity ........................................................................................ 15

2.6

Related works ............................................................................................. 16

Chapter 3

Proposed hybrid PSO-GA ...................................................................... 18
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b)

Sentence length ......................................................................................... 22

c)

Sentence position ...................................................................................... 22

d)

Number of proper nouns ........................................................................... 23

e)

Coverage ................................................................................................... 23
3.4.2 Fitness function ................................................................................ 24

3.5

Proposed strategies for operators ............................................................. 25
3.5.1 Initialization ..................................................................................... 25
3.5.2 Selection ........................................................................................... 26
3.5.3 Crossover ......................................................................................... 27
3.5.4 Mutation ........................................................................................... 28
3.5.5 Evaluation Convergence .................................................................. 28
3.5.6 Adaptive PSO strategy ..................................................................... 29

Chapter 4
4.1

Experimentation...................................................................................... 32
Evaluation metrics ..................................................................................... 32
4.1.1 Precision, recall and f-score ............................................................ 32

a)

Recall ........................................................................................................ 32

b)

Precision.................................................................................................... 32

c)

F-score ...................................................................................................... 33
4.1.2 Rouge measure ................................................................................. 33

a)

Rouge 1 ..................................................................................................... 33

b)

Rouge 2 ..................................................................................................... 34

c)

Rouge L..................................................................................................... 35

4.2

Preparation for experiment ...................................................................... 35
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4.2.1 Datasets ............................................................................................35
4.2.2 Environment setup ............................................................................37
4.3
Chapter 5

Experimental result .................................................................................... 38

Conclusion and future works ................................................................. 42

5.1

Conclusion ................................................................................................... 42

5.2

Future works ............................................................................................... 42

References ...................................................................................................................... 43
Appendix ........................................................................................................................ 48

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List of Figures
Figure 2.1 Two approaches to summarization. ................................................................. 5
Figure 2.2 The basic structure of Genetic Algorithm [8]. ................................................ 7
Figure 3.1 The steps of the proposed hybrid PSO-GA for single documents. ............... 19
Figure 3.2 Velocity and Position Updating of adaptive PSO. ........................................ 30
Figure 3.3 Flow chart of the adaptive PSO. .................................................................... 31
Figure 4.1 Rouge Scores (Recall) (%) on DUC2001...................................................... 39
Figure 4.2 Rouge Scores (Recall) (%) on DUC2002...................................................... 40
Figure 4.3 Rouge Scores (F1) (%) on CNN/Daily Mail. ................................................ 41

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List of Tables
Table 2.1 One-Point crossover example ......................................................................... 10
Table 2.2 Two-Point crossover example ......................................................................... 10
Table 2.3 Uniform crossover example ............................................................................ 10
Table 2.4 Bit-flip mutation example ............................................................................... 11
Table 4.1 Dataset statistics .............................................................................................. 36
Table 4.2 CNN/Daily Mail description ........................................................................... 36
Table 4.3 Parameter list ................................................................................................... 37
Table 0.1 Rouge Scores (Recall) (%) of the Hybrid PSO-GA compared with other
research. The experiment was carried out on 309 test documents of the DUC2001 corpus
......................................................................................................................................... 48
Table 0.2 Rouge Scores (Recall) (%) of the Hybrid PSO-GA compared with other
research. The experiment was carried out on 567 test documents of the DUC2002 corpus
......................................................................................................................................... 49
Table 0.3 Rouge Scores (F1) (%) of the Hybrid PSO-GA comparing with other research.
The experiment was carried out on 11490 test documents of CNN/Daily Mail corpus . 50

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List of Equations
Equation 2.1 Term frequency- inverse document frequency. ......................................... 15
Equation 2.2 Cosine Similarity. ...................................................................................... 15
Equation 3.1 The constraint on summary’s length. ........................................................ 19
Equation 3.2 The similarity to the topic sentence feature............................................... 21
Equation 3.3 The sentence length feature. ...................................................................... 22
Equation 3.4 The sentence position feature. ................................................................... 22
Equation 3.5 The evaluation of the proper noun feature. ............................................... 23
Equation 3.6 The coverage feature. ................................................................................ 24
Equation 3.7 Fitness function. ........................................................................................ 25
Equation 3.8 Sum of weighting to each feature. ............................................................. 25
Equation 3.9 The Rank selection strategy. ..................................................................... 26
Equation 3.10 The Roulette wheel selection strategy. .................................................... 27
Equation 3.11 Uniform crossover strategy ..................................................................... 27
Equation 3.12 Random mutation strategy....................................................................... 28
Equation 3.13 Evaluation Convergence strategy ............................................................ 28

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Acronyms
GA

Genetic Algorithm

PSO

Particle Swarm Optimization

EA

Evolutionary Algorithm

GA-PSO

Genetic Algorithm – Particle Swarm Optimization

TF-IDF

Term Frequency - Inverse Document Frequency

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Chapter 1 Introduction
1.1 Motivation
Today, with the development of all aspects of life, from culture, education to
technology, the amount of information provided to people is becoming more and more
diverse and rich. One question is how people can quickly and efficiently access such a huge
amount of information? The goal of an automatic text summarization system is to produce a
concise and fluent summary while still showing the main content and overall meaning of the
original text, allowing the user to grasp the information available in that text, but with a
much shorter reading time. There are two basic approaches to document summarization
(Hahn & Mani, 2000) [1], namely, extractive summary and abstractive summary. Extractive
summarization is to select sentences from the text that best express the meaning of the
content without using external words. This technique consists of sentences and phrases
ranked by importance and selects the most important elements of the document to construct
a summary. There is a huge diversity of techniques to automatically generate extractive
summaries for a single document which can be grouped into two directions: supervised and
unsupervised. The former methods are based on machine learning models [2] or deep
learning models [3]. Those require a huge training dataset, including human-generated
summaries, then very costly and time-consuming. The latter approaches, on the other hand,
do not require any training corpus but aim to rank all the sentences from the original
document by exploring their relationship. The sentences with the highest-ranking scores are
then selected to build the summary. In this research direction, many techniques have been
proposed for extractive summarization, such as Hidden Markov Model [4], graph-based
model [5], algebraic reduction [6] and evolutionary algorithms for instance, Genetic
Algorithm (GA) [7][8], Particle Swarm Optimization (PSO) [9]. Abstractive summaries tend
to "interpret" a text to be short and concise. It involves creating entirely new phrases and
sentences to capture the meaning of the text, requiring advanced techniques such as
interpretation, generalization, combining real-world knowledge and so on. Due to the

difficulty of summarizing, most of the research on text summarization is based on extractive
summarization.
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The thesis focuses on improving evolutionary algorithms (EA) in extractive
summarization. Many previous works proposed some evolutionary algorithm, especially
genetic algorithm (GA), for selecting the best sentences to create a summary. However,
using GA individually may suffer from a weak local search capability and slow convergence
speed. On the one hand, the fast convergence capability of PSO is leveraged to overcome
the low-speed limitation of GA. Additionally, the local optimum phenomenon of PSO can
be avoided by using GA. Therefore, I propose a hybrid method, namely hybrid PSO-GA,

which exploits the advantages of both PSO and GA approaches. More specifically, the study
will improve evolutionary algorithm in extractive text summarization to increase the
accuracy of the summary and the performance of the proposed model.

1.2 Objective and scope
In this thesis, I investigate to improve the evolutionary algorithm in extractive
summarization. Evolutionary algorithms are a heuristic-based approach to tackling problems
that cannot be easily solved in polynomial time. GA is a well-known algorithm, which is
inspired by the biological evolution process. PSO, Ant Colony Optimization (ACO) are
swarm intelligence algorithms, where it shares many similarities with evolutionary
computation techniques such as GA. The hybrid algorithms that integrated GA and another
algorithm, such as PSO, were proposed previously. However, there has been no previous
study in which PSO and GA were combined to increase the quality of the summary. My goal
is to take advantage of these two algorithms so that the generated population is more diverse
and converges faster.

1.3 Structure of thesis
The rest of this thesis is organized as follows.
Chapter 2 provides a concise review of the basic knowledge necessary to understand the
solutions and methods discussed in the thesis. First, I will discuss text summarizing,
including extractive and abstractive text summarization. Following that, I discussed the
genetic algorithm, particle swarm optimization algorithm, and their components. Finally, I
also discuss the equations that I use to create my model.
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Chapter 2 Theoretical Background and
Related works
This chapter contains a broader overview of text summarization. The application is
based on existing algorithms; therefore, a detailed description of the implemented
algorithms is given here. Firstly, I will start by explaining text summarization and
classification. Following that, I will give a quick overview of Genetic Algorithms and
Particle Swarm Optimization. I would like to discuss a few commonly used equations to my
model and its improvements, which will be described in Chapter 3. Finally, some previous
studies in text summarization are presented to describe an overview of the current research
situation.

2.1 Text summarization

Based on the output type of the summary, text summarization techniques can be
broadly grouped into extractive and abstractive approaches. Extractive methods produce
summaries by identifying essential sections of the text and combining extracted parts
coherently. Abstractive methods, in contrast, may generate novel words or phrases which
are not in the source text - as human-written summaries. While the former is strongly
concerned with the most salient sentences from the input document, the latter requires
advanced language generation techniques such as paraphrasing, generalizing, incorporating
real-world knowledge, etc. The abstractive-based approach, therefore, is much more
complex than the extractive one.
A summary is typically shorter than the original document, and the greater the
compression (i.e., the shorter the summary), the greater the loss of information. As a result,
the goal of developing methods for summarizing a text is to keep the length as short as
possible while minimizing information loss as much as possible.

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To assess the effectiveness of a summary, the ROUGE evaluation toolkit [10] is
usually used, which was found to highly correlate with human judgments [11]. It compares
the summaries generated by the program with the human-generated (gold standard)
summaries. (This measure will be learned and used later in section 4.1.2).
Based on the input type, it is divided into single and multi-document summarization.
In single-document summarization, the summary of only one document is built, while in
multi-document summarization, the summary of a whole collection of documents (such as
all today’s news or all search results for a query) is built.

Figure 2.1 Two approaches to summarization.
2.1.1

Abstractive summarization
An abstractive summary is an arbitrary text that describes the contexts of the source

document. Abstractive summarization process consists of “understanding” the original text
and “re-telling” it in fewer words. Namely, an abstractive summarization method uses
linguistic methods to examine and interpret the text and then to find new concepts and
expressions to best describe it by generating a new shorter text that conveys the most
important information from the original document. While this may seem the best way to
construct a summary (and this is how human beings do it), in real-life setting immaturity of
the corresponding linguistic technology for text analysis and generation currently renders
such methods practically infeasible.
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2.1.2

Extractive summarization
An extractive summary, in contrast, is composed with a selection of sentences (or

phrases, paragraphs, etc.) from the original text, usually presented to the user in the same
order—i.e., a copy of the source text with most sentences omitted. An extractive
summarization method only decides, for each sentence, whether or not it will be included in
the summary. The resulting summary reads rather awkward; however, the simplicity of the
underlying statistical techniques makes extractive summarization an attractive, robust,
language-independent alternative to more “intelligent” abstractive methods. In this thesis, I

consider single extractive summarization.

2.2 Genetic Algorithm
Evolutionary algorithms (EAs) have shown promising results in solving the problem
of extractive summarization. In this context, EAs are cast as a clustering method that aims
to search for the most relevant sentences from the input document. The search process is
guided by fitness functions that assign a value to each candidate solution (i.e., candidate
summary) in the search space to assess its quality. Most studies adopted Genetic Algorithms
(GAs) and focused on exploring the effectiveness of different strategies to formalize fitness
functions (Meena & Gopalani, 2015; Anh et al., 2019) [12][8]. A genetic algorithm (Thede,
2004) [13] is a popular probabilistic, iterative controlled search technique used for global
optimization that is inspired by Charles Darwin’s theory of natural evolution. This algorithm
simulates the process of natural selection where the fittest individuals are selected for
reproduction in order to produce offspring of the next generation. Therefore, offspring
inherit the characteristics of the parents and will be added to the next generation. If parents
have better fitness, their offspring will be better than parents and have a better chance at
surviving. This process keeps on iterating, and in the end, a generation with the fittest
individuals will be found. Each generation consists of a population of individuals and each
individual represents a point in search space and possible solution. Each individual is
represented as a string of character/integer/float/bits. This string is analogous to the
Chromosome. I consider a set of solutions for a problem and select the set of best ones out
of them. The working cycle of GA has four basic steps, namely, initialization, selection,
crossover, and mutation that are described in Figure 2.2.
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The essential advantage of GAs is the capacity to maintain the diversity of candidate
solutions thanks to genetic operators (i.e., selection, crossover and mutation). However, the
complexity of the evolution process often leads to a slow convergence speed. Indeed, the
computation time of GA increases non-linearly in the case of large population size.

Figure 2.2 The basic structure of Genetic Algorithm [8].
Genetic algorithms have three main genetic operators: crossover, mutation, and
selection. These genetic operators play their essential roles and can be very different.
• Crossover: This operator exchanges the genetic information of two parents in order
to create children. It is conducted on randomly chosen parent couples in order to generate a
child population similar to size to the parent population.
Crossover is primarily an action that occurs in a subspace. This point becomes evident
in a binary system where the strings are composed of the characters 𝑎 and 𝑏. For instance,
regardless of the crossing actions taken by two strings 𝑆1 = [𝑏𝑎𝑏𝑎] and 𝑆2 = [𝑏𝑏𝑎𝑏], their
offspring will always be of the form [𝑏 … ]. That is, the crossover can only produce solutions
in a subspace where the first component is always 𝑏. Additionally, no matter how the

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crossover is administered, two identical solutions will result in two identical offspring. This
implies that crossover occurs within a subspace and that the converged solutions/states
remain converged.
• Mutation: This operator augments the new child population with new genetic
information. This is accomplished by flipping some chromosomal bits. Mutation resolves
the local minimum problem and promotes diversification.
More specifically, mutation frequently results in a solution that is not contained inside
the subspace. If the mutation occurs on the first 𝑎 and it flips to 𝑏 in the preceding example,
then the solution 𝑆3 = [𝑏𝑎𝑏𝑏] does not belong to the prior subspace. Indeed, mutation

frequently yields solutions that are divergent from present solutions, hence expanding the
population's diversity. This enables the people to break out from a suffocating local
optimum. A critical point to consider is random selection within the population. For instance,
crossover necessitates the presence of two parents in a population. Are they chosen randomly
or are I biased toward the solutions with the highest fitness? One method is to pick using a
roulette wheel; another is to utilize fitness-proportional selection. Obviously, additional
selection methods are used, such as linear ranking selection, tournament selection, and
others.
• Selection of the fittest, or elitism: individuals are selected for the reproduction of
offspring. The selected individuals are then arranged in pairs of two to enhance reproduction.
Parent selection is very crucial to the convergence rate of the GA as good parents drive
individuals to better and fitter solutions.
Both crossover and mutation operate independently of an aim or fitness landscape. On
the other hand, selection of the fittest, or elitism, does use the fitness landscape to determine
what to choose and hence affects an algorithm's search behavior. What is selected and how
it is selected is algorithm-dependent, as are the objective function values. This elitism
ensures that only the greatest solutions survive. However, excessive elitism may result in an
early convergence. It is worth noting how basic these genetic operators are. Additional
operators may take various forms, and hybrid operators may also be used. To grasp the
fundamental behavior of genetic algorithms, I will concentrate on these crucial operators in
2.2.1, 2.2.1 and 2.2.2.
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2.2.1

Initialization
The Genetic Algorithm Process begins with population initialization. Population is a

subset of current generation solutions. Traditionally, solutions are represented in binary as
strings of 0s and 1s.
Additionally, population P can be described as a collection of chromosomes.
Typically, the initial population 𝑃(0), or the first generation, is generated randomly.
Populations 𝑃(𝑡), at generation t (t =1, 2, ...) are formed through an iterative procedure.
When working with genetic algorithms, it is critical to maintain population variety;
otherwise, a phenomenon known as Premature Convergence may occur. In evolutionary
algorithms, "premature convergence" refers to the algorithm's convergence before the global
optimal solution is attained. Premature convergence occurs when an evolutionary algorithm
becomes locked in local minima. When this occurs, parental solutions are unable to develop
offspring that are genetically superior to their parents. Premature convergence is frequently
triggered by the following factors: loss of diversity, too strong selective pressure towards a
best solution or too much exploitation of existing building blocks from the current

population (e.g., by recombining them, or mutating them only slightly).
2.2.2

Crossover
The crossover operator is analogous to reproduction and biological crossover. In this,

more than one parent is selected and one or more offspring are produced using the genetic
material of the parents. Crossover is usually applied in a GA with a high probability – across.
a) N-Point Crossover
A crossover point is randomly chosen for two individuals (parents) obtained by
selection. All data beyond that point in the organism string is swapped between the two
parent organisms. This crossover operates at the individual level. Assume the one-point
crossover point happens at random after the seventh bit, as shown in Table 2.1. Then, after
the seventh bit, all parent bits are switched to produce the following two children. This is a
particular application of the N-point Crossover technique.

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Chromosome2

1111|01010100|0011

Offspring1

1011|01010100|1010

Offspring2

1111|10001010|1010

b) Uniform Crossover:
Each gene (bit) is selected randomly from one of the corresponding genes of the parent
chromosomes. Use the tossing of a coin as an example technique. Suppose the second, third,
fourth, ninth, tenth and eleventh bits positions (of the original parents) are swapped. Table
2.3 shows crossover using the uniform crossover.
Table 2.3 Uniform crossover example
Chromosome1

0|000|1101|010|0011

Chromosome2

1|101|0101|101|0101

Offspring1

0|101|1101|101|0011

Offspring2

1|000|0101|010|0101

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2.2.3

Mutation
In simple terms, mutation is a little random change to the chromosome that results in

a new solution. It is typically utilized with a low probability – amut – to preserve and introduce
variation into genetic populations. When the probability is really high, the GA gets reduced
to a random search.
Mutation is the component of the GA that is responsible for "exploring" the search
space. It has been noted that while mutation is required for GA convergence, crossover is
not.
With bit-flip mutation, I select one or more random bits and flip them, as shown in
Table 2.4. This is used for binary-encoded GAs.
Table 2.4 Bit-flip mutation example
Chromosome

000011010100011

Offspring

110011110100011

2.3 Particle swarm optimization
Eberhart and Kennedy (Eberhart & Kennedy, 1995) [14] proposed the particle swarm
optimization (PSO) algorithm, which is a stochastic optimization technique based on swarm
(1995). The PSO algorithm models the social behavior of animals such as insects, herds,
birds, and fish. These swarms follow a cooperative food-finding strategy, with each member
of the swarm modifying the search pattern in response to its own and other members'
learning experiences. The PSO algorithm's main design concept is based on two studies: One
is the evolutionary algorithm, which, like the evolutionary algorithm, uses a swarm mode to
search a vast region in the solution space of the optimized objective function at the same
time. Artificial life, on the other hand, is the study of artificial systems with life-like qualities.
Since its introduction in 1995, it has undergone numerous upgrades. As academics gained
knowledge of the technique, they developed new versions to address specific requirements,

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created new applications in a variety of fields, published theoretical papers examining the
impact of various factors, and proposed numerous variants of the algorithm.
2.3.1

Particle and swarm
The PSO algorithm can be summarized as follows based on this: PSO algorithm is a

swarm-based search procedure in which each individual is referred to as a particle and is
described as a potential solution to the optimum problem in D-dimensional search space,

and it can remember the swarm's and its own optimal positions, as well as velocity. Each
generation combines the particle's information to alter the velocity of each dimension, which
is then utilized to determine the particle's new position. Particles in the multi-dimensional
search space constantly alter their states until they reach balance or the ideal state, or they
go beyond the calculation limits. The objective functions introduce a unique relationship
between different dimensions of the issue space.
The PSO uses a number of particles that constitute a swarm. The particles that make
up the PSO system fly around in a multidimensional search space; during this flight, each
particle modifies its position based on its own and surrounding particles' experiences, using
the optimal position found by itself and its neighbors. Particles can update their positions
and velocities according to the environment change, namely it meets the requirements of
proximity and quality. Particles in PSO can keep their stable movement in the search space,
while change their movement mode to adapt the change in the environment. The set of
surrounding particles and its historical experience define a particle's swarm direction [15].
2.3.2

Objective function

Every iteration, each particle changes its position according to the new velocity as
inrespectively. Considering a swarm with P particles, there is a position vector 𝑋𝑗 =
𝑗

𝑗

𝑗

𝑗

𝑗

𝑗

𝑗

𝑗

{𝑥1 , 𝑥2 , 𝑥3 , … , 𝑥𝑁 } and a velocity vector 𝑉𝑗 = {𝑣1 , 𝑣2 , 𝑣3 , … , 𝑣𝑁 } at a t iteration for each
one of the 𝑖 − 𝑡ℎ particle that composes it. These vectors are updated through the dimension
j according to the following equations:
𝑗
𝑗
𝑗
𝑗
𝑗
𝑗
𝑉𝑖 (𝑡 + 1) = 𝜔 ∗ 𝑉𝑖 (𝑡) + 𝑐𝑝 ∗ 𝑟𝑎𝑛𝑑1𝑖 ∗ (𝑝𝑏𝑒𝑠𝑡𝑖 (𝑡) − 𝑋𝑖 (𝑡)) + 𝑐𝑔 ∗ 𝑟𝑎𝑛𝑑2𝑖 ∗
𝑗

(𝑔𝑏𝑒𝑠𝑡 𝑗 (𝑡) − 𝑋𝑖 (𝑡))
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Improving evolutionary algorithm for document extractive summarization cải tiến thuật toán trong tóm tắt trích rút văn bản

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