Optimizing project resources using the hybrid multi objective algorithm and decision making method

VIETNAM NATIONAL UNIVERSITY HO CHI MINH CITY
HO CHI MINH CITY UNIVERSITY OF TECHNOLOGY

TRAN KHANH NHAN

OPTIMIZING PROJECT RESOURCES USING THE HYBRID
MULTI-OBJECTIVE ALGORITHM AND DECISION-MAKING
METHOD
Major:

CONSTRUCTION MANAGEMENT

Major code:

8580302

MASTER’S THESIS

HO CHI MINH CITY, July 2023


THIS THESIS IS COMPLETED AT
HO CHI MINH CITY UNIVERSITY OF TECHNOLOGY – VNU-HCM
Supervisor:

Assoc. Prof. Dr. Tran Duc Hoc

Examiner 1:

Dr. Nguyen Thanh Viet

Examiner 2:

Assoc. Prof. Dr. Luong Duc Long

This master’s thesis is defended at HCM City University of Technology,
VNU-HCM on July 12th, 2023.
Master’s Thesis Committee:
(Please write down full name and academic rank of each member of the Master
Thesis Defense Council)
1. Assoc. Prof. Dr. Do Tien Sy

- Chairman

2. Dr. Nguyen Anh Thu

- Member, Secretary

3. Dr. Nguyen Thanh Viet

- Reviewer 1

4. Assoc. Prof. Dr. Luong Duc Long

- Reviewer 2

5. Dr. Nguyen Van Tiep

- Member

Approval of the Chairman of Master’s Thesis Committee and Dean of Faculty of

Civil Engineering after the thesis being corrected (If any)
CHAIRMAN OF THESIS COMMITTEE

HEAD OF FACULTY OF CIVIL
ENGINEERING

Assoc. Prof. Dr. Do Tien Sy

Assoc. Prof. Dr. Le Anh Tuan


i

VIETNAM NATIONAL UNIVERSITY-HO CHI MINH CITY
HO CHI MINH CITY UNIVERSITY OF TECHNOLOGY

SOCIALIST REPUBLIC OF VIETNAM
Independence – Freedom – Happiness

THE TASK SHEET OF MASTER’S THESIS
Full name: Tran Khanh Nhan

Student code: 2170880

Date of birth: March 16th, 1997

Place of birth: Ho Chi Minh city, Vietnam

Major: Construction Management

Major code: 858032

I.

THESIS TOPIC:
Optimizing Project Resources Using The Hybrid Multi-Objective Algorithm
And Decision-Making Method.
Tối Ưu Cân Bằng Tài Nguyên Dự Án Sử Dụng Lai Ghép Thuật Toán Đa Mục
Tiêu và Phương Pháp Ra Quyết Định.

II.

TASKS AND CONTENTS:
Introducing a new algorithm that combines SGO, Fuzzy Logic in addition to
Multiple-criteria decision-making (MCDM) methods to solve the optimization
problem requiring resources along with quality control in construction with the
integration of uncertainty that occurs in the actual project or built into the model.

III.

TASKS STARTING DATE: February 2nd, 2023

IV.

TASKS ENDING DATE: June 10th, 2023

V.

INSTRUCTOR: Assoc. Prof. Dr. Tran Duc Hoc
Ho Chi Minh City, June 10th, 2023

ADVISOR

Assoc. Prof. Dr. Tran Duc Hoc

HEAD OF DEPARTMENT

Dr. Le Hoai Long


ii

DEAN OF FACULTY OF CIVIL ENGINEERING

Assoc. Prof. Dr. Le Anh Tuan


iii

ACKNOWLEDGEMENT
I would like to express my deepest appreciation and gratitude to all those who have
In order to successfully complete this Master's program, I would like to extend my heartfelt
appreciation to the esteemed faculty members of Ho Chi Minh City University of
Technology, especially the professors and instructors of the Department of Construction
and Construction Management within the Department of Construction and Construction
Management. Their invaluable guidance and instruction, encompassing both theoretical
knowledge and practical applications, have greatly enhanced my academic journey over
the past two academic years.
Furthermore, I would like to express my profound gratitude to Associate Professor,
Dr. Tran Duc Hoc for his exceptional mentorship and unwavering support throughout the
entire research process. Drawing upon Dr. Tran Duc Hoc's prior research contributions,

coupled with the dedicated guidance and constructive feedback from these esteemed
professionals, I have been able to strengthen my research capabilities and foster a genuine
enthusiasm for scholarly exploration.
Also, I extend my sincere thanks to my fellow colleagues and classmates of IMP
CM 2021. Through our collaborative efforts, we have fostered an environment of
knowledge sharing and mutual support, which has played an instrumental role in my thesis
completion.
Last but not least, I would like to express my gratitude to my family for their
unwavering support during this transformative period of my academic pursuits. Their
constant presence and encouragement have been a source of strength and motivation.
Sincerely,

Tran Khanh Nhan


iv

ABSTRACT
Schedule, cost, quality control, and rational use of labor and resources are key
factors that project management aims to achieve, and these factors have a complex
relationship with each other. However, almost all existing trade-off analysis models have
only focused on addressing the time-cost issue without simultaneously considering the
impact of collision activities on quality costs. Moreover, the results will be influenced by
several external elements that are uncertain and hard to identify, such as weather
conditions, machine and equipment capability, and labor efficiency, among others.
Therefore, this research aims to develop an optimal model of project resource balance with
quality considerations (TCQT) by applying fuzzy logic, the multi-objective social group
optimization (MOSGO) algorithm, and the multi-criteria decision-making method
(MCDM), while also considering the uncertainty of input variables. In this paper, fuzzy
logic is used to select input and defuzzification to filter the results according to various

factors. Additionally, the MOSGO algorithm is applied to determine a set of Pareto-optimal
time-cost-quality curves, and multi-criteria decision-making methods are used to obtain
the best outcome. The expected research outcome is the introduction of an optimization
model that combines SGO, fuzzy techniques, and MCDM to optimize problems requiring
resources along with quality control (TCQT) and integrate uncertainty that occurs in actual
large-scale projects.
Keywords: Fuzzy logic, hybrid multi-objective, social group optimization, time –
cost – quality trade-off, uncertainty.


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TĨM TẮT LUẬN VĂN THẠC SĨ
Tiến độ, chi phí, kiểm soát chất lượng và sử dụng hợp lý lao động và nguồn lực là
những yếu tố chính mà quản lý dự án hướng tới và những yếu tố này có mối quan hệ phức
tạp với nhau. Tuy nhiên, hầu hết các mơ hình phân tích đánh đổi hiện tại mới chỉ tập trung
giải quyết vấn đề chi phí thời gian mà không xem xét đồng thời tác động của các hoạt động
va chạm đến chi phí chất lượng. Hơn nữa, kết quả sẽ bị ảnh hưởng bởi một số yếu tố bên
ngồi khơng chắc chắn và khó xác định, chẳng hạn như điều kiện thời tiết, khả năng của
máy móc và thiết bị, hiệu quả lao động, v.v. Do đó, nghiên cứu này nhằm phát triển một
mơ hình tối ưu về cân bằng nguồn lực dự án có xét đến chất lượng (TCQT) bằng cách áp
dụng logic mờ, thuật toán tối ưu hóa nhóm xã hội đa mục tiêu (MOSGO) và phương pháp
ra quyết định đa tiêu chí (MCDM), đồng thời xem xét tính khơng chắc chắn của các biến
đầu vào. Trong bài báo này, logic mờ được sử dụng để chọn đầu vào và giải mờ để lọc kết
quả theo các yếu tố khác nhau. Ngồi ra, thuật tốn MOSGO được áp dụng để xác định
một tập hợp các đường cong chất lượng-chi phí-thời gian tối ưu Pareto và các phương pháp
ra quyết định đa tiêu chí được sử dụng để đạt được kết quả tốt nhất. Kết quả nghiên cứu dự
kiến là giới thiệu một mơ hình tối ưu hóa kết hợp SGO, kỹ thuật mờ và MCDM để tối ưu
hóa các vấn đề yêu cầu tài nguyên cùng với kiểm sốt chất lượng (TCQT) và tích hợp sự
không chắc chắn xảy ra trong các dự án quy mơ lớn thực tế..

Từ khóa: Logic mờ, lai ghép đa mục tiêu , tối ưu hóa nhóm xã hội, đánh đổi thời
gian – chi phí – chất lượng, sự khơng chắc chắn


vi

AUTHOR’S COMMITMENT
The undersigned below:
Student full name:

Tran Khanh Nhan

Student ID:

2170880

Place and date of born:

Ho Chi Minh City, Vietnam, March 16th, 1997

Address:

District 3, Ho Chi Minh City

With this declaration, the author finishes his master’s thesis entitled
“OPTIMIZING PROJECT RESOURCES USING THE HYBRID MULTIOBJECTIVE ALGORITHM AND DECISION-MAKING METHOD” under the
advisor's supervision. All works, ideas, and materials that was gain from other references
have been cited correctly.
Ho Chi Minh City, June 10th, 2023

Tran Khanh Nhan


vii

TABLE OF CONTENTS
THE TASK SHEET OF MASTER’S THESIS ........................................................... i
ACKNOWLEDGEMENT .......................................................................................... iii
ABSTRACT ................................................................................................................ iv
AUTHOR’S COMMITMENT ................................................................................... vi
TABLE OF CONTENTS .......................................................................................... vii
TABLE LIST .............................................................................................................. ix
FIGURE LIST ............................................................................................................. x
ABBREVIATION LIST ............................................................................................. xi
CHAPTER 1. GENERAL INTRODUCTION ......................................................... 1
1.1. Research Problem ............................................................................................... 1
1.2. Research Objectives ............................................................................................ 4
1.3. Scope of Research ............................................................................................... 4
1.4. Research Procedure ............................................................................................. 6
1.5. Expected Research Packaging ............................................................................. 7
CHAPTER 2. LITERATURE REVIEW & THEORETICAL BASIC................... 8
2.1. Literature review ................................................................................................. 8
2.2. Relative Research.............................................................................................. 13
2.3. Multi-objective optimization ............................................................................. 16
2.4. Soft Logic ......................................................................................................... 18
2.5. Multiple-criteria decision-making (MCDM)...................................................... 18
2.5.1. Overview of Multiple-criteria decision-making (MCDM) ............................. 18

2.5.2. The Evidential Reasoning (ER) method ......................................................... 21
2.6. Social Group Optimization (SGO) .................................................................... 22

2.7. Optimize project scheduling ............................................................................. 26
2.8. Cost................................................................................................................... 28
2.9. Quality .............................................................................................................. 30
2.10. Fuzzy logic ...................................................................................................... 31
2.10.1. Fuzzy number ............................................................................................ 32
2.10.2. Defuzzification .......................................................................................... 36
CHAPTER 3. RESEARCH METHODOLOGY.................................................... 38
3.1. Data processing ................................................................................................. 39
3.2. Scheduling and Estimating ................................................................................ 39


viii

3.3. Optimization Using Mutiple Objective Social Group Optimization Algorithm
(MOSGO) ................................................................................................................ 44
3.3.1. Initialization ................................................................................................ 44
3.3.2. Decision variables ....................................................................................... 47
3.3.3. Objective function ....................................................................................... 47
3.3.4. Improving phase .......................................................................................... 48
3.3.5. Acquiring phase........................................................................................... 49
3.3.6 The population solution choice ..................................................................... 49
3.3.6 Conditions for discontinuation ...................................................................... 50
CHAPTER 4. THE APPLICATION TO CASE STUDIES .................................. 51
4.1. Case study ......................................................................................................... 51
4.2. Optimization outcomes ...................................................................................... 58
4.3. Multi-criteria decision making ........................................................................... 68
4.4 . Results comparison ......................................................................................... 72
CHAPTER 5. CONCLUSION AND FURTHERMORE....................................... 75
REFERENCE ............................................................................................................ 79
APPENDIX ................................................................................................................ 85

ix

TABLE LIST
Table 2.1: Summary of some previous relative research ................................................ 13
Table 2.2: Multiple-criteria decision-making assessment .............................................. 19
Table 2.3: General relationships in the project network diagram ................................... 27
Table 4.1: Data of case study 1 ..................................................................................... 54
Table 4.2: Data of case study 2...................................................................................... 56
Table 4.3: Optimal solution for the uncertainty levels of case 1 .................................... 58
Table 4.4: Optimal solution for the uncertainty levels of case 2 .................................... 64
Table 4.5: The result of the solution with the best utility score rating ............................ 71
Table 4.6: Comparison the Optimum Solution from the Three Algorithms case 1 ........ 72
Table 4.7: Comparison of the Optimum Solution from the Three Algorithms case 2 ..... 73


x

FIGURE LIST
Figure 2.1: Project Cost Curves ........................................................................... 29
Figure 2.2: Triangle fuzzy number ....................................................................... 33
Figure 2.3: Trapezoidal fuzzy number ................................................................. 34
Figure 2.4: Defuzzification using CoG method .................................................... 37
Figure 3.1: MOSGO flowchart for the TCQT Problem ........................................ 38
Figure 3.2: Centroid method of defuzzification Time........................................... 45
Figure 3.3: Centroid method of defuzzification Cost............................................ 45
Figure 3.4: Centroid method of defuzzification Quality ....................................... 45
Figure 3.5: Population selection procedure .......................................................... 50
Figure 4.1: Time - Cost - Quality 3D view of optimal solutions for each respective

uncertainty level in case study 1 ........................................................................... 61
Figure 4.2: Trade of Time - Cost of optimal solutions for each respective uncertainty
level in case study 1 .............................................................................................. 61
Figure 4.3: Trade of Time - Quality of optimal solutions for each respective uncertainty
level in case study 1 .............................................................................................. 62
Figure 4.4: Trade of Quality - Cost of optimal solutions for each respective uncertainty
level in case study 1 .............................................................................................. 62
Figure 4.5: Time - Cost - Quality 3D view of optimal solutions for each respective
uncertainty level in case study 2 ........................................................................... 66
Figure 4.6: Trade of Time - Cost of optimal solutions for each respective uncertainty
level in case study 2 .............................................................................................. 66
Figure 4.7: Trade of Time - Quality of optimal solutions for each respective uncertainty
level in case study 2 .............................................................................................. 67
Figure 4.8: Trade of Quality - Cost of optimal solutions for each respective uncertainty
level in case study 2 .............................................................................................. 67
Figure 4.9: Utility assessment of each solution – case study 1 ............................. 70
Figure 4.10: Utility assessment of each solution – case study 2............................ 71


xi

ABBREVIATION LIST

ACO: Ant Colony Optimization
AHP: Analytical Hierarchy Process
CoG: Center of Gravity
DE: Differential Evolution
DMOEA: Dynamic Multi-Objective Evolutionary Algorithm

ER: Evidential Reasoning

GA: Genetic Algorithms
HS: Harmony Search
MCDM: Multiple-criteria decision-making
MODTFLP: Multi-Objective Dynamic Facility Problems
MOEAs: Multi-objective evolutionary algorithms
MOO: Multi-objective optimization
MOPSO: Multi-Objective Particle Swarm Optimization
MOSGO: Multi-objective Social Group Optimization
Non-dominated Sorting Genetic Algorithm II: NSGA-II
PSO: Particle Swarm Optimization
RDGA: Rank-Density Based Genetic Algorithm
SAW: Simple Additive Weighting
SGO: Social Group Optimization
TCQT: Time Cost Quality Trade-off
TCRO: Time-Cost-Resource Optimization
TCT: Time Cost Trade-Off


xii

TOPSIS: Technique for Order Preference by Similarity to Ideal Solution
VEGA: The Vector Evaluated Genetic Algorithm
WSM: Weighted Sum Model


1

CHAPTER 1. GENERAL INTRODUCTION
1.1. Research Problem
In today's economy, the construction industry is experiencing a period of growth,

accompanied by a range of challenges. Despite the promising growth, construction
companies cannot overlook the obstacles that come their way. To ensure maximum
profitability in each project, it is imperative for construction corporations to enhance
not only their technical expertise but also their management skills. Effective project
management plays a pivotal role in this regard, encompassing a sequence of activities
such as planning, organizing, managing, and controlling. These activities are crucial
for successfully fulfilling the mission of construction projects and achieving desired
outcomes [1].
In the realm of construction, achieving organizational goals necessitates striking a
delicate equilibrium between progress, cost, quality, and resources, as these elements
intricately intertwine with one another. Depending on factors such as contractual
agreements and strategic considerations, organizations may prioritize minimizing
costs and time to enhance efficiency and profitability. Conversely, others may opt to
optimize control of quality, ensuring client satisfaction and long-term viability.
Successfully navigating these complex connections requires effective project
management, astute decision-making, and prudent resource allocation. By
comprehending the interdependencies at play, construction organizations can align
their goals with their chosen perspectives, contracts, and strategies, thereby fostering
project success [2].
According to Diaby et al. (2011) and Haquel et al. (2012) [3,4], to minimize project
time, the organization must sacrifice human resources, raw materials, machinery, and
equipment to complete the project on time. While overall costs, including direct and
indirect costs, are significantly impacted, the quality of the project also affects the
result, which can be considered positive or negative based on the nature of the
activities. Thus, the manager should allocate all resources efficiently to achieve the
goal related to time, cost, and quality, known as Time-Cost-Resource Utilization


2

Optimization. Failing to optimize these factors could lead to delays, increased
expenses, and unsatisfactory project outcomes. Therefore, it is crucial for managers
to prioritize resource allocation and closely monitor project progress to ensure that
all three factors are effectively managed.
Despite the use of traditional progress methods such as Metra Potential Method
(MPM), Critical Path Method (CPM), and Program Evaluation and Review
Techniques (PERT), these methods all lack realism, making it challenging to resolve
the time optimization issue [5]. These methods rely heavily on assumptions and
estimates, making it difficult to predict project outcomes accurately. As a result,
project managers may encounter delays, cost overruns, and quality issues, which can
ultimately impact project success. To overcome these limitations, project managers
need to adopt more advanced approaches to resource allocation, which involves
finding the most efficient use of resources while minimizing waste. This means using
data-driven approaches to identify potential bottlenecks, allocating resources based
on task priority, and utilizing laborers' skills and expertise effectively.
Time-Cost-Resource Optimization (TCRO) is a commonly used approach that
involves categorizing optimization methods into three groups: heuristic-based, linear
program-based, and meta-heuristic-based. One popular algorithm in the metaheuristic approach is Social Group Optimization (SGO), as suggested by [6]. Other
commonly used algorithms in the meta-heuristic approach include Genetic
Algorithms [7], Particle Swarm Optimization (PSO) [8], and Ant Colony
Optimization (ACO) [9]. However, each methodology has its own advantages and
disadvantages. While the advantages of a particular approach may make it the most
suitable option, the disadvantages can include an imbalance between time and cost
(TCT) for large-volume projects. Optimizing only a single standard function may not
be sufficient for large-scale projects, and achieving the optimal goal could require a
considerable amount of time [10].
In the scope of this research, MOSGO will be utilized for multi-goal decision-making
to optimize algorithms and time as previously mentioned. By leveraging the strengths

3

of MOSGO, which has demonstrated superiority over various state-of-the-art
algorithms, including GA, PSO, DE, ABC, and TLBO, this study aims to address the
complexity of project management in the construction industry more effectively.
Additionally, the outcomes will be affected by external factors that are uncertain and
difficult to identify, such as weather conditions, machine and equipment capabilities,
and labor efficiency. These factors are related to resource allocation and quality in
order to achieve the project's goals. Incorporating all of these elements into the
resource balance will enable the development of a comprehensive and effective
project management strategy. Therefore, integrating MOSGO with the resource
balance module is critical for optimizing the project's performance and achieving the
desired outcomes.
Previous studies have successfully applied Fuzzy logic to introduce uncertainty into
the time-cost optimization model, as demonstrated by the work of [11]. However,
there is still a lack of research that uses Fuzzy logic to optimize project resources.
Additionally, there is a need for a time-cost trade-off model that takes into account
collision activities and their impact on quality costs. To address these research gaps,
this study aims to develop an optimal project resource balance model that considers
quality and incorporates uncertainty using Fuzzy logic and MOSGO combined with
a multi-criteria decision-making method. By doing so, the proposed model can
account for uncertainties related to external factors like weather conditions,
equipment capabilities, and labor efficiency, which can impact the project's resource
allocation and quality. This research has the potential to contribute significantly to
the field of project management by introducing a more robust and effective approach
to resource balance optimization.
The urgency of this study stems from the critical importance of efficient project
management in the construction industry, where challenges and complexities abound.
Construction companies face constant pressure to deliver projects within strict
timelines, budget constraints, and quality expectations. The traditional project

management methods have limitations in accurately predicting outcomes, leading to


4

delays, cost overruns, and unsatisfactory results. As construction projects involve
significant investments and societal impact, optimizing the use of resources and
implementing high-quality outcomes are paramount. By integrating Fuzzy logic and
MOSGO with a multi-criteria decision-making approach, this research aims to
address the gaps in existing models, introducing a more comprehensive and effective
resource balance optimization method. Such advancements will empower project
managers to make informed decisions, proactively address uncertainties, and achieve
the desired goals efficiently. The urgency to undertake this study lies in its potential
to revolutionize project management practices, contributing to the overall success,
sustainability, and profitability of construction projects in a rapidly evolving industry.
1.2. Research Objectives
-

Propose a novel model for resource balancing in project management.

-

Combine the Multi-objective Social Group Optimization (MOSGO) algorithm
with Fuzzy logic.

-

Optimize Time, Cost, and Quality (TCQ) objectives while considering
uncertainty.

-

Minimize project duration through the proposed approach.

-

Generate a set of Pareto solutions using MOSGO.

-

Represent uncertainty in project parameters using Fuzzy logic.

-

Apply the model to large-scale realistic projects.

-

Demonstrate the model's effectiveness in resource balancing and optimizing
TCQ objectives.

1.3. Scope of Research
-

Testing of the effectiveness of a hybrid algorithm for project management,
applied to the project planning phase.

-

The analysis focuses on the trade-off between time, cost, and quality in general

construction projects.

-

Uncertainty is addressed using fuzzy logic for modeling imprecise data and
project parameter uncertainty.


5

-

The models are implemented in MATLAB using the SGO algorithm, Fuzzy
Logic and MCDM offering efficient optimization capabilities.

-

Applying 2 case studies, one used in the analysis applied from previous
research, the other from real-life data to provide real-world scenarios to
evaluate and identify receive.


6

1.4. Research Procedure

RESEARCH PROCEDURE
Collect the required data to build
the model time - cost - quality
trade-off

of the project.
Start
Research theoretical basic:
- Multi-objective optimization
- SGO Algorithm
- Fuzzy Logic
- MCDM

Step 1

Determination
Of Objective
Function

Development of MOSGO
algorithm combined with Fuzzy
Logic to select input to solve the
problem of Time – Cost –
Quantity Trade-off

Step 2

Problem
Programming
(MATLAB)

Programmatically solve the math
problem using the MOSGO
algorithm ranking of factors

Step 3

Export Pareto
Set

Review the solution of the Math
Problem

Step 4

Choosing by
Advantages
method

Selecting the Optimal Solution

Step 5

Compare results of MOSGO
algorithm with other evolutionary
algorithm

Step 6

Conclusion/Suggestion

Step 7

Refer to
previous

research,
experiences


7

1.5. Expected Research Packaging
In terms of Academic
Introducing a new algorithm that combines SGO, Fuzzy algorithms in addition to
Multiple-criteria decision-making (MCDM) methods to solve the optimization
problem requiring resources along with quality control in construction with the
integration of Uncertainty that occurs in the actual project or built into the model.
In terms of Reality
This research could provide support for managers. Moreover, it also provides a
decision-making tool for the management level to select the most efficient approach
during the planning stage.


8

CHAPTER 2. LITERATURE REVIEW & THEORETICAL BASIC
2.1. Literature review
The conventional Time Cost trade-off (TCT) concern has been the topic of intensified
research since the advancement of the Critical Path Method (CPM) in the 1950s. The
literature includes much different research of sculpting the TCT problem in
construction projects. Various techniques, ranging from mathematical and heuristic
to metaheuristic and evolutionary have been tried to present to cope with the TCT
problem. Mathematical models have been widely used in tackling the TCT problem
in construction projects. These models aim to optimize the allocation of time and cost
resources by formulating the problem as an optimization program. By considering

project constraints, objectives, and variables, mathematical models provide a
systematic approach to finding optimal solutions to the TCT problem.
Additionally, heuristic methods such as Genetic Algorithms and Simulated
Annealing have been applied to solve the TCT problem [12], [13] Heuristic methods,
such as Genetic Algorithms and Simulated Annealing, have also been employed to
solve the TCT problem. These methods use iterative procedures to search for nearoptimal solutions by mimicking natural processes like evolution and thermal
annealing. By exploring different solutions and gradually improving them, heuristic
methods offer efficient and effective approaches to the TCT problem.
Similarly, metaheuristic methods like Particle Swarm Optimization (PSO) and Ant
Colony Optimization (ACO) have also been proposed for solving the TCT problem
[14]. These methods draw inspiration from the behavior of natural systems, such as
swarms of particles or ant colonies, to search for optimal or near-optimal solutions.
By leveraging the collective intelligence and adaptive behavior of these systems,
metaheuristic methods provide robust and scalable approaches to the TCT problem.
The TCQT problem has gained attention as an extension of the TCT problem in the
construction industry [14], [16]. While the TCT problem focuses on balancing project
completion within a given deadline and minimizing costs, it fails to account for the


9

crucial aspect of project quality. Optimizing time and cost alone may lead to
compromised quality, which can have detrimental effects on project stakeholders and
outcomes. The TCQT problem expands the TCT problem to address this limitation
by introducing a third objective: optimizing project quality as well as considering the
interdependencies between time, cost, and quality factors. It promotes a
comprehensive evaluation of trade-offs, leading to improved project outcomes [18].
The Time-Cost-Quality trade-off (TCQT) problem has been a significant concern in
the construction industry for many years, and various approaches have been proposed
to address it. One approach is to use mathematical models, which have been

extensively used in the literature to optimize the TCQT problem [19]. These models
allow the simultaneous consideration of multiple project parameters, such as time,
cost, and quality, and can handle complex and nonlinear relationships among them.
Another effective approach for optimizing the TCQT problem is to use heuristic
algorithms like Genetic Algorithms, Particle Swarm Optimization, and Ant Colony
Optimization, as noted in prior research [20], [21]. These algorithms are well-suited
for handling complex optimization problems and have been used to consider multiple
objectives and constraints when optimizing the trade-off problem. By leveraging
heuristic algorithms, project managers can generate solutions that are highly efficient
and effective, while also accounting for the multiple factors that can impact the
project's resource allocation and quality. Overall, the use of heuristic algorithms
provides another valuable tool for optimizing the TCQT problem in project
management.
Multi-criteria decision-making methods have been widely used to address the TCQT
problem [22]. These methods, such as the Analytical Hierarchy Process (AHP),
Technique for Order Preference by Similarity to Ideal Solution (TOPSIS), Simple
Additive Weighting (SAW), and Weighted Sum Model (WSM), among others, allow
decision-makers to consider multiple criteria and objectives simultaneously when
making decisions. AHP and TOPSIS are commonly used methods to solve the TCQT


10

problem, with AHP used to prioritize and weight the relative importance of different
criteria and TOPSIS used to identify the best trade-off solution [23].
In previous studies related to the SGO algorithm in the context of time-cost trade-off
(TCT) in construction projects, researchers have explored various optimization
methods and approaches to address this complex problem. Duc Hoc Tran proposed
SGO on optimizing time-cost tradeoffs in generalized construction projects using the
Multiple Objective Social Group Optimization (MOSGO) algorithm. This research

demonstrated the efficiency of MOSGO in generating non-dominated solutions for
tradeoff decisions involving time, cost
The utilization of both Fuzzy logic and metaheuristic algorithms in a hybridized
approach has been suggested as an effective solution to tackle the issue of uncertainty
in the TCQT problem [24]. Several studies have investigated the use of this approach
to enhance the optimization algorithms in this area.[25] proposed a hybrid algorithm
that combines fuzzy logic and a Multi-Objective Particle Swarm Optimization
(MOPSO) algorithm to address the TCQT problem. The fuzzy logic approach was
used to handle the uncertainty in the project parameters, while the MOPSO algorithm
was used to optimize the project's time, cost, and quality objectives. The results
showed that the proposed approach was effective in finding high-quality solutions
under different scenarios.
Similarly, [26] proposed a hybrid algorithm that combines fuzzy logic and a Genetic
Algorithm (GA) to address the TCQT problem. The fuzzy logic approach was used
to model the imprecise and vague information in the project parameters, while the
GA was used to optimize the project's time, cost, and quality objectives. The results
showed that the proposed approach outperformed other traditional approaches
regarding solution quality and convergence speed. Moreover, [27] proposed a hybrid
algorithm that combines fuzzy logic and a Differential Evolution (DE) algorithm to
address the TCQT problem. The fuzzy logic approach was used to handle the
uncertainty in the project parameters, while the DE algorithm was used to optimize


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the project's time, cost, and quality objectives. The results showed that the proposed
approach was effective in finding high-quality solutions under different scenarios.
Moreover, to address the TCQ trade-off problem, [28] proposed a hybrid algorithm
that combines fuzzy logic and Harmony Search (HS). The fuzzy logic approach was
used to manage the uncertainty of project parameters, while the HS algorithm was

used to optimize the project's time, cost, and quality objectives. The study found that
this approach outperformed traditional approaches in terms of both solution quality
and convergence speed. By combining fuzzy logic and HS, project managers can
more effectively balance the trade-off between time, cost, and quality, while also
accounting for the uncertainty of project parameters.
In previous studies related to the Social Group Optimization (SGO) algorithm in the
context of time-cost trade-off (TCT) in construction projects, researchers have been
exploring various optimization methods and approaches to address this complex
problem. One such study conducted by Khoa et al. [29] focused on the risk section of
project progress. Their proposed social group multi-objective algorithm and multicriteria decision-making method consider time, cost, and risk factors, providing
valuable insights for project management
One notable contribution in this area was made by Duc Hoc Tran [30], who proposed
a novel approach called Multiple Objective Social Group Optimization (MOSGO)
for optimizing time-cost tradeoffs in generalized construction projects. Tran's
research demonstrated the efficiency of MOSGO in generating non-dominated
solutions for tradeoff decisions involving time and cost. By incorporating MOSGO
into the project planning phase, project managers can effectively balance the tradeoffs
between project duration and cost, leading to successful project completion within
the shortest period and at the lowest cost.
Moreover, another significant study by Huynh et al. (2021) [31] introduced MOSGO
for optimizing multiple objectives, including time, cost, quality, and carbon dioxide
emissions (TCQC), in generalized construction projects. Their research showcased