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

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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

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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

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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 HEAD OF DEPARTMENT

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DEAN OF FACULTY OF CIVIL ENGINEERING

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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,

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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

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TÓM TẮT LUẬN VĂN THẠC SĨ

Tiến độ, chi phí, kiểm sốt 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 tốn 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 không 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 soát chất lượng (TCQT) và tích hợp sự khơng chắc chắn xảy ra trong các dự án quy mô lớn thực tế

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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 MULTI-OBJECTIVE 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

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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

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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

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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

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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

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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

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

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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]

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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 heuristic-based One popular algorithm in the meta-heuristic 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]

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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

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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

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

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1.4 Research Procedure

Start

RESEARCH PROCEDURE

Collect the required data to build the model time - cost - quality

trade-off of the project.

Research theoretical basic:- Multi-objective optimization- SGO Algorithm

- Fuzzy Logic- MCDM

Programmatically solve the math problem using the MOSGO algorithm ranking of factorsRefer to previous research, experiencesProblem Programming (MATLAB)

Review the solution of the Math Problem

Export Pareto Set

Selecting the Optimal SolutionChoosing by

Advantages method

Compare results of MOSGO algorithm with other evolutionary

algorithm

Conclusion/SuggestionDevelopment of MOSGO algorithm combined with Fuzzy Logic to select input to solve the

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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

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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 near-optimal 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

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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

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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

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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 objective algorithm and multi-criteria 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

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the effectiveness of MOSGO in generating non-dominated solutions for tradeoff decisions involving multiple objectives simultaneously By addressing time, cost, quality, and environmental impact, their approach enables project managers to make more informed decisions and select compromise solutions that align with sustainability goals

The absence of considering uncertainty in project parameters in the previous studies using MOSGO and other optimization approaches creates a notable gap in the literature While these studies demonstrated the efficiency of MOSGO in tradeoff decisions involving time, cost, quality, and other factors, they did not address the crucial aspect of uncertainty that often arises in real-world construction projects This gap in accounting for uncertainties hinders the development of a comprehensive and robust optimization approach for project management

As a response to this gap, the current research aims to bridge the limitation by integrating MOSGO with Fuzzy Logic By leveraging Fuzzy Logic's capability to handle uncertainty, the hybrid algorithm seeks to enhance MOSGO's optimization performance and adaptability in complex project scenarios Through the application of this novel approach to real-world construction projects, our research endeavors to contribute valuable insights into effectively managing uncertainties, balancing tradeoffs, and achieving more efficient project management outcomes

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2.2 Relative Research

Table 2.1: Summary of some previous relative research

No Author Topic Trade-off Fuzzy Methodology

T C Q Other T C Q

1 Ya-ping & Ying, (2006) [32]

Time-Cost Trade-off Analysis Using Ant

Colony Optimization Algorithm √ √ ACO

2

D.-H Tran et al., (2016) [33]

A Novel Multiple Objective Symbiotic Organisms Search (MOSOS) for Time-Cost-Labor Utilization Tradeoff Problem

√ √ MOSOS

3

H Tran & Duc Long, (2018)

[34]

Project scheduling with time, cost and risk trade-off using adaptive multiple

objective differential evolution

√ √ √ (Risk) SGO MCDC 4 Akin et al., (2021) [35]

A crashing-based time-cost trade-off model considering quality cost and

contract clauses

√ √ √ PSO

GA

5

Duc Long et al.,

(2018) [36] Optimizing multi-mode

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using opposition multiple objective difference evolution

6

Huynh et al., (2021) [31]

Multiple Objective Social Group Optimization for Time–Cost–Quality–

Carbon Dioxide in Generalized Construction Projects √ √ √ √ carbon dioxide (CO2) MOSGO 7 H Tran, (2020) [30]

Optimizing time–cost in generalized construction projects using multiple-objective social group optimization and multi-criteria decision-making methods

√ √ MOSGO

MCDM

8 Son & Khoi,

(2022) [37]

Utilizing artificial intelligence to solving

time – cost – quality trade-off problem √ √ √ SMA

9

Acar Yıldırım & Akcay, (2019)

[11]

Time-cost optimization model proposal for construction projects with genetic

algorithm and fuzzy logic approach

√ √ √ √ GA

Fuzzy

10 Haque & Hasin,

(2012) [4]

Genetic Algorithm for Time-Cost

optimization in Fuzzy Environment √ √ √

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11 Eshtehardian et al., (2009) [38]

Fuzzy-based MOGA approach to

stochastic time-cost trade-off problem √ √ √ √

MOGA Fuzzy 12 Banihashemi & Khalilzadeh, (2022) [39]

Time-cost-quality-risk Trade-off Project Scheduling Problem in Oil and Gas Construction Projects: Fuzzy Logic

and Genetic Algorithm

√ √ √ √ Risk √ GA Fuzzy 13 Kalhor et al.,

(2011) [40] Stochastic time–cost optimization using

non-dominated archiving ant colony approach √ √ √ √ ACO Fuzzy 14 Alzarrad & Fonseca, (2018) [41]

A new model to improve project

time-cost trade-off in uncertain environments √ √ √ √ Fuzzy

15 Eshtehardian et

al., (2008) [42]

Time–cost optimization: using GA and

fuzzy sets theory for uncertainties in cost √ √ √

GA Fuzzy

16 This Study √ √ √ √ √ √ MOSGO

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2.3 Multi-objective optimization

Multi-objective optimization (MOO) involves the simultaneous optimization of two or more conflicting objectives It is an essential component of optimization operations and holds significant practical importance, as the majority of real-world optimization problems can be effectively modeled using multiple conflicting objectives While traditional methods for solving such problems often aim to transform multiple goals into a single objective, there exist numerous evolutionary algorithms specifically designed to tackle multi-objective optimization problems [43]

MOO problems are typically solved using various methods, including the global criteria method, the weighted sum method, the ε constraint method, and others However, these methods often involve complexity and difficulties in applying mathematical equations In contrast, there are two simpler approaches to solve MOO problems without requiring complex mathematical equations: the Pareto method and the scalar method The Pareto method involves identifying superior and non-superior solutions through iterative update algorithms The superior solution represents the best compromise between conflicting objectives, while the non-superior solutions are obtained through iterations On the other hand, the scalar method transforms the multi-objective function into a single-objective solution using weights In scalar scaling, there are three types of weights: equal weights, ordinal weights, and weight sums [44]

Multi-objective optimization (MOO) is a widely used technique in many fields, including engineering, finance, and operations research, to name a few In MOO, there are multiple objectives that are to be optimized simultaneously, but these objectives may conflict with each other MOO aims to find a set of solutions that are Pareto optimal, meaning that no other solution in the solution space can outperform them in all objectives simultaneously [45] The Pareto optimal solutions form the Pareto front, which represents the trade-off between the conflicting objectives [46]

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If both requirements are met, solution X1 dominates solution X2:

∀𝑖 ∈ (1, 2, … , 𝑘) ∶ 𝑓 (𝑋1) ≤ 𝑓 (𝑋2) (2)

∃𝑖 ∈ (1, 2, … , 𝑘) ∶ 𝑓𝑖 (𝑋1) < 𝑓𝑖 (𝑋2) (3)

a In all objectives, solution X1 is not inferior to solution X2 b X1 is obviously superior to X2 in at least one objective There are three possible dominance relationships among any two solutions:  A has an advantage over B1 and B2

 A has the dominant position with B0  A and B3 are non-dominant to one another

The set of all possible solutions that are not dominant in X is called the Pareto optimal set For a given Pareto optimal set, the corresponding objective function values in the objective space are called Pareto Front The goal of multi-objective optimization algorithms is to identify solutions in the Pareto optimal set In fact, proving that a solution is optimal is often computationally infeasible Therefore, a practical approach to the multi-objective optimization problem is to determine the set of solutions that are the best possible representation of the Pareto optimal set; such a set of solutions is called the Best-known set Pareto [47]

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2.4 Soft Logic

Soft logic refers to a condition where project activities can be performed in any sequence, while still adhering to their dependencies This scheduling approach is commonly used in repetitive projects For instance, consider a foundation work that needs to be completed for four units, A, B, C, and D Employing soft logic, the foundation work can be carried out in various orders, such as A-B-C-D, D-C-B-A, A-C-D-B, A-D-B-C, and so on Subsequently, the next activity, which follows the foundation work, is executed in the same order as the unit that finishes first in the previous activity In repetitive project scheduling, once an activity in one unit is completed, resources must be transferred to another unit to perform the same task However, this transfer must consider the work dependencies If the next unit has not finished the previous activity, the resources should wait until it completes before starting their work

Similarly, if an activity in one unit is ready for execution due to the completion of the previous activity in that unit, the required resources may not be available if they have not yet finished working in the previous unit Consequently, the execution time in that unit must be delayed due to the unavailability of resources These two conditions can result in a longer project duration Conversely, in another scenario, when the resources are available and the unit is ready to begin, the activity can be executed immediately This situation may lead to a shorter project duration compared to the previous two conditions Thus, altering the activity sequence in the project can impact the project duration, either prolonging or shortening it

2.5 Multiple-criteria decision-making (MCDM)

2.5.1 Overview of Multiple-criteria decision-making (MCDM)

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algorithms to select the best solution from a set of non-dominated solutions generated by the optimization algorithm In a multi-objective optimization problem, there may be multiple conflicting objectives, and the solution space consists of a set of solutions that are not dominated by any other solution with respect to all the objectives This set of solutions is called the Pareto set

MCDM techniques help to rank the solutions in the Pareto set by taking into account multiple criteria, such as time, cost, and quality, to determine the most suitable solution for a particular application These techniques involve a set of methods for evaluating and comparing different options based on their performance against multiple criteria Mostly all Multiple-criteria decision-making (MCDM) issues may be written in the following form:

𝑚𝑖𝑛{𝑓 ( 𝑥), 𝑓 ( 𝑥), , 𝑓 ( 𝑥) | } (4)

Where X is a finite set of possible options (solutions) {x1, x2, …, xn} is a set of evaluation criteria

Let's consider some criteria to be maximization and others to be minimization The decision maker's expectation is to determine an optimal solution choice across all criteria The data of the usual multi-criteria problem is described in the table below:

Table 2.2 Multiple-criteria decision-making assessment

x f1(.) f2(.) … … fk(.)

x1 f1(x1) f2(x1) … … fk(x1)

x2 f1(x2) f2(x2) … … fk(x2)

… … … … … …

xn f1(xn) f2(xn) … … fk(xn)

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and additional information is necessary to assist decision-makers in selecting the most suitable solution The dominance relationship plays a crucial role in multi-objective decision problems, as defined in Section 2.3.1 When comparing two solutions, X1 and X2, there are three dominant relationships: X1 is superior to X2, X1 is dominated by X2, Neither X1 nor X2 influence each other

This definition provides clarity in determining the dominant relationship between options An option is considered to dominate another option when it is better or equal in all criteria while having at least one superiority criterion If neither option is superior, it implies that X1 and X2 cannot be directly compared, and additional supporting information is needed This supporting information may include:

- Compromises between goals: Finding a balance or trade-off between different objectives

- Single objective function: Combining evaluation criteria into a single objective function to solve the problem as a one-objective optimization - Weighting: Assigning weights to each goal to represent their relative

importance

- Priority Limits: Defining constraints or limits on specific objectives based on their priorities

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2.5.2 The Evidential Reasoning (ER) method

The Evidential reasoning (ER) method is a decision-making approach that utilizes evidence and uncertainty to support rational decision-making under conditions of incomplete or imperfect information It is based on the principles of Dempster-Shafer theory of evidence, which allows for the combination of multiple sources of evidence to derive and make informed decisions The Evidential reasoning method shares a relationship with Bayesian probability theory as both approaches involve updating subjective beliefs based on new evidence However, the main distinction between these two theories lies in the ability of evidence theory to combine evidence and handle situations of ignorance during the evidence combination process In contrast, Bayesian probability theory focuses on updating beliefs based on observed data using the principles of conditional probability [52]

The ER (Evidential Reasoning) method is recognized as a state-of-the-art approach capable of effectively handling MCDM (Multi-Criteria Decision Making) problems used by uncertainty and complexity [53] It is currently the only method known to date that specifically addresses these challenges When dealing with a set of Pareto solutions, the ER method optimal an analytical approach to rank the alternatives that are not dominated and identify the best solution The evidence-reasoned (ER belief) approach represents a general framework for analyzing MCDM problems, incorporating multiple criteria and dealing with various types of uncertainty within a unified Information within the ER method involves employing rule-based priority-based techniques to transform and synthesize qualitative and quantitative information, demonstrate the necessary prioritization and equal valuation of criteria The application of the ER method to an MCDM problem typically involves the following steps [54]:

1 Identify and analyze the multi-criteria decision-making problem at hand 2 Transform the various belief structures associated with the problem into a

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3 Synthesize the available information using analytical reasoning based on the ER theory

4 Generate distributions, ratings, priority scores, or intervals to handle any missing information In this step, the solution with the highest priority score is favored over solutions with lower values

By following these steps, the ER method empowers decision-makers to navigate the complexities of multi-criteria decision-making problems It enables them to transform diverse belief structures into a unified framework, synthesize information, and handle missing information effectively Ultimately, the ER method facilitates decision-making by providing a systematic and strict approach to incorporating uncertainty and multiple criteria in the decision process By following these steps, the ER method provides a robust and comprehensive approach to addressing MCDM problems, allowing decision-makers to effectively handle uncertainty, prioritize criteria, and make informed decisions based on a unified belief structure

2.6 Social Group Optimization (SGO)

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multi-criteria decision-making method, the strengths of MOSGO align perfectly with our goals

MOSGO has demonstrated superior performance when compared to various state-of-the-art algorithms like Genetic Algorithms (GA), Particle Swarm Optimization (PSO), Differential Evolution (DE), Artificial Bee Colony (ABC), and Teaching-Learning-Based Optimization (TLBO) The algorithm not only provides optimal solutions but also exhibits remarkable computational efficiency In the context of construction project management, where quick and accurate decision-making is vital, this advantage becomes highly significant

Furthermore, MOSGO's capacity for adaptation and learning adds to its appeal As individuals within the algorithm possess the ability to adapt, learn, and share knowledge with others in the population, it fosters a collaborative environment for collective problem-solving This characteristic enables a better understanding of the problem space and results in improved problem-solving abilities, leading to enhanced solutions for project management

The experimental results from Naik and Satapathy's work support the efficacy of MOSGO in finding optimum solutions It consistently outperformed other algorithms, including HS, Intelligent Bug Algorithm (IBA), and various ABC and TLBO variants With MOSGO's ability to achieve optimal solutions using fewer fitness evaluations, it emerges as an efficient and reliable optimization method for resource balance in construction projects Additionally, MOSGO's multi-objective nature aligns perfectly with our research goals Its capability to simultaneously optimize multiple objectives, such as project time, cost, and quality, is particularly valuable in construction project management Striking a balance between these factors is paramount for successful project outcomes Based on the robust evidence provided by Naik and Satapathy's research, MOSGO emerges as the most suitable candidate for developing our optimal project resource balance model

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important aspect of the algorithm as it allows individuals to improve their solutions and explore new areas of the search space Each person learns, gains knowledge, and possesses some potential for issue-solving This is equivalent to adaptation The best candidates are considered the best solution The best person (best possible solution) tries to impart knowledge to everyone, which in turn helps to raise and enhance the understanding and knowledge of all team members This helps to raise the overall understanding and knowledge of the group, leading to better problem-solving ability and improved solutions

Also, according to Suresh Satapathy & Anima Naik (2016) the procedure of SGO is divided into two parts The first part consists of the ‘improving phase’; the second part consists of the ‘acquiring phase’ In the ‘improving phase,’ the knowledge level of each person in the group is enhanced with the influence of the best person in the group The best person in the group is the one having the highest level of knowledge and capacity to solve problems And in the ‘acquiring phase,’ each person enhances his/her knowledge with the mutual interaction with another person in the group and the best person in the group at that point in time

SGO uses NP vectors, the D dimension is mathematically interpreted as follows:

Xi, G = { 𝑥, , 𝑥, ,…, 𝑥, } (4)

With: i = 1, 𝑁𝑃 is the population sequence for each iteration Xi, i= 1,2,3,…, NP is a member of a social group

D is the number of traits assigned to a person which determines the dimensions of a person

G is the current generation under consideration and fi,j=1,2,3, ,NP are their corresponding fitness values

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The first part consists of the ‘improving phase’:

During the "improving phase" of the SGO algorithm, the best (𝐺 ), which represents the best solution in the current generation, plays a crucial role in enhancing

the knowledge of all individuals within the social group The best (𝐺 ) acts as a

knowledge source, sharing its expertise, insights, and solution strategies with other

members of the group By imparting knowledge, the best (𝐺 ) helps to elevate the

understanding and problem-solving capabilities of other individuals in the group This knowledge transfer process facilitates the dissemination of valuable information and techniques that are effective in achieving high-quality solutions As a result, individuals in the group can learn from the best (𝐺 ) and improve their own knowledge, leading to better problem-solving abilities and the generation of improved solutions

𝐺 = min {fi, i = 1,2,3, , NP} (5)

The interaction between the best (𝐺 ) and other individuals during the improving

phase fosters a collaborative and cooperative environment within the social group It promotes the exchange of ideas, perspectives, and experiences, enabling individuals to gain insights into different solution approaches and problem-solving strategies This collective learning process the overall knowledge base of the group, contributing to the continuous improvement and advancement of solutions throughout the optimization process In this phase, the update per individual could be determined as follows:

𝑋, = 𝛼𝑋, + 𝛽(𝐺 − 𝑋, ); j = 1, 𝐷 (6)

α ⸦ (0; 1) is the self-observation parameter

β is a randomly selected number in the range (0; 1)

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During the acquiring phase of the SGO algorithm, individuals in a social group engage in interactions to acquire new knowledge This phase involves two main

components First, each person interacts with the best person (𝐺 ) in the group,

who possesses the highest level of knowledge and expertise These interactions with

(𝐺 ) provide individuals with the opportunity to directly learn from their superior

knowledge and insights Second, individuals also engage in random contacts with other group members, regardless of their current knowledge level These interactions allow individuals to gather different perspectives and insights from their partners Acquiring phase is shown below:

𝐺 = min {f (X), 1,2,3, , N} (7)

The acquisition of new knowledge occurs when an individual interacts with someone who possesses more knowledge than themselves If an individual engages with another group member who has a higher level of knowledge or expertise, they can

learn from them and enhance their own understanding of the problem Xi is the last

updated value of the improving phase, to the acquiring phase, each individual will find a common solution regarding the comprehension modification process as follows:

𝑋, =[ 𝑋, + β (X, − X , ) + β (𝐺 − X , ), 𝑓(X ) < 𝑓(X )

𝑋,: + β (X ,: − X,: ) + β (𝐺 − X, ), 𝑓(X ) ≥ 𝑓(X ) (8) where Xk is a random person in the current group (i ≠ k);

β1 and β2 are two independent random values 2.7 Optimize project scheduling