HO CHI MINH CITY UNIVERSITY OF TECHNOLOGYMULTI-OBJECTIVE OPTIMIZATION OF DYNAMIC CONSTRUCTION SITE LAYOUT USING ARTIFICIAL INTELLIGENT ALGORITHM Major: Construction Management Major cod
Construction Site Layout Planning
Researchers across various fields, like engineering and architecture, have extensively studied how to optimize the layout of construction sites These sites house various facilities, from machinery to work areas, that each serve a specific purpose As product designs and services constantly evolve, designing an effective site layout becomes crucial for a project's success [1, 2]
A well-planned layout allows for quick adaptation to changing needs, while a poorly designed one can lead to issues like material pile-up, equipment overload, and delays [3] This is why site layout planning is considered a significant factor in production efficiency and overall project economics [4] Studies show that an optimal layout can reduce operational costs by 20-50%, while a bad layout can inflate material handling costs by up to 36% [5, 6]
However, designing such layouts presents a complex challenge It's a classic computer science problem known to be extremely difficult to solve perfectly within a reasonable timeframe, especially when dealing with a large number of facilities[7, 8] For n facilities, the number of possible alternatives is n! For 10 facilities, the number of possible alternatives is well above 10! 3,628,000
Traditional methods like quadratic assignment problems (QAP) treat all facilities as interchangeable units that can fit anywhere on the site [9] While techniques like branch-and-bound or dynamic programming have been used to tackle this problem [10-13], the dynamic nature of construction sites with constantly changing activities necessitates new approaches
Modern construction projects require efficient resource utilization and optimal layout planning to ensure success Unlike static layouts, construction sites are constantly evolving with multiple activities happening
STUDENT: PHẠM MINH HUY 2 simultaneously, making manual planning methods inefficient and prone to errors, leading to cost increases and delays This is where Artificial Intelligence (AI) algorithms are gaining traction Optimizing dynamic construction site layout using AI is a rapidly growing field with the potential to significantly impact project timelines and costs By efficiently utilizing resources and strategically arranging facilities, AI can revolutionize construction project management
The complexity of construction sites, with their existing facilities, material storage areas, and ever-moving equipment, further highlights the need for advanced solutions Tower cranes and other large machinery can significantly obstruct pathways and constantly change position, hindering productivity Therefore, implementing advanced technological solutions like
AI to address the challenges of dynamic construction site layout is critical.
Reason for choosing the topic - Research objectives
For large and complex problems, finding the absolute optimal solution can be impractical This is where heuristic approaches come in These are like clever shortcuts that provide solutions that are close to the optimal one, but can be found much faster
In recent years, researchers have been focusing on iterative metaheuristics, which are like step-by-step improvement techniques These include methods like simulated annealing, genetic algorithms, and ant colony optimization [14-18] Even newer advancements involve scatter search, particle swarm optimization, and tabu search [19-21] While these techniques have been applied to various optimization problems, their effectiveness is limited by their inherent capabilities
Evolutionary techniques, like genetic algorithms, have been around since the 1980s and have proven successful in tackling highly complex problems across various fields [22, 23] They excel at exploring intricate
STUDENT: PHẠM MINH HUY 3 search spaces and finding good solutions for difficult problems where exact solutions are hard to come by [23] Genetic algorithms, for instance, have been used for optimizing facility layouts and storage locations [24-27] Another evolutionary method, differential evolution (DE), has been shown to outperform genetic algorithms in specific problems like manufacturing cell formation [28, 29]
Swarm intelligence techniques, inspired by how animals like bees or ants navigate and collaborate, are another powerful tool Particle swarm optimization (PSO) has been used effectively for warehouse layout design, even surpassing traditional methods like branch and bound [30] Similarly, the artificial bee colony (ABC) algorithm has been shown to outperform genetic algorithms for problems with multiple peaks or valleys in the search space [31] Other swarm intelligence methods like the firefly algorithm (FA) have also shown promise, with studies suggesting they may converge faster than PSO for certain problems [32, 33]
While these metaheuristics offer significant advantages, it's important to remember that they don't guarantee the absolute best solution They provide high-quality solutions in a reasonable amount of time, which is often a valuable trade-off Hybrid methods that leverage both AI's problem-solving power and human knowledge for specific constraints can be very effective This has led to the rise of hybrid metaheuristics, which combine concepts from different algorithms to create even more powerful optimization tools [34] However, combining algorithms requires careful selection and experimentation, as not all algorithms work well together Choosing the right hybrid approach is crucial for achieving the best results for complex problems
Several studies have been conducted in this field, highlighting the effectiveness of integrating artificial intelligence algorithms with site layout planning However, previous algorithm, such as GA, DE, PSO, BA, and FA has some limitations that have not yet completely solved this problem While artificial intelligence algorithms offer promising solutions for optimizing
STUDENT: PHẠM MINH HUY 4 dynamic construction site layouts, there are challenges in accurately modeling the dynamic nature of construction sites Hence, to improve the performance, this study proposes a new hybrid metaheuristic, which is the the Mountain Gazelle optimizer (MGO), which was recently developed by Benyamin Abdollahzadeh et al in 2022 MGO is inspired by the hierarchical organization and social structure of wild mountain gazelles The social and hierarchical needs of gazelles serve as the foundation for the mathematical simulation of the MGO The basic elements—maternity herds, bachelor male herds, territorial males, solitary, and foraging movements—are used to model the algorithm Four procedures are used to carry out the exploration (diversification) and exploitation (intensification) stages of the MGO concurrently Even though MGO performed quite well, simulations showed that early iterations can become stuck in undesirable search space domains when working with greater dimensions Stated differently, there exist issues wherein early processing cycles fail to attain solution diversity, and the majority of solutions are produced beyond the optimal region To address the limitations of the MGO algorithm, this study proposes a hybrid approach that combines MGO with Evolved Opposition-based learning (EOBL), which inspired by Opposition-based learning (OBL), enhances the algorithm's ability to explore the search space and avoid local optima Additionally, the Roulette wheel selection method is replaced with Tournament selection (TS) to improve convergence speed and accuracy
Name of the algorithm: Hybrid model of Mountain Gazelle Optimizer (HMGO)
Research Scope, Assumptions and Hypotheses
1 Application of proposed method in solving the CSLPs formulated as QAP
2 The methods focus on metaheuristic methods
3 CSLP objectives in minimize the cost (material handling and transportation) and work flows
4 Risks, dynamics, and emergencies that may occur during the construction process are not included in this study
Several assumptions and hypotheses for the model development process
1 All factors which affect the case study problems are already known
2 Most of CSLPs are NP-hard and may be resolved by metaheuristic methods
3 In case study problem, if there are no particular constraints area size, it means every location are adequate to accomodate the facility or material
1 All parameters required in PFDAcan be identidied concurently
2 Solving method for construction site layout problems can be improved by PFDA
3 Decision making in construction site layout problems can be facilitated by PFDA
Research Methodology
The research flow chart depicted in the figure outlines a systematic approach to conducting research, divided into four primary stages:
The detailed research flow chart provided outlines a comprehensive and structured approach to conducting research It breaks down the process into nine main steps, each with specific sub-tasks and considerations This detailed flow chart provides a thorough guide for researchers, ensuring all critical steps and considerations are addressed systematically, from initial problem identification to final conclusions and recommendations
1 Identify the Problems a Review the research’s interest b Specify research objective c Determine scope of study
2 Literatures Review a Review related concepts, theories b Review previous findings
3 Model Construction a Establish the model architecture b Develop the model
4 Model Evaluation and Application a Propose potential application b Draw conclusion and recommendation
Metaheuristic approach in construction management
3 Define the Scope of Study
Identify the assumption and limitation
Lit er at ur es R ev iew
4 Review Related Concepts and Theories
Mode l C ons tr uct ion 6 Establish Model Architecture
Model adaptation process Pseudo Code
Mode l I m pl em en tat ion 8 Model Application Propose potential applications
Figure 1-2 Detailed Research Flow Chart
Thesis Outline
Chapter 1 presents the importance of introducing a new optimization technique in solving CSLP This chapter also describes the research objectives, research scope, and research methodology
Chapter 2 presents some previous research on Metaheuristics to Construction Site Layout Planning and BIM Applications in Construction
Chapter 3 presents the CSLP as QAP and reviews the existing solution methodologies This chapter also defines brief introduction of the concepts of how to take advantage of the REVIT API combined with the proposed algorithm to be able to apply it to real projects Also, in this chapter, the concepts of various algorithms, such as MGO, Evolved Opposition based learning, Tournament Selection will be proposed, addition to that is the applications, advantages and disadvantages of each algorithm
Chapter 4 describes the development of the proposed algorithm including the main structure The improvement contributed by each algorithm towards the optimization process of hybrid algorithm is also discussed In addition, detail step of the proposed method are presented
Chapter 5 verifies the effectiveness of the HMGO model dealing with two model case studies and one real-world case study to demonstrate that HMGO can be trusted to solve the problem of facility layout on real construction sites Lastly, experimental results and discussion are given
Chapter 6 presents the final conclusion which describes the finding, contribution and recommendation for further research
Applying Metaheuristics to Construction Site Layout Planning
Facility layout problems involve extensive computational demands, requiring significant time, effort, and the use of powerful computers to address all possible computational scenarios Therefore, it may be beneficial to consider heuristic methods, which are approximate approaches that can yield near-optimal solutions within a reasonable timeframe
In 2012, Xu and Li introduced a fuzzy random multi-objective decision-making model aimed at improving dynamic CSLP [34] Creating a multi-objective site layout optimization system can significantly enhance construction safety, boost security levels, and provide better visibility for users regarding optimal site layout plans [35] A construction site model can support designers in examining site constraints, detecting potential problems, and maximizing both productivity and safety on-site [36] An optimal CSLP can help project managers and planners design superior construction sites by balancing conflicting objectives, such as minimizing construction costs and improving ease of supervision and control [37]
Research based on Meta-heuristic iterative approaches includes the simulated annealing hybrid algorithm [14], greedy heuristic algorithms in construction [15], genetic algorithms [16], techniques based on Meta- heuristics [17], and ant colony algorithms [18] Recent studies involving Heuristics related to facility layout problems include distributed search [19], swarm optimization [21], and tabu search [20] These studies address various optimization problems by applying algorithms under different constraints, and the effectiveness of the solutions found can be limited by the capabilities of the algorithms
Meta-heuristics are divided into two main categories: evolutionary methods and swarm intelligence methods
Evolutionary methods are a category of optimization algorithms inspired by the process of natural evolution They operate on a population of potential solutions, applying principles of genetic variation and natural selection to evolve these solutions toward an optimum Evolutionary methods include Evolutionary Programming (EP), Evolutionary Strategies (ES), and Genetic Algorithms (GA) These methods achieved significant success in the 1980s by addressing complex optimization issues and have been utilized as a method for solving problems [22] Evolutionary algorithms (EAs) have proven effective in solving NP-hard problems and exploring complex, nonlinear search spaces [23] Evolutionary algorithms like GA and Differential Evolution (DE) are widely used for optimization problems Specifically, the GA algorithm has been applied to solve the layout of facilities on the same level and at different elevations and for solving the problem of material storage location layout in multi-story buildings [24-27]
Particle swarm optimization (PSO) is a population-based stochastic approach for solving continuous and discrete optimization problems It belongs to the class of swarm intelligence techniques PSO was introduced by Kennedy and Eberhart (1995) It has roots in the simulation of social behaviors using tools and ideas taken from computer graphics and social psychology research PSO has been used to solve the problem of warehouse layout design, PSO is better than the branch and union method [30]
Table 2-1 Previous studies on Meta-heuristic in CSLP
No Year Authors Study Title Description
Particle Swarm Optimization for Construction Site Unequal-Area Layout
This study demonstrates the application of Particle Swarm Optimization (PSO) for optimizing the layout of construction sites with unequal-area facilities, highlighting the method's effectiveness in spatial optimization
A Hybrid Swarm Intelligence Based Particle- Bee Algorithm for Construction Site Layout Optimization
Investigates a hybrid algorithm combining Particle Swarm Optimization with a Bee Algorithm to address complex site layout challenges, improving both the efficiency and efficacy of the layout process
A Comparative Study of GA, PSO and ACO for Solving Construction Site Layout
Compares Genetic Algorithms (GA), Particle Swarm Optimization (PSO), and Ant Colony Optimization (ACO) in the context of construction site layout, providing insights into the strengths and weaknesses of each
Optimization Algorithm for Construction Site Layout Problems
Details an enhanced version of the Ant Colony Optimization algorithm specifically tailored for optimizing construction site layouts, focusing on efficiency and solution quality
Kaveh, A., Khanzadi, M., Alipour, M., and Moghaddam, M.R
Construction Site Layout Planning Problem Using Two New Metaheuristic Algorithms
Introduces two novel meta-heuristic algorithms designed for construction site layout planning, emphasizing their adaptability and effectiveness in handling real-world layout complexities
A Decision- Making System for Construction Site Layout Planning
Presents a decision-making system enhanced by meta-heuristic algorithms to aid in the planning and optimization of construction site layouts, aiming for optimal resource allocation and space utilization
Application of the Entropy Technique and Genetic
Explores the use of entropy techniques combined with Genetic Algorithms to optimize the layout of medium-sized construction projects, improving
Algorithms to Construction Site Layout Planning of Medium-Size Projects logistical efficiency and operational workflow
Genetic search for solving construction site- level unequal- area facility layout problems
A genetic algorithm based on Darwin's theory of evolution is used to solve the problem of facility placement on a construction site, presented as the allocation of facilities to a set of locations predetermine and simultaneously satisfy constraints
A hybrid CAD- based construction site layout planning system using genetic algorithms
The GA genetic algorithm model was developed to find an almost optimal solution in arranging the facilities of the assembled concrete workshop on the construction site with different transportation costs
Dynamic construction site layout planning using max-min ant system
The Max-min MMAS ant colony system initializes the initial population better than the randomly initialized initial population of the GA The MMAS-GA algorithm is formed by connecting MMAS in the initialization step of the GA Proposals to solve problems of arranging facilities on construction sites
Optimization of tower crane and material supply locations in a high-rise building site by mixed- integer linear programming
Proposing the optimization of hoist usage to transport materials and material storage locations in high-rise buildings using the mixed integer program MIP Research needs to extend the formulation of the problems by adding additional linear constraints to consider more complex situations
A particle swarm optimization algorithm for the multiple-level warehouse layout design problem
A swarm optimization (PSO) algorithm is developed for optimal layout that minimizes annual transportation costs in a distribution warehouse, where different products are received from different suppliers, stored in warehouse for a specified period of time and distributed to different customers
BIM Applications in Construction
Building Information Modeling (BIM) integrates the planning, information, and resources of an engineering project across its life cycle into a single model, facilitating both construction and maintenance [38, 39] As an advancement beyond 3D CAD technology, BIM further modernizes construction engineering management Unlike 3D CAD, BIM uses three- dimensional digital technology to simulate real building information, creating a coordinated and consistent information model for design and construction This approach helps integrate design and construction across various disciplines, reducing project costs and ensuring timely and high-quality project completion [40, 41]
Wayne et al suggest that building construction safety can be addressed through the automatic safety regulations embedded within the building information model (BIM) This system allows for the automatic analysis of detected hazard sources, and implements corresponding preventive measures to mitigate high-altitude fall accidents [42] The automatic safety detection platform notifies engineers and managers about the causes, locations, timings, and safety measures required to prevent accidents before construction begins Assaf et al emphasize that the integrated design and collaboration capabilities of BIM technology can be leveraged to enhance construction site safety and facilitate safe construction planning [43] BIM possesses unique properties that can be integrated with construction safety management to prevent hazards To expand security management using these technologies and extend their application to broader security management practices, it is essential to define the functions and advantages of BIM [44]
BIM's effectiveness hinges on several aspects Project scale, clear communication within the team, and even external organizational factors all play a role in its success [45] BIM goes beyond just the building itself It encompasses everything from the geometry and layout to the properties and quantities of every component [46] This allows for safety checks to be
STUDENT: PHẠM MINH HUY 14 integrated before construction even begins, improving overall site safety throughout the project [47, 48] BIM shines during the design phase, enabling designers, builders, and owners to address concerns collaboratively, leading to a more efficient process [46] For construction teams, BIM benefits extend to scheduling and cost estimating, as well as managing changes, tracking shop drawings, and overseeing site logistics, temporary structures, and services – all while keeping safety paramount [32] In fact, a survey revealed that BIM is most valued for its ability to visualize and coordinate work across Architecture, Engineering, and Construction (AEC) disciplines, preventing errors, and ultimately enhancing project productivity, schedule, safety, cost, and quality [46]
BIM technology is rapidly maturing as its use becomes widespread and government policies continue to evolve [49] This powerful tool leverages informational techniques like model building and simulations to identify potential problems before construction even starts By proactively proposing solutions and improvements, BIM helps to ensure project quality, minimize risks, and extend the life of the building BIM also excels at managing complex data It sorts and categorizes this data, while allowing for real-time input of actual cost information This readily available data empowers project managers to conduct swift and multifaceted cost analyses, saving on labor, materials, and finances Ultimately, BIM contributes to a significant boost in construction project management efficiency [50, 51]
Construction Site Layout Planning
The Construction Site Layout problem (CSLP) is focused on the optimal placement of departments, machines, or facilities within a specified area It involves three main tasks: defining the size and shape of these facilities, recognizing the constraints among them, and determining their positions to ensure both efficiency and compliance with these constraints The challenge of CSL involves effectively managing limited space on construction sites to house temporary structures such as fabrication shops, trailers, material and equipment storage areas, and office spaces, facilitating their efficient operation [24]
A facility is any entity that supports job performance, ranging from machine tools and manufacturing cells to departments and warehouses Layout planning is crucial in manufacturing due to its significant economic impact Proper CSL is a key task for managers at construction sites, aimed at enhancing project and overall company performance Notably, material handling costs represent between 20% and 50% of the total operating expenses in manufacturing [6], prompting numerous studies to explore strategies for reducing these costs Facility layout represents a major investment and any changes to it are costly and disruptive, affecting material flow and worker productivity [52]
The strategic importance of facility layout design cannot be overlooked Effective CSL planning can significantly cut construction costs, including expenses related to plant, labor, and materials, boost productivity of labor and equipment, and enhance safety and health on construction sites
Layout challenges vary widely depending on the specifics of the manufacturing systems in question Factors such as production volume and variety, the type of material handling system employed, part flow allowances,
STUDENT: PHẠM MINH HUY 16 facility configurations, and the logistics of machine placement across floors all play a role in defining these challenges [53]
Traditionally, the construction layout issue has been formulated as a Quadratic Assignment Problem (QAP), as proposed by Koopmans and Beckmann in 1957 This approach involves assigning 'n' facilities to 'n' exclusive sites, where each facility is assumed to occupy an equivalent area, allowing for any facility to be placed in any site The name "quadratic assignment" stems from the quadratic nature of the objective function, which aims to minimize material handling costs calculated as the product of workflow and travel distance The goal of the QAP is to find the optimal placement of facilities to sites, minimizing costs and maximizing efficiency The overall minimum material handling cost is usually modeled by minimizing the product of interdepartmental flow and distance The
X ij i j n where xij = 1, if facility i is assigned to site j; 0, otherwise cij = fixed (location) cost associated with assigning facility i to site j djm = distance between sites j and m (proportional to travel cost), djj = 0 fik = work flow between facilities i and k, fii = 0
Aijkm = fik, djm if i k or j m,
The QAP has been applied to a wide range of facility layout problems since the early 1960s Currently, there is no single method for solving all QAPs, so each problem is solved independently based on specific project assumptions and well-defined information There are various approaches to address the different types of QAPs formulated in the literature These approaches aim to find either good solutions that satisfy certain constraints given by the decision-maker or to search for global or local optimum solutions based on one or several performance objectives There are two main types of approaches: exact methods, such as branch and bound, and approximate methods, such as heuristics and metaheuristics [53]
Some exact approaches include branch-and-bound [10], dynamic programming [12], semi-definite programming [13], and integer linear programming [11]
Since exact approaches are often not suitable for large-scale problems, researchers have developed numerous heuristics and metaheuristics Construction approaches progressively build the sequence of facilities until the complete layout is obtained Construction heuristics include CORELAP, ALDEP, COFAD, and SHAPE Examples of improvement heuristics are CRAFT, FRAT, and DISCON Recent developments based on metaheuristic approaches include hybrid simulated annealing [14], constructive greedy heuristic [15], GAs [16], metaheuristic-based technique [17], and ant colony algorithm [18] More recent work with metaheuristics for the facility layout problem includes scatter search [19], PSO [21], and tabu search [20]
Studies by Kouvelis et al (1992) and Heragu and Alfa (1992) showcase the effectiveness of SA in tackling QAP By combining SA with penalty methods or using a hybrid SA approach, these researchers achieved impressive results Jajodia et al (1992) further extended the application of SA to optimize layouts within cellular manufacturing environments
Algorithms in real-life problems via Revit API
While CSLP are a well-discussed topic, achieving optimal efficiency often remains elusive This section proposes a framework for integrating research findings into the early engineering stages
By applying algorithms to real-world scenarios, various constraints can be factored into the design phase before construction begins These constraints might include existing structures, crane placement zones, material and equipment storage areas, and temporary facilities like offices and parking Additionally, factors like minimizing travel distance and avoiding obstacles are considered
This research utilizes the HMGO Algorithm Implemented through a MATLAB code, the algorithm assigns values to different points in the construction site: unoccupied areas are marked as 2, obstacles are marked as -1, the starting point is marked as 1, and the destination is marked as 0 The code then searches for the optimal solution (shortest distance, least workflow, or lowest cost, depending on user input) from the starting point to the destination, automatically excluding obstacles marked as -1
To integrate this approach into existing workflows, developers can create new functions within the Revit software environment These functions would be housed in a separate project file and appear as a custom ribbon within the Revit interface By leveraging the Revit API (Application Programming Interface), programmers can directly modify BIM elements or access data to perform specialized tasks like generating optimized travel solution (as shown in Table 3-1)
Automatically read the coordinates of each components on the selected construction site, based on the selected relevant point, an excel file is created including all (x, y) coordinates information
Automatically reads the optimal solution generated by MATLAB software leveraging the proposed HMGO algorithm, and then plot the optimized travel solution in the selected construction site model
The logic of the framework is presented in Figure 3-1 The first step is to determine if an existing Revit model is available If it is, the subsequent steps will then guide the process to automatically find an optimal solution for the problem Figure 3-2 shows the envisioned relationships and data transitions through Revit, Excel, and MATLAB The first step of the interface is for a user to select “Read Coordinates” This selection allows users to choose existing buildings and facilities on a construction site, as well as input fixed points and relative coordinates An Excel file is then automatically generated, including all these components The next step involves running MATLAB code on the coordinates to obtain an optimized solution The MATLAB code is designed to automatically output the coordinates of the efficient solution into an Excel file The final step involves using another add- in created in Revit Once this selection is made, the generated solution is automatically presented in a BIM By leveraging the Revit API, the algorithm seeks the optimal solution and avoids obstacles, with the calculations performed in MATLAB and then plotted in the original Revit model
Figure 3-2 Relationships between Revit, MATLAB and Excel file
The system allows users to freely modify the type, location, and size of any element on the construction site, including the overall site dimensions Additionally, users can randomly place components for various scenarios This flexibility empowers users to define different construction phases or experiment with layout designs By simply adding obstacles and selecting relevant components, the system automatically calculates and displays the optimal solution within the Revit model
Determine the appropriate input for the problem
Optimal solution is calculated through Matlab Automatically plot the optimal solution in Revit model by created Revit add-ins Get the construction geometric plan view
Read coordinates by Revit add-ins Create a simplified construction site layout
Figure 3-1 Framework for CSLP Optimization
Optimal solution Revit add-ins Coordinates
Optimal solution MATLAB code Coordinates
Mountain Gazelle Optimizer (MGO)
Territory Solitary males (TSM)
Upon reaching adulthood, male gazelles gain the physical capability to defend themselves and establish isolated, well-protected territories, spaced apart from each other Adult males engage in combat to gain control over female territories or ownership While mature males strive to safeguard their territories, adolescent males seek to capture these territories or gain access to the females The illustration below depicts the territory of an adult male gazelle:
Here, 𝑚𝑎𝑙𝑒𝑔𝑎𝑧𝑒𝑙𝑙𝑒 = position vector of the best male adult
𝑋(𝑡) = the initial position of the gazelle
𝛽 1 and 𝛽 2 = random numbers with values of 1 or 2
𝐵𝐻 = the coefficient vector of the young male herd
𝐶𝑜𝑓𝑟 = randomly generated coefficient vector that is updated following each iteration to improve the search region's efficacy
𝑋𝑟𝑎 = young male in the range of 𝑟𝑎
𝑀𝑝𝑟 = average number of populations ⌈ 𝑁 3 ⌉ that were arbitrarily nominated
N = the whole population of gazelles
𝑟 1 Ō 4 = arbitrary values in between 0 to 1
𝑁 1 = arbitrary number drawn from the standard distribution
𝑁 2 Ō 4 = arbitrary numbers in the normal range and the dimensions of the problem
𝑀𝑎𝑥𝑖𝑡 = the maximum number of generations
𝑖𝑡 = the maximum number of current generation
Maternity herds (MH)
Mountain gazelles are a species that rely on maternity herds to produce healthy male offspring, which is a vital aspect of their life cycle Besides aiding young males in their attempts to possess females, male gazelles may also assist with the birth of new gazelles This behavior is characterized as follows:
𝑋𝑟𝑎𝑛𝑑 = A gazelle's vector position is randomly selected from the entire population
𝐶𝑜𝑓 1, 𝑟 /2, 𝑟 = the arbitrarily chosen coefficient vectors.
Bachelor male herd (BMH)
As male gazelles mature, they tend to establish territories and assert control over female gazelles At this stage, young male gazelles begin to challenge adult males for dominance over the females, often leading to violent confrontations This behavior is mathematically expressed as follows:
Here, X(t) = the vector position of gazelle in the current iteration
𝛽 5 , 𝛽 6 = the random number chosen between 1 or 2
𝑟 6 = the random number ranges from 0 to 1.
Migration in search of food (MSF)
Mountain gazelles traverse vast distances in search of food, continuously seeking new food sources Additionally, they possess remarkable running speed and strong leaping abilities This behavior of exploring great distances for food and migration can be mathematically expressed as follows:
𝑟 7 = the arbitrary number between 0 to 1.
Opposition-based learning (OBL)
Opposite number
The candidate solution of the optimization problem represents in coordinate form: 𝑀 = {𝑀 1 , 𝑀 2 , …, 𝑀𝑛} with 𝑀𝜖𝑅𝑛 demarcated between lower and upper bounds as 𝑀𝑖𝜖 [𝐿𝑖, 𝑈𝑖], 𝑖= 1, …, 𝑛; Thereafter, the opposite candidate solution 𝑀̄ = {𝑀 1 , 𝑀 2 , …, 𝑀 𝑛 } is characterized as:
Suppose 𝑓(𝑀) the objective function employed for estimating the value of the candidate solution 𝑀, which is arbitrarily initialized As the iteration progress, the current candidate and opposite solution (𝑀 and 𝑀) are computed and then evaluated (𝑓(𝑀) and 𝑓(𝑀)) During the optimization process, the most favorable solutions are retained while the least favorable ones are discarded based on their fitness values This evaluation is performed at each iteration of the algorithm until a stopping criterion is met Consider Fig 3-2, which illustrates a one-dimensional objective function as an intuitive example of OBL Similarly, Figs 3-3 and 3-4 represent the structure of OBL in two and three dimensions, respectively
Figure 3-4 Structure of OBL in one dimension
Figure 3-5 Structure of OBL in two dimensions
Figure 3-6 Structure of OBL in three dimensions
Evolved opposition-based learning (EOBL)
Evolved-opposite number
The candidate solution of the optimization problem represents as 𝑛- dimensional space in coordinate form: 𝑀 = {𝑀 1 , 𝑀 2 , …, 𝑀𝑛} with 𝑀𝜖𝑅𝑛 enumerated between lower and upper bounds as 𝑀𝑖𝜖 [𝐿𝑖, 𝑈𝑖], 𝑖 = 1, …, 𝑛; Afterwards, the evolved-opposite candidate solution 𝑀̄ = {𝑀1, 𝑀2, …, 𝑀 𝑛 } is expressed as:
2 and 𝑟𝑎𝑛𝑑 represents a range of random values between 0 and 1 The algorithm leverages the cosine function's continuous wave nature to reposition candidate solutions around each other The Euclidean distance (denoted by 𝑛𝑜𝑟𝑚) between a particle's location and the starting point is considered Equation (3.11) refines the update criteria compared to Equation (3.10) This aims to prevent getting stuck in local optima (suboptimal solutions) while accelerating convergence (finding the optimal solution faster) and maintaining good diversity (exploring a wide range of possibilities) The figures (Fig 3-7, Fig 3-8, Fig 3-9) illustrate the
STUDENT: PHẠM MINH HUY 28 concept in one, two, and three dimensions, respectively Essentially, the algorithm focuses on a specific area between two solutions, increasing the chance of finding promising regions in the search space However, it also allows solutions to explore beyond this area to ensure a comprehensive search
Figure 3-7 Structure of EOBL in one dimension
Figure 3-8 Structure of EOBL in two dimensions
Figure 3-9 Structure of EOBL in three dimensions
Tournament selection (TS)
Evolutionary algorithms, such as genetic algorithms, often face a trade- off between exploration and exploitation This trade-off refers to the balance between exploring new areas of the search space to find potentially better solutions (exploration) and exploiting known good solutions and improve them (exploitation) Tournament selection is a commonly used method in optimization algorithms to balance exploration and exploitation, and also because of its simplicity and effectiveness in maintaining genetic diversity, which is crucial for avoiding premature convergence on suboptimal solutions
Choose a number 𝑘, which represents how many individuals are randomly selected from the population for each tournament Randomly pick
𝑘 individuals from the population Assess each selected individual based on their fitness score The individual with the highest fitness among the 𝑘 participants wins the tournament and is selected for the next generation Continue this process until you've selected the desired number of individuals for the next generation
HYBRID MODEL OF MOUNTAIN GAZELLE OPTIMIZER (HMGO)
This section introduces the HMGO algorithm, which combines the strengths of three existing algorithms (EOBL, TS, and MGO) to achieve a more comprehensive exploration of the search space One of the key advantages of HMGO is that it requires fewer adjustments compared to similar algorithms Additionally, incorporating EOBL and TS doesn't necessitate changes to the MGO configuration However, it significantly improves the accuracy of the final solution HMGO's thorough exploration capabilities also allow for reducing the initial search agent pool size, leading to faster convergence towards the optimal solution This translates to a potential 50% improvement in finding optimal solutions within a shorter timeframe.
Initialize population by EOBL
The first step in HMGO involves setting up the initial parameters for the MGO algorithm Following this, MGO generates a random set of candidate solutions (𝑁 solutions, each with 𝐷𝑖𝑚 dimensions) The HMGO algorithm utilizes the EOBL technique to create an "opposite solution" for each candidate solution within the initial population Then, both the original solutions and their opposites are evaluated using a fitness function within the MGO framework (denoted by 𝑀 and its opposite symbol) Finally, to select the best starting population, HMGO combines both sets of solutions (originals and opposites) and picks the top 𝑁 solutions based on their fitness scores This ensures a strong starting point for the optimization process.
Update new generation of gazelles
Tournament selection is added to this step to eliminate poor candidates thereby increasing the chance of finding better candidates after each iteration
The TS will generate a random number r and compare it with tour_rate, thereby deciding whether the TS will be executed or not Each solution is updated in accordance with Equations (3.1), (3.6), (3.7), and (3.9) in this phase, and each is then assessed via the fitness function Thereafter, the fitness value and best possible solution are preserved The EOBL approach receives the updated solutions from the MGO at the same time and chooses some of them (50%) by determining the opposite population for this section According to the fitness functions employed in this study, the solutions in this section correspond to the best 50% of all possible solutions The fitness function re-evaluates the outcomes where the initial half of the gazelles are preserved for the next generation after ranking them from best to worst The HMGO updates the population in the next subsequent iteration In fact, the EOBL can be considered as the alteration operator, which can allow the algorithm to evade from the local optimum and upsurge the exploration ability with a probability of 𝐽𝑟=0.05 (EOBL_rate).
HMGO algorithm model
Problem Definition
Soaring land costs in major cities make high-rise buildings a necessity However, limited space on construction sites creates a hurdle for efficient material storage Traditionally, lower floors of a building under construction are used for material storage once they reach sufficient structural strength This approach aims to minimize material transportation times and enhance overall construction efficiency
The objective of this research is to design an optimal storage layout plan for completed floors in multi-story buildings This plan considers factors like horizontal movement between storage locations within a floor, the hoisting system used to transport materials between floors, and the vertical transportation of materials from one floor to another
The first case study focuses on optimizing material hoisting operations and storage locations in multi-story buildings It aims to design a storage layout plan for completed floors that minimizes both horizontal and vertical material movement
The building has 30 story floors, which is on each floor has 5 space storage cells for material storages, as can be seen in Figures 5-1 and 5-2 Only floor 1 until 8 that can be used for materials storage In this case study, there are some model assumptions:
The model assumes pre-determined and fixed quantities of materials, along with their designated storage locations
Material hoisting is simulated using a single lift within the model
Each storage cell is assumed to have ample space to accommodate all required materials
Lower floors of the building become available for material storage once construction progresses and they reach sufficient structural strength
The model does not factor in any costs associated with loading or unloading materials from the hoist system
Table 5-1 CS1: Demand quantity of materials in each building floor
Material type, j Material Name Demand of material type, Q j,m (in kg)
Figure 5-1 CS1: Side view of material hoist in high-rise building construction
Figure 5-2 CS1: Typical floor plan at 1 st until 8 th floor for installing material storage cells.
Fitness Function
Transportation cost divide into 3 type, horizontal movement cost, vertical movement from ground floor to storage floor cost, and vertical movement from storage floor to demanding floor cost For this case study, the multi-floor layout optimization problem can be formulated as the objective function in Eq (5.1)
- J is the total number of material types
- L is total number of storage floors
- K is total number of cells in a level
- M is total number of levels
- Q j,m is demand of material type j on floor m
- C V j l , is vertical unit transportation cost of material type j to the floor l from ground
- D l,k is distance from cell k to the material hoist on level l
- C H j is horizontal unit transportation cost of material type j
- 𝑥 j,l,k is binary decision variable of storing material j inside cell k on level l
- 𝐶 𝑗,𝑚 𝑉 is vertical unit transportation cost of material j to the floor m from ground
- j l k m , , , is auxiliary binary-type variable, where '1' means material j is transferred from floor l cell k to floor m, but '0' is otherwise
The horizontal distances from cell k on level l to the material hoist, can be seen in Table 5-2
Each type of material has different unit horizontal transportation cost and vertical transportation cost, as can be seen in Table 5-3 and Table 5-4
Table 5-2 CS1: Horizontal distances from cell k on floor l to material hoist
Table 5-3 CS1: Horizontal transportation cost, 𝐶 𝑗 𝐻
Table 5-4 CS1: Vertical transportation cost (in $/kg) from ground to a floor m or l, C V j,m
Model Application
Permutation-based representation is adopted to encode the candidate solutions Each solution can be presented by a m x n permutation matrix which in each rows and columns are labeled by materials and storage locations, respectively Because there is only one material in one storage cell, so there is only one "1" in each row and column, the rest are "0" The corresponding row and column number with "1" indicates the location where the materials are stored Because the building has 8 floor that can be used as storage, and each floor has 5 storage cells, so there are 40 storage cells available for only
10 types of materials, so the position matrix for this problem will be (40X10)
For the Meta-heuristic HMGO algorithm we only have 2 input parameters:
Experiment Results
The experiment is run for 10 times to evaluate the performance of the proposed algorithm
Table 5-5 CS1: Result of Material hoisting operations and storage location in multi-story building
No Solution (Position) Times (s) Cost (USD)
Figure 5-3 CS1: Chart of Material hoisting operations and storage location in multi-story building cost
Cost value average is 4,293,258 USD
The value ranges from 4,293,020 USD to 4,293,548 USD
The graph has a median value of 4,293,268 USD, very close to the average value
The standard deviation is 213.86 USD, which extremely small value compared to the average value (0.005%)
From this problem, it can be seen that HMGO gives good and consistent results
To show that HMGO gives contribution and improvement, this study also compares HMGO with the previous research results The first research employed GA to solve the case study, it was applied by Fung et al in 2008 Then, Huang et al in 2010 adopted mix integer programming (MIP) to solve the problem The comparison results are presented in Table 5-7
Table 5-7 CS1: Result comparison with previous research, GA and MIP
Optimized storage location (floor, cell)
The results show that in terms of optimal results, the HMGO algorithm outperforms the GA algorithm, 4,293,020 compared to 4,562,620, a decrease of 5.9%, and has the same value as the MIP algorithm However, when considering the optimal execution time, the proposed algorithm HMGO produces better results than the two algorithms mentioned above, taking only 1.49s compared to 246s for GA and 8s for MIP respectively
If use mathematical formulation, the possibility for the search space can be calculated by:
P k,n : number of permutations for k materials to be located in n locations From the case study, there are 10 materials to be stored, hence the possible layout arrangement is given: 𝑃10,40 = (40−10)! 40! = 40! 30! = 3.075 × 10 15 The number of these options is too large to perform calculations in the usual way The HMGO algorithm only takes about 1.594 seconds to find the optimal solution Therefore, the HMGO algorithm proposed in this case study can be effectively and efficiently employed to solve practical high dimension construction engineering problems for materials storage layout.
Case study 2: Construction site layout planning problem based on closeness
Problem Definition
An optimal CSL planning is vital for project management It can reduce the transportation flows and thus the costs of a project In real construction operations, experienced site managers will consider the construction method, work flows, and costs caused by transportation of materials and equipment based on their own experiences It is necessary to
STUDENT: PHẠM MINH HUY 44 properly design the layout which can affect the resource flows of construction site
Second case study is arranging the construction site layout problem based on closeness index This case study was adopted by Lam et al in 2009 They attempt to conjoin MMAS (Max-min ant system) to GA to solve the problem [26] The objective of designing the construction facilities site layout is to minimize the transportation of work flow among facilities The work flows depend on closeness index between the site facilities and the distance between the site locations
In this problem, there are some assumptions as follows:
The geometric layout of available locations is predetermined and fixed
Each predetermined location has a guaranteed size for even the largest facilities
The site layout has 9 facilities and 27 available locations Site office, main gate and material hoist are fixed
Figure 5-4 CS2: Construction site layout
Fitness Function
To minimize the movement of materials, equipment, and other resources between facilities on a construction site, this research employs a
"closeness index." This index reflects the frequency of transportation workflows between facilities Facilities with a higher frequency of interaction are considered "closer" in this context, and should ideally be situated near each other Conversely, facilities with a lower interaction frequency should be placed farther apart
The objective of this case study is to minimize the overall transportation of workflows between facilities on the site This objective depends primarily on two factors:
Closeness Index of Workflow (C ij ): This index, presented in Table 5-8, reflects the frequency of interaction between each pair of facilities
Distance (d kl ): The physical distance between each pair of locations on the site, as shown in Table 5-9
The specific mathematical formula for the objective function used in this case study (CSLP) will be presented in the following section
(5.2) subject to the following constraints
The location of each facility is then assigned and located in accordance with these constraints:
- C ij is the closeness index of work flow between facilities i and j
- d kl is the distance between facilities k and l
- x ik means when facility i is assigned to location k
- x jl means when facility j is assigned to location l
- The constraint of x ij will be a binary variable which takes value 1 if facility i is assigned to location j and 0 otherwise
Table 5-8 CS2: Work flows between the site facilities
Closeness index of work flow between facilities
Table 5-9 CS2: Distance between location in the site layout
Model Application
The model application is the same with the previous case studies, which use permutation-based representation In this case, there are some constraints, such as fixed facilities According these issues, there are some adjustments for the permutation matrix
Each solution of the problem is determined by a permutation matrix (m x n), m rows will correspond to the total number of positions that can be used for layout and n columns correspond to temporary bases
The problem has 27 locations that can be used to arrange temporary facilities However, there are 3 permanent locations of facilities 7, 8, and 9 in cells 26, 27, 25 respectively Therefore, the problem is to allocate the remaining 6 temporary facilities to 24 locations remaining The position matrix for this problem will be (27X9)
We also have 2 input parameters:
Experiment Results
The experiment is run for 10 times to evaluate the performance of the proposed algorithm
Table 5-10 CS2: Results of Construction site layout planning problem based on closeness index
No Solutions Times (s) Optimal work flow
Figure 5-5 CS2: Chart of Optimal Workflow in Construction site layout planning problem based on closeness index
Optimal workflow value average is 690.033 USD
The value ranges from 688.400 to 691.230
The graph has a median value of 689.972 USD, very close to the average value
The standard deviation is 1.109, which extremely small value compared to the average value (0.161%)
From this problem, it can be seen that HMGO gives good and consistent results
To show that HMGO gives contribution and improvement, this study also compares HMGO with the previous research results Previous search compared original GA and MMAS-GA performance in this case study It was researched by Lam et al in 2009 Site layout comparison can be seen in Figures 5-7, 5-8, 5-9 The comparison results are presented in Table 5-12
Figure 5-6 CS2: Optimal construction site layout by HMGO
Figure 5-7 CS2: Optimal construction site layout by GA
Figure 5-8 CS2: Optimal construction site layout by Max-min Ant System GA
Table 5-12 CS2: Result comparison with previous research
The results show that HMGO can outperform others algorithm (GA and MMAS-GA) HMGO can get the most minimum work flow, HMGO generates 688.4 better than GA (857.99) and MMAS-GA (698.3) result
In mathematical formula, the search space can be calculated by
Since the problem has 3 fixed bases, the number of possible arrangements is 96,909,120 possibilities The number of these options is too large to perform calculations in the usual way The HMGO algorithm only takes about 0.734 seconds to find the optimal solution Therefore, the HMGO proposed in this case study can be used very effectively to solve technical problems in real-world construction for CSL
Case study 3: Utilize algorithms in practical projects
Project information
Project name: Charm Long Hải Resort & Spa
Location: Long Hai town, Long Dien district, Ba Ria - Vung Tau
Type of construction: Resort complex
Figure 5-9 CS3: Perspective drawing of the project
Table 5-13 CS 3: Distance between location in the site layout
Model Application
There are 33 places in the problem where temporary facilities can be set up Similar to case study 2, facilities 7, 8, and 9 have three permanent placements, which are, respectively, in cells 31, 32, and 33 As a result, the issue is how to divide up the 30 remaining sites among the 6 temporary facilities For this task, the position matrix will be (33X9)
2 input parameters remain the same:
A digital aerial photograph of the construction then redrawn by the researcher in BIM to evaluate the effectiveness of the created tool on active construction sites (Figure 5-11 Ō 5-12) In Figure 5-12, the orange grid line is the boundaries of construction works, red boxes are the simplified obstacles, which are existed construction areas, green squares measuring 15x15m are created by the researcher as empty locations into which facilities can be placed and are numbered from 1-33
Note that in the framework of this research, the process of converting construction site images to technical drawings to apply the algorithm is performed manually by the researcher However, as suggested in section 3-2, a software add-in from Revit can be written to automate this process
Figure 5-10 CS3: The construction site layout was taken by drone
Figure 5-11 CS3: Create the Simplified Construction Site in Revit
Experiment Results
Table 5-14 CS3: Result of Applying construction site layout planning problem based on closeness index into actual construction project
No Solutions Times (s) Optimal work flow
Figure 5-12 CS3: Optimal construction site layout project by HMGO
Given the fitness functions and assumptions of the problem, the distance between locations is a crucial factor that influences the workflow and the overall output However, we notice that two points closer to the fixed points, specifically position 23 and position 29, are not among the optimal choices This is because the problem must also consider the workflow between the facilities as outlined in the problem statement Additionally, the results were obtained in just 0.955 seconds Therefore, without the assistance of algorithms, solving the layout problem at the construction site manually would be extremely challenging and time-consuming
The reason for combining the TS and EOBL algorithms with the MGO algorithm (MGO-TS-EOBL) to achieve better results is due to leveraging the strengths of these different algorithms to both improve the weaknesses and enhance the inherent strengths of MGO The TS algorithm helps eliminate poor individuals through a comparison and selection step within a randomly selected group of individuals, thereby increasing the chances of finding a better candidate after each iteration Compared to using the roulette wheel algorithm, TS speeds up convergence By considering the opposite positions in the search space, EOBL broadens the search area, reduces the risk of local optima, enhances global exploration capabilities, and promotes exploitation through the convergence acceleration parameter
Conclusions
In this study, a new hybrid algorithm called HMGO - Hybrid Model of Mountain Gazelle Optimizer was introduced as a novel search and optimization tool for solving construction site layout problems HMGO is a hybrid algorithm that integrates the original MGO algorithm with auxiliary algorithms like Evolved Opposition-based Learning (EOBL) and Tournament Selection (TS) MGO excels in both local and global search TS enhances the algorithm by eliminating poor individuals through a comparison and selection process within a randomly chosen group, thereby increasing the likelihood of finding better candidates with each iteration This method accelerates convergence compared to the roulette wheel algorithm EOBL improves the search by considering opposing locations in the search space, expanding the search area, reducing the risk of local optima, and enhancing global exploration and exploitation through its convergence acceleration parameter This hybrid approach combines the strengths and mitigates the weaknesses of each algorithm, effectively solving discrete problems in the quadratic assignment problem (QAP) optimally [56-59]
HMGO is evaluated through two model problems and one real-world project problem in chapter 5 to showcase its effectiveness In terms of optimal time, HMGO outperforms most current algorithms Additionally, HMGO produces superior results for the objective function of each problem The experimental findings demonstrate HMGO's robustness, reliability, and consistency in finding optimal solutions for construction site layout problems
This research offers a comprehensive approach to solving the optimization problem, enhancing global convergence and achieving higher optimal results compared to other algorithms It provides construction managers with a fresh perspective on site layout, integrating their practical experience with the powerful capabilities of the HMGO algorithm This
STUDENT: PHẠM MINH HUY 60 combined approach aids in addressing real-world situations, devising strategic measures to improve work efficiency, accelerating project progress, and reducing costs Ultimately, this leads to the overarching goal of project success By leveraging HMGO, construction managers can enhance decision- making processes, optimize resource allocation, and achieve better outcomes, contributing to the successful execution and completion of construction projects.
Recommendations
In this study, the HMGO algorithm is utilized to solve discrete combinatorial optimization problems, such as Construction Site Layout Problems (CSLPs) Future research could be conducted to demonstrate the effectiveness of the HMGO algorithm in continuous optimization problems The HMGO algorithm can be applied to other case studies, such as optimization in structural design, optimizing the arrangement of facilities on the current layout of ready-mix concrete plants, and multi-objective optimization problems involving trade-offs between schedule, cost, quality, and safety
HMGO is more suitable for problems in continuous domains, and future research for discrete problems could focus on the number of iterations and evaluation of the objective function The convergence capability of the HMGO algorithm can be improved
As proposed in section 3-2, an add-in from Revit could be developed to optimize the process of converting satellite images into creating a Simplified Construction Site to apply the algorithm The Revit API can be leveraged to create custom tools for users By using the Autodesk Revit API, the capabilities of the existing application can be extended by writing programs or scripts that add new functionalities to the software Integrating the software with the proposed algorithm will address more general cases and incorporate some risk constraints of dynamic problems, as well as
STUDENT: PHẠM MINH HUY 61 emergencies that may arise during construction, making the problem closer to reality To achieve this, research needs to survey transportation costs for different types of materials, density indices between facilities, etc., at construction sites in Vietnam This tool is intended to be used in the planning stages to help sequence work and allocate positions on the construction site throughout the project development process
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