Muhammad Salman Khan
Current Organizations / Institutes
The organizations/institutes from the scholar's latest article
Muhammad Salman Khan has a total of 28 co-authors. Here are the top co-authors by number of shared publications:
Mohanad Muayad Sabri Sabri
Peter the Great St. Petersburg Polytechnic University, St. Petersburg, Russia
5 shared publicationsAsad Khan
Department of Bridge Engineering, College of Civil Engineering, Tongji University, Shanghai, China
3 shared publicationsMahmood Ahmad
Institute of Energy Infrastructure, Universiti Tenaga Nasional, Kajang, Malaysia
3 shared publications- Mahmood Ahmad
Institute of Energy Infrastructure, Universiti Tenaga Nasional, Kajang 43000, Malaysia
3 shared publications Abdullah Alzlfawi
Department of Civil and Environmental Engineering, College of Engineering, Majmaah University, Al Majmaah, Saudi Arabia
2 shared publications- Asad Khan
College of Civil Engineering, Department of Bridge Engineering, Tongji University, Shanghai, China
2 shared publications
Latest Publications
- Open Access
- 2 March 2026
- Published by Springer Nature in Scientific Reports
- Vol. 16 (1) , 7938
An integrated physics-guided machine learning approach for predicting asphalt concrete fracture parameters
Accurate prediction of fracture energy (G f ) in asphalt mixtures is important for durable asphalt pavements designing. Traditional experimental approaches are reliable but need resources, whereas numerical simulations, such as finite element models (FEM), offer flexibility but needs accurate input parameters and calibration. Recent advances in machine learning offer rapid prediction capabilities; however, interpretability and physical relevance remain challenging in this regard. This study presents a hybrid framework that integrates experimental Single Edge Notch Beam (SENB) tests, finite element simulations, and machine learning models to predict fracture parameters for asphalt mixtures. Experimental testing quantified fracture energy, while FEM simulations replicated the fracture response numerically. Machine learning models, including Linear Regression, Gradient Boosting, and AdaBoost, were trained on mixture properties such as stability, flow, air voids, and Stiffness Modulus at 20 °C (ITSM20) to predict surrogate fracture energy. A novel, dimensionally consistent surrogate equation was proposed to link key mixture properties to fracture energy, validated against both experimental and numerical results. The surrogate model demonstrated best accuracy with a mean relative error compared to experimental data. This novel integrated approach, adopted in this study, provides a practical and physics-guided methodology for rapid and reliable prediction of fracture behavior in asphalt mixtures, bridging experimental observations, numerical simulations, and data-driven machine learning modeling, and offering insights for mixture optimization and pavement design.
- 2 March 2026
- Published by Springer Nature in Scientific Reports
- Vol. 16 (1) , 7938
Open AccessAn integrated physics-guided machine learning approach for predicting asphalt concrete fracture parameters
Accurate prediction of fracture energy (G f ) in asphalt mixtures is important for durable asphalt pavements designing. Traditional experimental approaches are reliable but need resources, whereas numerical simulations, such as finite element models (FEM), offer flexibility but needs accurate input parameters and calibration. Recent advances in machine learning offer rapid prediction capabilities; however, interpretability and physical relevance remain challenging in this regard. This study presents a hybrid framework that integrates experimental Single Edge Notch Beam (SENB) tests, finite element simulations, and machine learning models to predict fracture parameters for asphalt mixtures. Experimental testing quantified fracture energy, while FEM simulations replicated the fracture response numerically. Machine learning models, including Linear Regression, Gradient Boosting, and AdaBoost, were trained on mixture properties such as stability, flow, air voids, and Stiffness Modulus at 20 °C (ITSM20) to predict surrogate fracture energy. A novel, dimensionally consistent surrogate equation was proposed to link key mixture properties to fracture energy, validated against both experimental and numerical results. The surrogate model demonstrated best accuracy with a mean relative error compared to experimental data. This novel integrated approach, adopted in this study, provides a practical and physics-guided methodology for rapid and reliable prediction of fracture behavior in asphalt mixtures, bridging experimental observations, numerical simulations, and data-driven machine learning modeling, and offering insights for mixture optimization and pavement design.
- Open Access
- 17 June 2025
- Published by Institute of Electrical and Electronics Engineers (IEEE) in IEEE Access
- Vol. 13, 105165-105182
Machine Learning Models for Predicting Seismic Response of a Novel Two-Stage Friction Pendulum Isolated Bridge Structure
Bridges are critical infrastructure, and their vulnerability to seismic events necessitates efficient methods for predicting structural responses. Traditional methods, such as Nonlinear Time History Analysis (NLTHA), are computationally intensive, time-consuming, and require an expert analyst. Additionally, innovative structural elements like Two-Stage Friction Pendulum Bearings (TSFPBs) are not readily available in commercial software. This study proposes a Machine Learning (ML) approach as a faster and simplified alternative to NLTHA for predicting the structural response of TSFPB-isolated bridge structures. A comprehensive dataset of 500,000 data points was meticulously generated through NLTHA. Force-displacement laboratory tests under various loading and displacement conditions were conducted to validate the TSFPB nonlinear element developed in OpenSees. Utilizing this extensive dataset, seven ML models were trained and evaluated using statistical key performance indicators (KPIs). Results revealed that Extreme Gradient Boosting (XGB) achieved the highest accuracy (R2 = 0.959) on the testing dataset, while Adaptive Boosting (AB) showed the lowest accuracy (R2 = 0.761). Furthermore, a comparison of different surrogate models was conducted for global feature interpretation, while SHAP analysis was used for local interpretation to identify the influence of input parameters on individual structural responses. A graphical user interface (GUI) was developed using the best-performing model (i.e., XGB), offering engineers an accessible tool for seismic response prediction. This study demonstrates the potential of ML as an efficient alternative to NLTHA while providing valuable insights into key parameters influencing the seismic performance of TSFPB-isolated bridges, enhancing decision-making and design optimization.
- 17 June 2025
- Published by Institute of Electrical and Electronics Engineers (IEEE) in IEEE Access
- Vol. 13, 105165-105182
Open AccessMachine Learning Models for Predicting Seismic Response of a Novel Two-Stage Friction Pendulum Isolated Bridge Structure
Bridges are critical infrastructure, and their vulnerability to seismic events necessitates efficient methods for predicting structural responses. Traditional methods, such as Nonlinear Time History Analysis (NLTHA), are computationally intensive, time-consuming, and require an expert analyst. Additionally, innovative structural elements like Two-Stage Friction Pendulum Bearings (TSFPBs) are not readily available in commercial software. This study proposes a Machine Learning (ML) approach as a faster and simplified alternative to NLTHA for predicting the structural response of TSFPB-isolated bridge structures. A comprehensive dataset of 500,000 data points was meticulously generated through NLTHA. Force-displacement laboratory tests under various loading and displacement conditions were conducted to validate the TSFPB nonlinear element developed in OpenSees. Utilizing this extensive dataset, seven ML models were trained and evaluated using statistical key performance indicators (KPIs). Results revealed that Extreme Gradient Boosting (XGB) achieved the highest accuracy (R2 = 0.959) on the testing dataset, while Adaptive Boosting (AB) showed the lowest accuracy (R2 = 0.761). Furthermore, a comparison of different surrogate models was conducted for global feature interpretation, while SHAP analysis was used for local interpretation to identify the influence of input parameters on individual structural responses. A graphical user interface (GUI) was developed using the best-performing model (i.e., XGB), offering engineers an accessible tool for seismic response prediction. This study demonstrates the potential of ML as an efficient alternative to NLTHA while providing valuable insights into key parameters influencing the seismic performance of TSFPB-isolated bridges, enhancing decision-making and design optimization.
- Open Access
- 13 May 2025
- Published by Frontiers Media SA in Frontiers in Materials
- Vol. 12, 1613549
Corrigendum: Performance optimization of asphalt pavements using binder film thickness as a criterion in innovative mix design compared to Marshall and Superpave methods
Incorrect Funding In the published article, there was an error in the Funding statement. [The research is partially funded by the Ministry of Science and Higher Education of the Russian Federation as part of the World-class Research Center program: Advanced Digital Technologies (contract No. 075-15-2022-311 dated 20.04.2022)]. The correct Funding statement appears below.FUNDINGThis research was supported by a grant from the Russian Science Foundation No. 22-79-10021, https://rscf.ru/project/22-79-10021/.The authors apologize for this error and state that this does not change the scientific conclusions of the article in any way. The original article has been updated.
- 13 May 2025
- Published by Frontiers Media SA in Frontiers in Materials
- Vol. 12, 1613549
Open AccessCorrigendum: Performance optimization of asphalt pavements using binder film thickness as a criterion in innovative mix design compared to Marshall and Superpave methods
Incorrect Funding In the published article, there was an error in the Funding statement. [The research is partially funded by the Ministry of Science and Higher Education of the Russian Federation as part of the World-class Research Center program: Advanced Digital Technologies (contract No. 075-15-2022-311 dated 20.04.2022)]. The correct Funding statement appears below.FUNDINGThis research was supported by a grant from the Russian Science Foundation No. 22-79-10021, https://rscf.ru/project/22-79-10021/.The authors apologize for this error and state that this does not change the scientific conclusions of the article in any way. The original article has been updated.
- Open Access
- 6 May 2025
- Published by Frontiers Media SA in Frontiers in Earth Science
- Vol. 13, 1613561
Corrigendum: Numerical and experimental evaluation of shear strength and consolidation properties of cohesive soils in high water table areas
Incorrect Funding In the published article, there was an error in the Funding statement. [The research is partially funded by the Ministry of Science and Higher Education of the Russian Federation as part of the World-class Research Center program: Advanced Digital Technologies (contract No. 075-15-2022-311 dated 20.04.2022)]. The correct Funding statement appears below.FUNDINGThis research was supported by a grant from the Russian Science Foundation No. 22-79-10021, https://rscf.ru/project/22-79-10021/.The authors apologize for this error and state that this does not change the scientific conclusions of the article in any way. The original article has been updated.
- 6 May 2025
- Published by Frontiers Media SA in Frontiers in Earth Science
- Vol. 13, 1613561
Open AccessCorrigendum: Numerical and experimental evaluation of shear strength and consolidation properties of cohesive soils in high water table areas
Incorrect Funding In the published article, there was an error in the Funding statement. [The research is partially funded by the Ministry of Science and Higher Education of the Russian Federation as part of the World-class Research Center program: Advanced Digital Technologies (contract No. 075-15-2022-311 dated 20.04.2022)]. The correct Funding statement appears below.FUNDINGThis research was supported by a grant from the Russian Science Foundation No. 22-79-10021, https://rscf.ru/project/22-79-10021/.The authors apologize for this error and state that this does not change the scientific conclusions of the article in any way. The original article has been updated.
- Open Access
- 10 March 2025
- Published by Frontiers Media SA in Frontiers in Earth Science
- Vol. 13, 1522488
Numerical and experimental evaluation of shear strength and consolidation properties of cohesive soils in high water table areas
The geotechnical properties of soil are crucial in determining the stability of foundations and construction safety in regions with high groundwater levels, such as Warsak Road in Peshawar, Pakistan. Due to its proximity to the Warsak Dam and intersecting irrigation canals, the area experiences a consistently high water table, which significantly impacts soil stability, leading to potential issues such as excessive settlement, reduced shear strength, and increased structural instability. These groundwater conditions pose unique challenges for foundation stability, making it essential to develop a comprehensive understanding of the soil’s consolidation behavior and shear strength properties. To address these concerns, this study employs a combined experimental and numerical approach, aiming to evaluate these critical soil properties in detail. The experimental phase involved collecting three undisturbed soil samples from each of the five distinct sites along Warsak Road, spaced approximately 5 km apart. These samples were subjected to standardized laboratory tests, including grain size distribution, specific gravity, Atterberg Limits, direct shear, unconfined compression, and oedometer tests, per ASTM standards. To further validate the laboratory findings, numerical analysis using PLAXIS software was conducted, along with analytical evaluations using the Meyerhof and Vesic bearing capacity equations. This integrated methodology provided a comprehensive understanding of the soil’s behavior under varying conditions, revealing distinct variations in the average values of the three samples from each site. Specifically, Site 1 exhibited an average cohesion of 18.22 kN/m2, making it suitable for low-rise structures, whereas Site 2, with an average cohesion of 15.23 kN/m2, indicated the need for stabilization due to its high consolidation potential. Site 3, averaging 13.3 kN/m2, showed higher settlement risk, necessitating deep foundations, while Site 4, with the lowest average cohesion of 9.94 kN/m2, was deemed unsuitable for heavy loads without reinforcement. In contrast, Site 5, having the highest average cohesion of 20.2 kN/m2, demonstrated excellent stability, ideal for multi-story buildings and other heavy structures. The numerical results from PLAXIS offered a more accurate understanding of soil behavior compared to the traditional Meyerhof and Vesic methods, highlighting the necessity of integrating advanced numerical techniques with conventional approaches. Accordingly, targeted soil improvement measures are recommended for weak and highly compressible soils to ensure the long-term stability and safety of structures in the region.
- 10 March 2025
- Published by Frontiers Media SA in Frontiers in Earth Science
- Vol. 13, 1522488
Open AccessNumerical and experimental evaluation of shear strength and consolidation properties of cohesive soils in high water table areas
The geotechnical properties of soil are crucial in determining the stability of foundations and construction safety in regions with high groundwater levels, such as Warsak Road in Peshawar, Pakistan. Due to its proximity to the Warsak Dam and intersecting irrigation canals, the area experiences a consistently high water table, which significantly impacts soil stability, leading to potential issues such as excessive settlement, reduced shear strength, and increased structural instability. These groundwater conditions pose unique challenges for foundation stability, making it essential to develop a comprehensive understanding of the soil’s consolidation behavior and shear strength properties. To address these concerns, this study employs a combined experimental and numerical approach, aiming to evaluate these critical soil properties in detail. The experimental phase involved collecting three undisturbed soil samples from each of the five distinct sites along Warsak Road, spaced approximately 5 km apart. These samples were subjected to standardized laboratory tests, including grain size distribution, specific gravity, Atterberg Limits, direct shear, unconfined compression, and oedometer tests, per ASTM standards. To further validate the laboratory findings, numerical analysis using PLAXIS software was conducted, along with analytical evaluations using the Meyerhof and Vesic bearing capacity equations. This integrated methodology provided a comprehensive understanding of the soil’s behavior under varying conditions, revealing distinct variations in the average values of the three samples from each site. Specifically, Site 1 exhibited an average cohesion of 18.22 kN/m2, making it suitable for low-rise structures, whereas Site 2, with an average cohesion of 15.23 kN/m2, indicated the need for stabilization due to its high consolidation potential. Site 3, averaging 13.3 kN/m2, showed higher settlement risk, necessitating deep foundations, while Site 4, with the lowest average cohesion of 9.94 kN/m2, was deemed unsuitable for heavy loads without reinforcement. In contrast, Site 5, having the highest average cohesion of 20.2 kN/m2, demonstrated excellent stability, ideal for multi-story buildings and other heavy structures. The numerical results from PLAXIS offered a more accurate understanding of soil behavior compared to the traditional Meyerhof and Vesic methods, highlighting the necessity of integrating advanced numerical techniques with conventional approaches. Accordingly, targeted soil improvement measures are recommended for weak and highly compressible soils to ensure the long-term stability and safety of structures in the region.
- Open Access
- 7 January 2025
- Published by Frontiers Media SA in Frontiers in Materials
- Vol. 11, 1488310
Performance optimization of asphalt pavements using binder film thickness as a criterion in innovative mix design compared to Marshall and Superpave methods
The performance of asphalt pavements is significantly influenced by the mix design and the binder film thickness (BFT) around aggregates. Adjusting the proportions of binders and aggregates modifies the properties of asphalt mixtures, with different mix designs substantially impacting these properties. This study evaluates the influence of two traditional mix designs (i.e., Marshall and Superpave Gyratory Compacted) and one innovative mix design (the one using BFT as a criterion) on asphalt pavement performance Two methods, which are modifications of the Hveem Surface Area Factor method, were used to calculate the optimum BFT. The mix with 3.5% asphalt content (AC) was selected for the innovative mix design as it showed the optimal BFT. For the Marshall and Superpave mix designs, the optimum binder content was determined using the respective Marshall and Superpave Gyratory Compacted methods, yielding values of 4.3% and 4.4%, respectively. Samples were prepared from each type of mix design and then tested using a Universal Testing Machine (UTM) and a Double Wheel Tracker (DWT). Performance tests showed that the innovative mix design samples had superior rutting resistance under DWT, the Marshall samples had the highest Resilient Modulus (Mr) and moisture resistance, and the Superpave samples exhibited the best fatigue resistance, enduring the most cycles until failure in the Indirect Tensile Fatigue Test (ITFT). These findings underscore the importance of considering BFT as a critical mix design criterion, demonstrating its significant potential to enhance the overall performance and durability of asphalt pavements.
- 7 January 2025
- Published by Frontiers Media SA in Frontiers in Materials
- Vol. 11, 1488310
Open AccessPerformance optimization of asphalt pavements using binder film thickness as a criterion in innovative mix design compared to Marshall and Superpave methods
The performance of asphalt pavements is significantly influenced by the mix design and the binder film thickness (BFT) around aggregates. Adjusting the proportions of binders and aggregates modifies the properties of asphalt mixtures, with different mix designs substantially impacting these properties. This study evaluates the influence of two traditional mix designs (i.e., Marshall and Superpave Gyratory Compacted) and one innovative mix design (the one using BFT as a criterion) on asphalt pavement performance Two methods, which are modifications of the Hveem Surface Area Factor method, were used to calculate the optimum BFT. The mix with 3.5% asphalt content (AC) was selected for the innovative mix design as it showed the optimal BFT. For the Marshall and Superpave mix designs, the optimum binder content was determined using the respective Marshall and Superpave Gyratory Compacted methods, yielding values of 4.3% and 4.4%, respectively. Samples were prepared from each type of mix design and then tested using a Universal Testing Machine (UTM) and a Double Wheel Tracker (DWT). Performance tests showed that the innovative mix design samples had superior rutting resistance under DWT, the Marshall samples had the highest Resilient Modulus (Mr) and moisture resistance, and the Superpave samples exhibited the best fatigue resistance, enduring the most cycles until failure in the Indirect Tensile Fatigue Test (ITFT). These findings underscore the importance of considering BFT as a critical mix design criterion, demonstrating its significant potential to enhance the overall performance and durability of asphalt pavements.
- 3 December 2024
- Published by Springer Nature
- p. 1-13
Enhancing Seismic Performance of Bridges with a Novel Friction Tension Only Brace (FTOB)
- 3 December 2024
- Published by Springer Nature
- p. 1-13
Enhancing Seismic Performance of Bridges with a Novel Friction Tension Only Brace (FTOB)
- Open Access
- 1 November 2024
- Published by Frontiers Media SA in Frontiers in Materials
- Vol. 11, 1495750
Assessment of mechanical performance of sustainable structural mud insulated panels
Composite construction materials are extensively employed and have proven to be more effective than their individual components, such as steel and concrete. This is because composites combine the strengths of different materials, resulting in enhanced properties such as increased strength-to-weight ratios, better durability, and improved thermal efficiency. However, despite the strong structural properties and energy-saving benefits of reinforced concrete sandwich panels, their use is restricted in many rural regions of developing nations like Pakistan, largely because of the economic limitations faced by the communities. Therefore, this study introduces cost-effective structural mud insulated panels (SMIPs) that utilize mud wythes and evaluates their mechanical performance. These panels consist of a lightweight Expanded Polystyrene (EPS) foam core, sandwiched between two galvanized steel-reinforced mud layers. The study includes flexural, compression, diagonal tension, and water absorption tests. Flexural tests revealed that the panels have substantial load-bearing capacity under bending forces. Whereas, Compression tests showed that the panels possess adequate strength and stiffness to support moderate structural loads. Additionally, Diagonal tension tests confirmed the panels’ ability to resist significant in-plane loads. Water absorption tests also indicated that the panels demonstrated adequate moisture resistance, staying within the acceptable limit of 15%. These findings highlight the mechanical and hydric properties of SMIPs, underscoring their potential in sustainable construction, especially in economically constrained regions.
- 1 November 2024
- Published by Frontiers Media SA in Frontiers in Materials
- Vol. 11, 1495750
Open AccessAssessment of mechanical performance of sustainable structural mud insulated panels
Composite construction materials are extensively employed and have proven to be more effective than their individual components, such as steel and concrete. This is because composites combine the strengths of different materials, resulting in enhanced properties such as increased strength-to-weight ratios, better durability, and improved thermal efficiency. However, despite the strong structural properties and energy-saving benefits of reinforced concrete sandwich panels, their use is restricted in many rural regions of developing nations like Pakistan, largely because of the economic limitations faced by the communities. Therefore, this study introduces cost-effective structural mud insulated panels (SMIPs) that utilize mud wythes and evaluates their mechanical performance. These panels consist of a lightweight Expanded Polystyrene (EPS) foam core, sandwiched between two galvanized steel-reinforced mud layers. The study includes flexural, compression, diagonal tension, and water absorption tests. Flexural tests revealed that the panels have substantial load-bearing capacity under bending forces. Whereas, Compression tests showed that the panels possess adequate strength and stiffness to support moderate structural loads. Additionally, Diagonal tension tests confirmed the panels’ ability to resist significant in-plane loads. Water absorption tests also indicated that the panels demonstrated adequate moisture resistance, staying within the acceptable limit of 15%. These findings highlight the mechanical and hydric properties of SMIPs, underscoring their potential in sustainable construction, especially in economically constrained regions.
- Open Access
- 24 July 2023
- Published by MDPI AG in Sustainability
- Vol. 15 (14) , 11457
Cost Optimization of Prestressed U-Shaped Simply Supported Girder Using Box Complex Method
The use of U-shaped girders has become increasingly popular in advanced projects such as metro rail systems due to their ability to provide greater vertical clearance beneath bridges. These girders, characterized by two webs and a bottom flange, contribute essential longitudinal stiffness and strength to the overall structure while effectively countering torsional forces in curved bridges. However, the design and construction of U-shaped girders present challenges, including their relatively higher self-weight compared to other girder types. Consequently, cost optimization has become a crucial focus in structural design studies. This research aims to develop an optimization model for prestressed U-shaped girders using the AASHTO LRFD bridge design specifications. The model is based on the Box complex method, with necessary modifications and improvements to achieve an optimal design. The objective is to minimize the total cost of materials, including concrete, steel reinforcement, and prestressing strands, while satisfying explicit and implicit design constraints. To facilitate the analysis, design, and optimization processes, a program is developed using Visual Studio 2010 and implemented in Visual Basic (VB.NET). The program incorporates separate subroutines for analysis, design, and optimization of the prestressed U-shaped girder, which are integrated to produce the desired results. When running the program, the optimization process required 229 iterations to converge to the optimal cost function value. The results demonstrate that the developed algorithm efficiently explores economically and structurally effective solutions, resulting in cost savings compared to the initial design. The convergence rate of the moment capacity constraint is identified as a key factor in achieving the optimal design. This research makes a significant contribution to the field of civil engineering by applying the classical Box complex method to the optimization of girders, an area where its utilization has been limited. Furthermore, this study specifically addresses the optimization of prestressed U-shaped girders in metro rail projects, where they serve as both the deck and support structure for train loading. By employing the Box complex method, this research aims to fill the research gap and provide valuable insights into the optimization of U-shaped girders. This approach offers a fresh perspective on designing these girders, considering their unique role in supporting metro rail loads. By leveraging the benefits of the Box complex method, researchers can explore new possibilities and uncover optimal design solutions for U-shaped girders in metro rail applications.
- 24 July 2023
- Published by MDPI AG in Sustainability
- Vol. 15 (14) , 11457
Open AccessCost Optimization of Prestressed U-Shaped Simply Supported Girder Using Box Complex Method
The use of U-shaped girders has become increasingly popular in advanced projects such as metro rail systems due to their ability to provide greater vertical clearance beneath bridges. These girders, characterized by two webs and a bottom flange, contribute essential longitudinal stiffness and strength to the overall structure while effectively countering torsional forces in curved bridges. However, the design and construction of U-shaped girders present challenges, including their relatively higher self-weight compared to other girder types. Consequently, cost optimization has become a crucial focus in structural design studies. This research aims to develop an optimization model for prestressed U-shaped girders using the AASHTO LRFD bridge design specifications. The model is based on the Box complex method, with necessary modifications and improvements to achieve an optimal design. The objective is to minimize the total cost of materials, including concrete, steel reinforcement, and prestressing strands, while satisfying explicit and implicit design constraints. To facilitate the analysis, design, and optimization processes, a program is developed using Visual Studio 2010 and implemented in Visual Basic (VB.NET). The program incorporates separate subroutines for analysis, design, and optimization of the prestressed U-shaped girder, which are integrated to produce the desired results. When running the program, the optimization process required 229 iterations to converge to the optimal cost function value. The results demonstrate that the developed algorithm efficiently explores economically and structurally effective solutions, resulting in cost savings compared to the initial design. The convergence rate of the moment capacity constraint is identified as a key factor in achieving the optimal design. This research makes a significant contribution to the field of civil engineering by applying the classical Box complex method to the optimization of girders, an area where its utilization has been limited. Furthermore, this study specifically addresses the optimization of prestressed U-shaped girders in metro rail projects, where they serve as both the deck and support structure for train loading. By employing the Box complex method, this research aims to fill the research gap and provide valuable insights into the optimization of U-shaped girders. This approach offers a fresh perspective on designing these girders, considering their unique role in supporting metro rail loads. By leveraging the benefits of the Box complex method, researchers can explore new possibilities and uncover optimal design solutions for U-shaped girders in metro rail applications.