Showing 36 results for Metaheuristic Algorithm
A. Kaveh, A. Zaerreza,
Volume 13, Issue 3 (7-2023)
Abstract
In this paper, three recently improved metaheuristic algorithms are utilized for the optimum design of the frame structures using the force method. These algorithms include enhanced colliding bodies optimization (ECBO), improved shuffled Jaya algorithm (IS-Jaya), and Vibrating particles system - statistical regeneration mechanism algorithm (VPS-SRM). The structures considered in this study have a lower degree of statical indeterminacy (DSI) than their degree of kinematical indeterminacy (DKI). Therefore, the force method is the most suitable analysis method for these structures. The robustness and performance of these methods are evaluated by the three design examples named 1-bay 10-story steel frame, 3-bay 15-story steel frame, and 3-bay 24-story steel frame.
S. Gholizadeh, C. Gheyratmand , N. Razavi,
Volume 13, Issue 3 (7-2023)
Abstract
The main objective of this study is to optimize reinforced concrete (RC) frames in the framework of performance-based design using metaheuristics. Three improved and efficient metaheuristics are employed in this work, namely, improved multi-verse (IMV), improved black hole (IBH) and modified newton metaheuristic algorithm (MNMA). These metaheuristic algorithms are applied for performance-based design optimization of 6- and 12-story planar RC frames. The seismic response of the structures is evaluated using pushover analysis during the optimization process. The obtained results show that the IBH outperforms the other algorithms.
A. Kaveh, A. Zaerreza,
Volume 13, Issue 4 (10-2023)
Abstract
This paper presents the chaotic variants of the particle swarm optimization-statistical regeneration mechanism (PSO-SRM). The nine chaotic maps named Chebyshev, Circle, Iterative, Logistic, Piecewise, Sine, Singer, Sinusoidal, and Tent are used to increase the performance of the PSO-SRM. These maps are utilized instead of the random number, which defines the solution generation method. The robustness and performance of these methods are tested in the three steel frame design problems, including the 1-bay 10-story steel frame, 3-bay 15-story steel frame, and 3-bay 24-story steel frame. The optimization results reveal that the applied chaotic maps improve the performance of the PSO-SRM.
H. Tamjidi Saraskanroud, M. Babaei,
Volume 13, Issue 4 (10-2023)
Abstract
Structural topology optimization provides an insight into efficient designing as it seeks optimal distribution of material to minimize the total cost and weight of the structures. This paper presents an optimum design of steel moment frames and connections of structures subjected to serviceability and strength constraints in accordance with AISC-Load and Resistance Factor Design (LRFD). In connection topology optimizations, different beam and column sections and connections and also to optimize two steel moment frames a genetic algorithm was used and their performance was compared. Initially, two common steel moment frames were studied, only for the purpose of minimizing the weight of the structure and the members of structure are considered as design variables. Since the cost of a steel moment frame is not solely related to the weight of the structure, in order to obtain a realistic plan, in the second part of this study, for the other two frames the cost of the connections is also added to the variables. The results indicate that the steel frame optimization by applying real genetic algorithm could be optimal for structural designing. The findings highlighted the prominent performance and lower costs of the steel moment frames when different connections are used.
V. Goodarzimehr, F. Salajegheh,
Volume 14, Issue 1 (1-2024)
Abstract
The analysis and design of high-rise structures is one of the challenges faced by researchers and engineers due to their nonlinear behavior and large displacements. The moment frame system is one of the resistant lateral load-bearing systems that are used to solve this problem and control the displacements in these structures. However, this type of structural system increases the construction costs of the project. Therefore, it is necessary to develop a new method that can optimize the weight of these structures. In this work, the weight of these significant structures is optimized by using one of the latest metaheuristic algorithms called special relativity search. The special relativity search algorithm is mainly developed for the optimization of continuous unconstrained problems. Therefore, a penalty function is used to prevent violence of the constraints of the problem, which are tension, displacement, and drift. Also, using an innovative technique to transform the discrete problem into a continuous one, the optimal design is carried out. To prove the applicability of the new method, three different problems are optimized, including an eight-story one-span, a fifteen-story three-span bending frame, and a twenty-four-story three-span moment frame. The weight of the structure is the objective function, which should be minimized to the lowest possible value without violating the constraints of the problem. The calculation of stress and displacements of the structure is done based on the regulations of AISC-LRFD requirements. To validate, the results of the proposed algorithm are compared with other advanced metaheuristic methods.
S. L. Seyedoskouei, Dr. R. Sojoudizadeh, Dr. R. Milanchian, Dr. H. Azizian,
Volume 14, Issue 3 (6-2024)
Abstract
The optimal design of structural systems represents a pivotal challenge, striking a balance between economic efficiency and safety. There has been a great challenge in balancing between the economic issues and safety factors of the structures over the past few decades; however, development of high-speed computing systems enables the experts to deal with higher computational efforts in designing structural systems. Recent advancements in computational methods have significantly improved our ability to address this challenge through sophisticated design schemes. The main purpose of this paper is to develop an intelligent design scheme for truss structures in which an optimization process is implemented into this scheme to help the process reach lower weights for the structures. For this purpose, the Artificial Rabbits Optimization (ARO) algorithm is utilized as one of the recently developed metaheuristic algorithms which mimics the foraging behaviour of the rabbits in nature. In order to reach better solutions, the improved version of this algorithm is proposed as I-ARO in which the well-known random initialization process is substituted by the Diagonal Linear Uniform (DLU) initialization procedure. For numerical investigations, 5 truss structures 10, 25, 52, 72, and 160 elements are considered in which stress and displacement constraints are determined by considering discrete design variables. By conducting 50 optimization runs for each truss structure, it can be concluded that the I-ARO algorithm is capable of reaching better solutions than the standard ARO algorithm which demonstrates the effects of DLU in enhancing this algorithm’s search behaviour.
P. Hosseini, A. Kaveh, A. Naghian, A. Abedi,
Volume 14, Issue 3 (6-2024)
Abstract
This study aimed to develop and optimize artificial stone mix designs incorporating microsilica using artificial neural networks (ANNs) and metaheuristic optimization algorithms. Initially, 10 base mix designs were prepared and tested based on previous experience and literature. The test results were used to train an ANN model. The trained ANN was then optimized using SA-EVPS and EVPS algorithms to maximize 28-day compressive strength, with aggregate gradation as the optimization variable. The optimized mixes were produced and tested experimentally, revealing some discrepancies with the ANN predictions. The ANN was retrained using the original and new experimental data, and the optimization process was repeated iteratively until an acceptable agreement was achieved between predicted and measured strengths. This approach demonstrates the potential of combining ANNs and metaheuristic algorithms to efficiently optimize artificial stone mix designs, reducing the need for extensive physical testing.
F. Biabani, A. A. Dehghani, S. Shojaee, S. Hamzehei-Javaran,
Volume 14, Issue 3 (6-2024)
Abstract
Optimization has become increasingly significant and applicable in resolving numerous engineering challenges, particularly in the structural engineering field. As computer science has advanced, various population-based optimization algorithms have been developed to address these challenges. These methods are favored by most researchers because of the difficulty of calculations in classical optimization methods and achieving ideal solutions in a shorter time in metaheuristic technique methods. Recently, there has been a growing interest in optimizing truss structures. This interest stems from the widespread utilization of truss structures, which are known for their uncomplicated design and quick analysis process. In this paper, the weight of the truss, the cross-sectional area of the members as discrete variables, and the coordinates of the truss nodes as continuous variables are optimized using the HGPG algorithm, which is a combination of three metaheuristic algorithms, including the Gravity Search Algorithm (GSA), Particle Swarm Optimization (PSO), and Gray Wolf Optimization (GWO). The presented formulation aims to improve the weaknesses of these methods while preserving their strengths. In this research, 15, 18, 25, and 47-member trusses were utilized to show the efficiency of the HGPG method, so the weight of these examples was optimized while their constraints such as stress limitations, displacement constraints, and Euler buckling were considered. The proposed HGPG algorithm operates in discrete and continuous modes to optimize the size and geometric configuration of truss structures, allowing for comprehensive structural optimization. The numerical results show the suitable performance of this process.
A. Kaveh, N. Khavaninzadeh,
Volume 14, Issue 4 (10-2024)
Abstract
In this paper, a neural network is trained for optimal nodal ordering of graphs to obtain a small wavefront using soft computing. A preference function consists of six inputs that can be seen as a generalization of Sloan's function. These six inputs represent the different connection characteristics of graph models. This research is done with the aim of comparing Sloan's theoretical numbering method with Sloan's developed method with neural networks and WSA meta-heuristic algorithm. Unlike the Sloan algorithm, which uses two fixed coefficients, six coefficients are used here, based on the evaluation of artificial neural networks. The weight of networks is obtained using Water Strider algorithm. Examples are included to demonstrate the performance of the present hybrid method.
Dr. V. Goodarzimehr, Dr. N. Fanaie, Dr. S. Talatahari,
Volume 15, Issue 1 (1-2025)
Abstract
In this study, the Improved Material Generation Algorithm (IMGA) is proposed to optimize the shape and size of structures. The original Material Generation Algorithm (MGA) introduced an optimization model inspired by the high-level and fundamental characteristics of material chemistry, particularly the configuration of compounds and chemical reactions for generating new materials. MGA uses a Gaussian normal distribution to produce new combinations. To enhance MGA for adapting truss structures, a new technique called Random Chaotic (RC) is proposed. RC increases the speed of convergence and helps escape local optima. To validate the proposed method, several truss structures, including a 37-bar truss bridge, a 52-bar dome, a 72-bar truss, a 120-bar dome, and a 200-bar planar structure, are optimized under natural frequency constraints. Optimizing the shape and size of structures under natural frequency constraints is a significant challenge due to its complexity. Choosing the frequency as a constraint prevents resonance in the structure, which can lead to large deformations and structural failure. Reducing the vibration amplitude of the structure decreases tension and deflection. Consequently, the weight of the structure can be minimized while keeping the frequencies within the permissible range. To demonstrate the superiority of IMGA, its results are compared with those of other state-of-the-art metaheuristic methods. The results show that IMGA significantly improves both exploitation and exploration.
M. Paknahd, P. Hosseini, A. Kaveh, S.j.s. Hakim,
Volume 15, Issue 1 (1-2025)
Abstract
Structural optimization plays a crucial role in engineering design, aiming to minimize weight and cost while satisfying performance constraints. This research presents a novel Self-Adaptive Enhanced Vibrating Particle System (SA-EVPS) algorithm that automatically adjusts algorithm parameters to improve optimization performance. The algorithm is applied to two challenging examples from the International Student Competition in Structural Optimization (ISCSO) benchmark suite: the 314-member truss structure (ISCSO_2018) and the 345-member truss structure (ISCSO_2021). Results demonstrate that SA-EVPS achieves significantly better solutions compared to previous studies using the Exponential Big Bang-Big Crunch (EBB-BC) algorithm. For ISCSO_2018, SA-EVPS achieved a minimum weight of 16543.57 kg compared to 17934.3 kg for the best EBB-BC variant—a 7.75% improvement. Similarly, for ISCSO_2021, SA-EVPS achieved 4292.71 kg versus 4399.0 kg for the best EBB-BC variant—a 2.42% improvement. The proposed algorithm also demonstrates superior convergence behavior and solution consistency, with coefficients of variation of 3.13% and 1.21% for the two benchmark problems, compared to 12.5% and 2.4% for the best EBB-BC variant. These results highlight the effectiveness of the SA-EVPS algorithm for solving complex structural optimization problems and demonstrate its potential for engineering applications.
A. Kaveh,
Volume 15, Issue 3 (8-2025)
Abstract
In this paper, a review is provided for the optimal analysis of structures using the graph theoretic force method. An analysis is defined as “optimal” if the corresponding structural matrices (flexibility or stiffness) are sparse, well-structured, and well-conditioned. An expansion process together with the union-intersection theorem is utilized for generating subgraphs, forming a special cycle basis, corresponding to highly localized self equilibration systems. Admissibility checks are used in place of the more common independence checks to speed up the formation of the basis. An efficient solution requires organizing the non-zero entries into various well-defined patterns. Algorithms are provided to form matrices having banded matrices and small profiles. Though the paper considers mainly skeletal structures, the presented concepts are easily extensible to other finite element models. References for such generalizations have been provided. A brief review of swift analysis methods that skirt the harder problem of matrix conditioning is also provided. The iterative nature of optimal structural design via metaheuristic algorithms rewards any speedup in the analysis process. This review recommends utilizing the force method instead of the alternative displacement method to achieve said speedup. The work concludes with a discussion of future challenges in the field of optimal analysis.
K. Farzad, S. Ghaffari,
Volume 15, Issue 3 (8-2025)
Abstract
The use of steel shear wall systems has increased significantly in recent years as an effective solution for resisting lateral loads in buildings. This study focuses on the seismic collapse safety assessment of steel frames with optimal positions of steel shear walls obtained through various metaheuristic optimization algorithms and concepts of performance-based design methodology. Due to potential irregularities and discontinuities in the lateral load-resisting system and the limitations of code-based linear analysis, nonlinear pushover analyses with multiple lateral load patterns are employed to estimate key structural responses during the optimization process. The seismic collapse performance of the optimized frames is further evaluated using the FEMA P-695 methodology, which involves nonlinear dynamic analysis to assess collapse capacity. The primary objective is to examine the influence of steel plate shear wall placement on the structural weight optimization of steel frames. To this end, two case studies, a 10-story and a 15-story steel frame equipped with steel shear walls, are presented. The results demonstrate the critical role of shear wall location in achieving optimal structural designs.
A. Kaveh, S.m. Hosseini, K. Biabani Hamedani,
Volume 15, Issue 3 (8-2025)
Abstract
This paper presents the application of the Plasma Generation Optimization (PGO) algorithm to the optimal design of large-scale dome trusses subjected to multiple frequency constraints. Such problems are notoriously challenging due to their highly non-linear and non-convex nature, characterized by numerous local optima. PGO is a physics-inspired metaheuristic that simulates the processes of excitation, de-excitation, and ionization in plasma generation, balancing global exploration and local refinement through its unique search mechanisms. The performance of PGO is evaluated on three well-established dome truss benchmarks: a 52-bar, a 120-bar, and a 600-bar structure, encompassing both sizing and sizing-shape optimization. A comprehensive statistical analysis based on multiple independent runs demonstrates the algorithm's effectiveness and robustness. The results show that PGO achieves the best-reported minimum weight for the 120-bar and 600-bar domes, while obtaining a highly competitive, near-optimal design for the 52-bar dome. Furthermore, PGO consistently produced low average weights across all problems, confirming its reliability. The convergence histories further validate the algorithm's efficiency in locating feasible, high-quality designs. The findings conclusively establish PGO as a powerful and reliable optimizer for handling complex structural optimization problems with dynamic constraints.
T. Payamifar, R. Sojoudizadeh, H. Azizian, L. Rahimi,
Volume 15, Issue 4 (11-2025)
Abstract
This paper presents an Enhanced Prairie Dog Optimization (IPDO) algorithm for solving complex engineering optimization problems. The proposed improvement integrates Lévy flight dynamics into the original PDO framework to enhance exploration-exploitation balance and accelerate convergence. The performance of IPDO is evaluated against seven established metaheuristics across four challenging civil engineering applications: (1) discrete sizing optimization of a 120-bar truss, (2) structural reliability analysis of a cantilever tube, (3) cost optimization of reinforced concrete beams, and (4) hyperparameter tuning of a Support Vector Machine (SVM) for shear strength prediction of steel fiber-reinforced concrete. Experimental results demonstrate that IPDO consistently achieves superior solution quality, robustness, and convergence speed. Notably, in SVM hyperparameter optimization, IPDO attained the lowest mean squared error (1.4881) with zero variance across runs, outperforming all competitors. The algorithm also proved highly effective in structural design and reliability problems, offering a reliable and efficient tool for real-world engineering optimization.
A. Kaveh, P. Salimi, H.a. Rahimi Bondarabadi,
Volume 15, Issue 4 (11-2025)
Abstract
This work investigates the optimization of concrete structures using metaheuristic algorithms-based reliability. One of the major challenges in the optimization of concrete structures is the extensive search domain, which may lead to convergence to local optima and incorrect results. In this study, instead of solely relying on optimization algorithms that are prone to local optima, a novel approach is proposed. Based on the Cascade Algorithm, this method discretized the search domain for section of beam and column dimensions and increased step by step. After each cross-section is created, it is assigned to the corresponding element. Subsequently, structural analysis is performed, and using reliability-based constraints and analysis, the least-cost section for each element is selected. Based on the obtained low-cost sections, the upper and lower bounds for each design variable are then narrowed. Finally, metaheuristic algorithms are applied to determine the optimal cross-sections with high precision. The results demonstrate that this approach significantly reduces the likelihood of falling into local optima and improves both the speed and accuracy of metaheuristic algorithms.
M. Shahrouzi, Y. Naserifar, A. M. Taghavi, S.-Sh Emamzadeh,
Volume 16, Issue 1 (1-2026)
Abstract
Although metaheuristic algorithms are popular tools for global optimization, none of them is reported as the best for all problems. Hybridization is an advanced solution to overcome the shortcomings of individual methods by using the power points of the others. Here, a popular swarm intelligent algorithm with high explorative capability is combined with an exploitative operator of differential evolution and some dynamic parameter variation, as well as a greedy operator to enhance the search refinement. The proposed method is evaluated on a variety of engineering and constrained engineering problems, including the optimal design of Belleville Spring, pressure vessel, car side impact problem, and Morrow point dam. According to the results, considerable improvement is observed with respect to the standard particle swarm optimizer as well as competitive performance with a number of metaheuristic algorithms.
K. Farzad, M. Javanmard Barbin,
Volume 16, Issue 1 (1-2026)
Abstract
This study investigates the optimal design of steel frames with chevron bracing systems and semi-rigid connections using a performance-based design framework and metaheuristic optimization algorithms. Optimization effectively balances design performance and cost in structural engineering. The three algorithms employed were selected based on their proven application to similar optimization problems, enabling identification of the most suitable approach for the present case. Chevron bracing offers architectural benefits and enhances lateral stiffness and strength. However, unbalanced vertical forces from tension and compression braces under seismic loading require nonlinear analysis for reliable capacity estimation. To address this, pushover analyses with multiple lateral load patterns are performed to capture responses consistent with performance-based design principles. Connection behavior plays a decisive role in the global performance of steel frames. Conventional assumptions of rigid or pinned connections oversimplify reality and produce inaccurate predictions. In this study, semi-rigid connections are modeled with greater fidelity by incorporating column panel zones (CPZs) and gusset plate stiffness at bracing joints. CPZs significantly influence energy dissipation and deformation, while gusset plates may contribute up to 40% of connection rotational stiffness. Neglecting these effects can underestimate interstory drift and misrepresent hinge mechanisms. Results show that accounting for initial connection stiffness improves both accuracy and cost efficiency. For 10- and 15-story frames, structural cost were reduced by about 7%, underscoring the value of realistic connection modeling in optimal design.
P. Hosseini, M. Paknahad, A. Kaveh,
Volume 16, Issue 1 (1-2026)
Abstract
Concrete mixture design optimization has evolved from traditional trial-and-error approaches to sophisticated computational methods. This paper presents a comprehensive review of optimization techniques applied to concrete mixture proportioning, covering statistical methods (Response Surface Methodology, Taguchi method), particle packing models, machine learning algorithms (Artificial Neural Networks, Random Forest, XGBoost, Support Vector Regression), and metaheuristic optimization techniques (Particle Swarm Optimization, Genetic Algorithms, EVPS, SA-EVPS). The review synthesizes findings from over 180 published studies, with detailed analysis of recent advances in artificial intelligence applications for multi-objective optimization of mechanical properties, cost, workability, durability, environmental sustainability, and structural performance. Key findings indicate that ensemble machine learning methods achieve superior prediction accuracy (R² > 0.95) for compressive strength, while metaheuristic algorithms effectively handle multi-objective trade-offs generating Pareto frontiers. The review also identifies critical research gaps including the need for standardized datasets, interpretable AI models, integration of life cycle assessment, and field validation of optimization results. Recent developments in self-adaptive algorithms (SA-EVPS) demonstrate improved convergence and solution quality for both material and structural optimization problems.
Mr V. Jabbari, Dr H. Azizian, Dr R. Sojoudizadeh, Dr L. Rahimi,
Volume 16, Issue 2 (4-2026)
Abstract
Structural design seeks to achieve optimal performance with minimum cost while meeting code requirements. Evaluating optimized designs usually depends on finite element analysis, which is computationally expensive. Recently, surrogate models have been developed to predict structural behavior more efficiently. Among these, Support Vector Machine (SVM) has become a reliable tool in civil engineering. However, the predictive power of SVM is highly dependent on proper parameter tuning. This study introduces the Improved Electric Eel Foraging Optimization Algorithm (I-EEFO) for training SVM to estimate the response of steel frames. Two benchmark structures, a 2‑story and a 7‑story steel frame, were analyzed, and the results were compared with other metaheuristic algorithms. The proposed method achieved very high accuracy: mean squared errors of 1.11E‑13 for the 2‑story frame and 2.99E‑07 meters for the 7‑story frame over 10 runs. The root mean square errors for displacement prediction on test data were 2.67E‑07 and 7.23E‑04 meters, respectively, confirming reliable estimates. Convergence curves demonstrated that I‑EEFO converges faster and more effectively than competing methods. These findings highlight the potential of the proposed approach as a robust and computationally efficient alternative to traditional simulations, offering engineers a practical tool to reduce costs in structural design without compromising accuracy.
