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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.
 

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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.
 

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The primary objective of this paper is to propose a novel technique for hybridizing various metaheuristic algorithms to optimize the size of discrete structures. To accomplish this goal, two well-known metaheuristic algorithms, particle swarm optimization (PSO) and enhanced colliding bodies optimization (ECBO) are hybridized to propose a new algorithm called hybrid PSO-ECBO (HPE) algorithm. The performance of the new HPE algorithm is investigated in solving the challenging structural optimization problems of discrete steel trusses and an improvement in results has been achieved. The numerical results demonstrate the superiority of the proposed HPE algorithm over the original versions of PSO, ECBO, and some other algorithms in the literature.
 

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In this study, the investigation of maximum inelastic displacement demands in steel moment- resisting (SMR) frames designed using the Performance-Based Plastic Design (PBPD) method is conducted under both near-fault and far-fault earthquake records. The PBPD method utilizes a target drift and predetermined yield mechanism as the functional limit state. To accomplish this, 6 steel moment frames having various heights were scaled using well-known sa(T1)  method and, then, were analyzed by OPENSEES software. A total of 22 far-fault records and 90 near-fault records were compiled and employed for parametric nonlinear dynamic analysis. The near-fault records were classified into two categories: T1/Tp≥1  and T1/Tp<1 . The study aimed at investigate their impacts on the inter-story drift and the relative distribution of base shear along the height of the structure. The results revealed that the records with T1/Tp≥1   exerted the greatest influence on the drift demands of upper stories in all frames. Conversely, the near-fault records with T1/Tp<1  demonstrated the most significant impact on the lower stories of mid-rise frames. Additionally, the distribution of relative story shears was examined through genetic programming for optimum PBPD design of steel moment frame structures. As a result, a proposed relationship, denoted as b (seismic parameter for design lateral force distribution), was developed and optimized for both near-fault and far-fault records. This relationship depends on the fundamental period of vibration and the total height of the structure. The accuracy of the predicted model was assessed using R2 , which confirmed the reliability of the proposed relationship.
 

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One of the important factors in the efficiency of construction operations is the proper replacement construction projects of the construction site layout planning (CSLP). That this would not be possible without oversight of the factors affecting it. Therefore, the study of factors affecting the replacement of construction site layout is considered vital in projects. Different factors are involved in the replacement of CSLP, which examine the economic dimension and the effects of changing costs and time during work. Due to the complexity of the subject, it is solved using hyper-innovative algorithms. This research is a linear programming model for optimizing the layout of equipment for Launcher/Receiver (L/R) stations. Due to the complexity of the problem, the invasive weed algorithm was used to achieve an optimal response. The goal is to minimize the total costs associated with transportation, relocation and relocation, and changes during implementation. The results of the calculations and output of the algorithm showed the variation of the answer in the optimal layout of the CSLP, which was obtained at the lowest distance and the most optimal mode. The results were presented in a similar scenario in the projects.
 

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This paper proposes a method for structural damage detection through the sensitivity analysis of modal shapes in the calculation of modal strain energy (MSE). For this purpose, sensitivity equations were solved to determine the strain energy based on dynamic data (i.e., modal shapes). An objective function was then presented through the sensitivity-based MSE to detect structural damage. Due to the nonlinearity of sensitivity equations, the objective function of the proposed formulation can be minimized through the shuffled shepherd optimization algorithm (SSOA). The first few modes were employed for damage detection in solving the inverse problem. The proposed formulation was evaluated in a few numerical examples under different conditions. The numerical results indicated that the proposed formulation was efficient and effective in solving the inverse problem of damage detection. The proposed method not only minimized sensitivity to measurement errors but also effectively identified the location and severity of structural damage.
 

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Most industrial-practical projects deal with nonlinearity phenomena. Therefore, it is vital to implement a nonlinear method to analyze their behavior. The Finite Element Method (FEM) is one of the most powerful and popular numerical methods for either linear or nonlinear analysis. Although this method is absolutely robust, it suffers from some drawbacks. One of them is convergency issues, especially in large deformation problems. Prevalent iterative methods such as the Newton-Raphson algorithm and its various modified versions cannot converge in certain problems including some cases such as snap-back or through-back. There are some appropriate methods to overcome this issue such as the arc-length method. However, these methods are difficult to implement. In this paper, a computational framework is presented based on meta-heuristic algorithms to improve nonlinear finite element analysis, especially in large deformation problems. The proposed method is verified via different benchmark problems solved by commercial software. Finally, the robustness of the proposed algorithm is discussed compared to the classic methods.
 

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During the process of continuum topology optimization some pattern discontinuities may arise. It is an important challenge to overcome such irregularities in order to achieve or interpret the true optimal layout. The present work offers an efficient algorithm based on graph theoretical approach regarding density priorities. The developed method can recognize and handle solid continuous regions in a pre-optimized media. An illustrative example shows how the proposed priority guided trees can successfully distinguish the most crucial parts of the continuum during topology optimization.
 

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Genetic algorithm is a robust meta-heuristic algorithm inspired by the theory of natural selection to solve various optimization problems. This study presents a method with the purpose of promoting the exploration and exploitation of genetic algorithm. Improvement in exploration ability is made by adjusting the initial population and adding a group of fixed stations. This modification increases the diversity among the solution population, which enables the algorithm to escape from local optimum and to converge to the global optimum even in fewer generations. On the other hand, to enhance the exploitation ability, increasing the number of selected parents is suggested and a corresponding crossover technique has been presented. In the proposed technique, the number of parents to generate offspring is variable during the process and it could be potentially more than two. The effectiveness of the modifications in the proposed method has been verified by examining several benchmark functions and engineering design problems.
 

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Seismic vibration control refers to a range of technical methods designed to reduce the effects of earthquakes on building structures and many other engineering systems. Most of the recently developed methods in this area have been investigated in vibration suppression of buildings structures each of which have advantages and disadvantages in dealing with complex structural systems and destructive earthquakes. This study aims to implement two of the well-known passive control systems as Base Isolation (BI) and Mass Damper (MD) control as a hybrid control scheme in order to reduce the seismic vibration of tall tubular buildings in dealing with different types of earthquakes. For this purpose, a 50-story tall building is considered with tubular structural system while the hybrid BI-MD control system ins implemented in the building for vibration control purposes. Since the parameter tuning process is one of the key aspects of the passive control systems, a metaheuristic-based parameter optimization process is conducted for this purpose in which a new upgraded version of the standard Gazelle Optimization Algorithm (GOA) is proposed as UGOA while the Chaos Theory (CT) is used instead of random movements in the main search loop of the UGOA in order to enhance the overall performance of the standard algorithm. The results show that the upgraded algorithm is capable of conducting better search in dealing with the optimal hybrid control of structural systems.
 

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Most industrial-practical projects deal with nonlinearity phenomena. Therefore, it is vital to implement a nonlinear method to analyze their behavior. The Finite Element Method (FEM) is one of the most powerful and popular numerical methods for either linear or nonlinear analysis. Although this method is absolutely robust, it suffers from some drawbacks. One of them is convergency issues, especially in large deformation problems. Prevalent iterative methods such as the Newton-Raphson algorithm and its various modified versions cannot converge in certain problems including some cases such as snap-back or through-back. There are some appropriate methods to overcome this issue such as the arc-length method. However, these methods are difficult to implement. In this paper, a computational framework is presented based on meta-heuristic algorithms to improve nonlinear finite element analysis, especially in large deformation problems. The proposed method is verified via different benchmark problems solved by commercial software. Finally, the robustness of the proposed algorithm is discussed compared to the classic methods.

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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.
 

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The sine-cosine algorithm is concerned as a recent meta-heuristic method that takes benefit of orthogonal functions to scale its walking steps through the search space. The idea is utilized here in a different manner to develop a modified sine-cosine algorithm (MSCA). It is based on the controlled perturbation about current solutions by applying a novel combination of sine and cosine functions. The desired transition from exploration to exploitation phases mainly relies on such a term that provides continued fluctuations within a dynamic amplitude. Performance of the proposed algorithm is further evaluated on a set of thirteen test functions with unimodal and multimodal search spaces, as well as on engineering and structural problems in a variety of discrete, continuous and mixed discrete-continuous types. Numerical simulations show that MSCA can find the best literature results for such benchmarks problems. Additional fair comparisons, declare competitive performance of the proposed method with other meta-heuristic algorithms and its enhancement with respect to the standard sine-cosine algorithm.

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In order to evaluate the damage state, value, and position of structural members more accurately, a multi-objective optimization (MO) method is utilized that is based on changes in natural frequency. The multi-objective optimization dynamic-based damage detection method is first introduced. Two objective functions for optimization are then introduced in terms of changing the natural frequencies and mode shapes. The multi-objective optimization problem (MOP) is formulated by using the two objective functions. Three considered MO algorithms consist of Colliding Bodies Optimization (MOCBO), Particle Swarm Optimization (MOPSO), and non-dominated sorting genetic algorithm (NSGA-II) to achieve the best structural damage detection. The proposed methods are then applied to three planar steel frame structures. Compared to the traditional optimization methods utilizing the single-objective optimization (SO) algorithms, the presented methods provide superior results.

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Spillway design poses a significant challenge in effectively managing the energy within water flow to prevent erosion and destabilization of dam structures. Traditional approaches typically advocate for standard hydraulic jump stilling basins or other energy dissipators at spillway bases yet constructing such basins can be prohibitively large and costly, particularly when extensive excavation is necessary. Consequently, growing interest in cascade hydraulic structures has emerged over recent decades as an alternative for energy dissipation. These structures utilize a series of arranged steps to facilitate water flow, effectively dissipating energy as it traverses the cascade. Commonly deployed in scenarios involving high dams or steep gradients, the stepped configuration ensures efficient aeration and substantial energy dissipation along the structure, thereby reducing the size and cost of required stilling basins. Despite extensive research on hydraulic characteristics using physical and numerical models and established design procedures, construction cost optimization of step cascades remains limited but promising. This paper aims to address this gap by employing two novel gradient-based meta-heuristic optimization techniques to enhance the efficiency and cost-effectiveness of cascade stilling basin designs. Through comparative analyses and evaluations, this study demonstrates the efficacy of these techniques and offers insights for future research and applications in hydraulic structures design optimization.

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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.

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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.

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Diagrids are of practical interest in high-rise buildings due to their architectural configuration and efficiency in withstanding lateral loads by exterior diagonal members. In the present work, diagrid models are screened based on a sizing optimization approach. Section index of each member group is treated as a discrete design variable in the optimization problem to be solved. The structural constraints are evaluated due to Load and Resistant Design Factor regulations under both gravitational and wind loadings. The research is threefold: first, falcon optimization algorithm is utilized as a meta-heuristic paradigm for such a large-scale and highly constrained discrete problem. Second, the effect of geometry variation in diagrids on minimal structural weight is studied for 18 diagrid models via three different heights (12, 20 and 30 stories) and three diagrid angles. Third, distinct cases of rigid and flexible bases are compared to study the effect of such boundary conditions on the results. The effect of soil flexibility beneath the foundation on the optimal design was found highly dependent on the diagrid geometry. The best weight and performance in most of the treated examples belong to the geometry that covers two stories by every grid line on the flexible-base.
 

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Structural optimization plays a critical role in improving the efficiency, cost-effectiveness, and sustainability of engineering designs. This paper presents a comparative study of single-objective and multi-objective optimization in the structural design process. Single-objective problems focus on optimizing just one objective, such as minimizing weight or cost, while other important aspects are treated as constraints like deflections and strength requirements. Multi-objective optimization addresses multiple conflicting objectives, such as balancing cost, with displacement treated as a secondary objective and strength requirements defined as constraints within the given limits. Both optimization approaches are carried out using Chaos Game Optimization (CGO). While single-objective optimization produces a definitive optimal solution that can be used directly in the final design, multi-objective optimization results in a set of trade-off solutions (Pareto front), requiring a decision-making process based on design codes and practical criteria to select the most appropriate design. Through a real-world case study, this research will assess the performance of both optimization strategies, providing insights into their suitability for modern structural engineering challenges.