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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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Predicting the bearing capability (q_rs) of geogrid-reinforced stone columns poses a significant challenge due to variations in soil and rock parameters across different locations. The behavior of soil and rock in one region cannot be generalized to other regions. Therefore, accurately predicting q_rs requires a complex and stable nonlinear equation that accounts for the complexity of rock engineering problems. This paper utilizes the Rock Engineering System (RES) method to address this issue and construct a predictive model.To develop the model, experimental data consisting of 219 data points from various locations were utilized. The input parameters considered in the model included the ratio between geogrid reinforced layers diameter and footing diameter (d/D), the ratio of stone column length to diameter (L/dsc), the q_rs of unreinforced soft clay (qu), the thickness ratio of Geosynthetic Reinforced Stone Column (GRSB) and USB to base diameter (t/D), and the settlement ratio to footing diameter (s/D). Following the implementation of the RES-based method, a comparison was made with other models, namely linear, power, exponential, polynomial, and multiple logarithmic regression methods. Statistical indicators such as root mean square error (RMSE), mean square error (MSE), and coefficient of determination (R2) were employed to assess the accuracy of the models. The results of this study demonstrated that the RES-based method outperforms other regression methods in terms of accuracy and efficiency.
 

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The balanced vehicle routing problem (BVRP) is one of the most famous research problems in operations, which has a very important position in combination optimization problems. In this problem, a fleet of vehicles with capacity Q starts moving from a node called the warehouse and returns to it after serving customers, provided that they visit each customer only once and never exceed the capacity Q. The goal is to minimize the paths traveled by vehicles provided that the distances traveled by the vehicles are the same as possible, for more justice in working time and income. This article presents the application of a hybrid imperialist competitive algorithm (HICA) to solve the problem. Unlike other optimization methods, this method is inspired by the socio-political process of societies and uses the competition between colonizing and colonized countries to reach the solution. To test the effectiveness of the algorithm, a set of standard examples are considered and the algorithm is implemented on it. The calculation results on these examples, which have a size of 50 to 200, show that the proposed algorithm has been able to compete well with well-known meta-heuristic algorithms in terms of the quality of the answers. In addition, the solutions close to the best answers obtained so far are generated for most of the examples.

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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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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.
 

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The main objective of this paper is to optimize the size and layout of planar truss structures simultaneously. To deal with this challenging type of truss optimization problem, the center of mass optimization (CMO) metaheuristic algorithm is utilized, and an extensive parametric study is conducted to find the best setting of internal parameters of the algorithm. The CMO metaheuristic is based on the physical concept of the center of mass in space. The effectiveness of the CMO metaheuristic is demonstrated through the presentation of three benchmark truss layout optimization problems. The numerical results indicate that the CMO is competitive with other metaheuristics and, in some cases, outperforms them.
 

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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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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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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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Tower cranes are essential for both vertical and horizontal movement of materials in construction and port operations. Optimizing their placement is crucial for reducing costs and enhancing overall efficiency. This study addresses the optimization of tower crane placement using the recently developed Mouth Brooding Fish (MBF) algorithm. The MBF algorithm is inspired by the life cycle of mouth-brooding fish, employing their behavioral patterns and the survival challenges of their offspring to find optimal solutions. The performance of the MBF algorithm is compared with the Genetic Algorithm (GA), Colliding Bodies Optimization (CBO), and Enhanced Colliding Bodies Optimization (ECBO). The results demonstrate that the MBF algorithm is effective and has potential advantages in tackling complex optimization problems.

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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.

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The multi-material size optimization of transmission tower trusses is carried out in the present study. Three real-size examples are designed, and statically analyzed, and the Black Hole Mechanics Optimization (BHMO) algorithm, a recently developed metaheuristic optimizer methodology, is employed. The BHMO algorithm's innovative search strategy, which draws inspiration from black hole quantum physics, along with a robust mathematical kernel based on the covariance matrix between variables and their associated costs, efficiently converges to global optimum solutions. Besides, three alloys of steel are taken into account in these examples for discrete size variables, each of which is defined in the problem by a weighted coefficient in terms of the elemental weight. The results also indicate that using multiple materials or alloys in addition to diverse cross-sectional sizes leads to the lowest possible cost and the most efficient solution.

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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.

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Earthquakes are random phenomena and there has been no report of similar earthquakes occurring worldwide. Therefore, traditional methods of designing buildings based on past earthquakes with inappropriate discontinuity joints are sometimes ineffective for vital structures. This may lead to collision and destruction of adjacent structures during a severe earthquake. As in the Iranian Standard No. 2800-4, this distance should be at least five-thousandths of the building height from the base level to the adjacent ground boundary for buildings up to eight stories to prevent or reduce this damage. Also, for important or/with more than eight-story buildings, this value is determined using the maximum nonlinear lateral displacement of the structures by considering the effects of the P-delta. Also, if the properties of the adjacent building are not known, this distance should be considered at least equal to 70% of the maximum nonlinear lateral displacement of the structures. The main objective of this study is to investigate the adequacy of the discontinuity joint introduced in the Iranian Standard No. 2800-4 based on the critical excitation method. This method calculates critical earthquakes for three buildings (e.g., three-, seven- and eleven-story moment frames) by considering some constraints on the energy, peak ground acceleration, Fourier amplitude, and strong ground motion duration. The results indicate that the minimum gap between two adjacent buildings derived from the existing codes is lower than those calculated using the critical excitation method. Therefore, oscillation might occur if a structure is designed according to the seismic codes and subjected to a critical earthquake.

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The optimization process of space structures considering the nonlinear material behavior requires significant computational efforts due to the large number of design variables and the complexities of nonlinear structural analysis. Accordingly, the Force Analogy Method (FAM) serves as an efficient tool to reduce computational workload and enhance optimization speed. In this study, the weight optimization of space structures in the inelastic region under seismic loading is carried out using the Shuffled Shepherd Optimization Algorithm (SSOA), with the nonlinear structural analysis based on the FAM. To do this, the FAM formulation for axially loaded members of space structures under seismic forces is presented. Subsequently, weight optimization is performed on two double-layer space structures: a flat double-layer structure with 200 members and a barrel vault structure with 729 members under the Kobe earthquake record. Based on the results, the optimized design using the inelastic behavior showed that the FAM provided accurate results when compared to the precise nonlinear structural analysis. The optimized design based on the FAM is considered acceptable, and the computational time for the optimization process has been significantly reduced.