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In this paper, set theoretical variants of the artificial bee colony (ABC) and water evaporation optmization (WEO) algorithms are proposed. The set theoretical variants are designed based on a set theoretical framework in which the population of candidate solutions is divided into some number of smaller well-arranged sub-populations. The framework aims to improve the compromise between diversification and intensification of the search and makes it possible to design various variants of a P-metaheuristic. In order to verify the stability and robustness of the set theoretical framework, the proposed algorithms are applied to solve three different benchmark structural design optimization problems. The results show that the set theoretical framework improves the performance of the ABC and WEO algorithms, especially in terms of robustness and convergence characteristics.

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The main purpose of the present work is to investigate the impact of soil-structure interaction on performance-based design optimization of steel moment resisting frame (MRF) structures. To this end, the seismic performance of optimally designed MRFs with rigid supports is compared with that of the optimal designs with a flexible base in the context of performance-based design. Two efficient metaheuristic algorithms, namely center of mass optimization and improved fireworks, are used to implement the optimization task. During the optimization process, nonlinear structural response-history analysis is carried out to evaluate the structural response. Two illustrative design examples of 6- and 12-story steel MRFs are presented, and it is observed that the performance-based design optimization considering soil-structure interaction decreases the structural weight and increases nonlinear structural response in comparison to rigid-based models. Therefore, in order to obtain more realistic optimal designs, soil-structure interaction should be included in the performance-based design optimization process of steel MRFs.

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In this work, a new hybrid Symbiotic Organisms Search (SOS) algorithm introduced to design and optimize spatial and planar structures under structural constraints. The SOS algorithm is inspired by the interactive behavior between organisms to propagate in nature. But one of the disadvantages of the SOS algorithm is that due to its vast search space and a large number of organisms, it may trap in a local optimum. To fix this problem Harmony search (HS) algorithm, which has a high exploration and high exploitation, is applied as a complement to the SOS algorithm. The weight of the structures' elements is the objective function which minimized under displacement and stress constraints using finite element analysis. To prove the high capabilities of the new algorithm several spatial and planar benchmark truss structures, designed and optimized and the results have been compared with those of other researchers. The results show that the new algorithm has performed better in both exploitation and exploration than other meta-heuristic and mathematics methods.

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Jellyfish Search (JS) is a recently developed population-based metaheuristic inspired by the food-finding behavior of jellyfish in the ocean. The purpose of this paper is to propose a quantum-based Jellyfish Search algorithm, named Quantum JS (QJS), for solving structural optimization problems. Compared to the classical JS, three main improvements are made in the proposed QJS: (1) a quantum-based update rule is adopted to encourage the diversification in the search space, (2) a new boundary handling mechanism is used to avoid getting trapped in local optima, and (3) modifications of the time control mechanism are added to strike a better balance between global and local searches. The proposed QJS is applied to solve frequency-constrained large-scale cyclic symmetric dome optimization problems. To the best of our knowledge, this is the first time that JS is applied in frequency-constrained optimization problems. An efficient eigensolution method for free vibration analysis of rotationally repetitive structures is employed to perform structural analyses required in the optimization process. The efficient eigensolution method leads to a considerable saving in computational time as compared to the existing classical eigensolution method. Numerical results confirm that the proposed QJS considerably outperforms the classical JS and has superior or comparable performance to other state-of-the-art optimization algorithms. Moreover, it is shown that the present eigensolution method significantly reduces the required computational time of the optimization process compared to the classical eigensolution method.

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The present work deals with optimization and reliability assessment of double layer barrel vaults. In order to achieve the optimization task an improved colliding bodies optimization algorithm is employed. In the first phase of this study, different forms of double layer barrel vaults namely, square-on-square, square-on-diagonal, diagonal-on-diagonal and diagonal-on-square are considered and designed for optimal weight by the improved colliding bodies optimization algorithm. In the second phase, in order to account for the existing uncertainties in action and resistance of the structures, the reliability of the optimally designed double layer barrel vaults is assessed using importance sampling method by taking into account a limit-state function on the maximum deflection of the structures. The results demonstrate that the minimum reliability index of the optimal designs is 0.92 which means that all the optimally designed double layer barrel vaults are reliable and safe against uncertainties.  

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Force Density Method is a well-known form-finding method for discrete networks that is based on geometrical equilibrium of forces and could be used to design efficient structural forms. The choice of force density distribution along the structure is mostly upon user which in most cases is set be constant, with peripheral members having relatively larger force density to prevent excessive shrinking. In order to direct FDM towards more efficient structures, an optimization strategy can be used to inform the form-finding process by minimizing certain objective function, e.g. weight of the structure. Desired structural, constructional or geometrical constraints can also be incorporated in this framework that otherwise user may not have direct control over. It has been shown that considerable weight reduction is possible compared to uniform force density in the structure while satisfying additional constraints. In this way, form-finding can be augmented and novel structural forms can be designed.

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The optimal design of dome structures is a challenging task and therefore the computational performance of the currently available techniques needs improvement. This paper presents a combined algorithm, that is supported by the mixture of Charged System Search (CSS) and Teaching-Learning-based optimization (TLBO). Since the CSS algorithm features a strong exploration and may explore all unknown locations within the search space, it is an appropriate complement to enhance the optimization process by solving the weaknesses with using another optimization algorithm’s strong points. To enhance the exploitation ability of this algorithm, by adding two parts of Teachers phase and Student phase of TLBO algorithm to CSS, a method is obtained that is more efficient and faster than standard versions of these algorithms. In this paper, standard optimization methods and new hybrid method are tested on three kinds of dome structures, and the results show that the new algorithm is more efficient in comparison to their standard versions.

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Natural frequencies of a structure give useful information about the structural response to dynamic loading. These frequencies should be far enough from the critical frequency range of dynamic excitations like earthquakes in order to prevent the resonance phenomenon sufficiently. Although there are many investigations on optimization of truss structures subjected to frequency constraints, just a few studies have been considered for optimal design of frame structures under these constraints. In this paper, a recently proposed metaheuristic algorithm called Adaptive Charged System Search (ACSS) is applied to optimal design of steel frame structures considering the frequency constraints. Benchmark design examples are solved with the ACSS, and optimization results are illustrated in terms of some statistical indices, convergence history and solution quality. The design examples include three planar steel frames with small to large number of design variables. Results show that the ACSS outperforms the charged system search algorithm in this sizing optimization problem.

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The arithmetic optimization algorithm (AOA) is a recently developed metaheuristic optimization algorithm that simulates the distribution characteristics of the four basic arithmetic operations (i.e., addition, subtraction, multiplication, and division) and has been successfully applied to solve some optimization problems. However, the AOA suffers from poor exploration and prematurely converges to non-optimal solutions, especially when dealing with multi-dimensional optimization problems. More recently, in order to overcome the shortcomings of the original AOA, an improved version of AOA, named IAOA, has been proposed and successfully applied to discrete structural optimization problems. Compared to the original AOA, two major improvements have been made in IAOA: (1) The original formulation of the AOA is modified to enhance the exploration and exploitation capabilities; (2) The IAOA requires fewer algorithm-specific parameters compared with the original AOA, which makes it easy to be implemented. In this paper, IAOA is applied to the optimal design of large-scale dome-like truss structures with multiple frequency constraints. To the best of our knowledge, this is the first time that IAOA is applied to structural optimization problems with frequency constraints. Three benchmark dome-shaped truss optimization problems with frequency constraints are investigated to demonstrate the efficiency and robustness of the IAOA. Experimental results indicate that IAOA significantly outperforms the original AOA and achieves results comparable or superior to other state-of-the-art algorithms.

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In this paper, the improved shuffled-based Jaya algorithm (IS-Jaya) is applied to the size optimization of the braced dome with the frequency constraints. IS-Jaya is the enhanced version of the Jaya algorithm that the shuffling process and escaping from local optima are added for it. These two modifications increase the population diversity and ability the escape from the local optima of the Jaya. The robustness and performance of the IS-Jaya are evaluated by the three design examples. The results show that the IS-Jaya algorithm outperforms other state-of-the-art optimization techniques considered in the literature.
 

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Design optimization of cable-stayed bridges is a challenging optimization problem because a large number of variables is usually involved in the optimization process. For these structures the design variables are cross-sectional areas of the cables. In this study, an efficient metaheuristic algorithm namely, momentum search algorithm (MSA) is used to optimize the design of cable-stayed bridges. The MSA is inspired by the Physics and its superiority over many metaheuristics has been demonstrated in tackling several standard benchmark test functions. In the current work, the performance of MSA is compared with that of two other metaheuristics and it is shown that the MSA is an efficient algorithm to tackle the optimization problem of cable-stayed bridges.
 

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In most practical cases, structural design variables are linked to a discrete list of sections for optimal design. Cardinality of such a discrete search space is governed by the number of alternatives for each member group. The present work offers an adaptive strategy to detect more efficient alternatives and set aside redundant ones during optimization. In this regard, the difference between the lower and the upper bounds on such variables is gradually reduced by a procedure that adapts history of the selected alternatives in previous iterations. The propsed strategy is implemented on a hybrid paritcle swarm optimizer and imperialist competitive algorithm. The former is a basic swarm intelligent method while the later utilizes subpopulations in its search. Spatial and large-scale structures in various shapes are treated showing successive performance improvement. Variation of a diversity index and resulting band size are traced and discussed to declare behavior merits of the proposed adaptive band strategy.  
 

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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.
 

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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.
 

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This paper deals with the optimum design of the mixed structures that consists of two parts, a lower part made of concrete and an upper part made of steel. Current codes and available commercial software packages do not provide analytical solutions for such structural systems, especially if a decoupled analysis is performed where the lower part is excited by ground motion and its response of total accelerations is used for the upper part. Due to irregular damping ratios, mass and stiffness, dynamic response of each part of a mixed structure differs significantly. The present paper aims at comparing of the optimum design of these structures under the coupled and decoupled models. Toward that goal, the coupled and decoupled time history analyses are performed and the optimum design of the two methods are compared. The results of the two approach show that the cost of the decoupled analysis is higher than the cost of the coupled analysis and the design of the decoupled method may be uneconomical, because the interaction between the two upper and lower parts is neglected.
 

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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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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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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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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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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.