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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 multiple tuned mass dampers (MTMDs) are considered among the control systems used for reducing the vibration of buildings under seismic excitations. A large number of the previous studies have mainly emphasized on the utilization and effectiveness of MTMD on linear structure responses, and few of them have investigated the effectiveness of MTMD on nonlinear multi-degree of freedom structures. Thus, in this paper, the effectiveness of MTMD on nonlinear buildings have been investigated. The effectiveness of the MTMD systems lies in their parameters, and the location of dampers in buildings. Accordingly, the optimization of MTMD’s properties, as well as its location, are taken into account in the present study. The Mouth Brooding Fish algorithm, which is a new optimization method is utilized for optimizing the properties corresponding to the MTMD system. The effectiveness levels of the MTMDs were compared with the efficiency of an equal optimally tuned mass damper (TMD), which was placed on the top of the building. The results of these comparisons revealed that MTMDs have provided a better efficiency compared to TMDs in reducing the maximum displacement of nonlinear structures. Moreover, MTMDs have a higher effectiveness when placed on different floors of the building.

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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 parametric study is carried out to investigate the effect of number of cells in optimal cost of the non-prismatic reinforced concrete (RC) box girder bridges. The variables are geometry of cross section, tapered length, concrete strength and reinforcement of the box girders and slabs that are obtained using ECBO metaheuristic algorithm. The design is based on AASHTO standard specification. The constraints are the bending and shear strength, geometric limitations and superstructure deflection. The link of CSiBridge and MATLAB software are used for the optimization process. The methodology carried out for two-cell, three-cell and four-cell box girder bridges. The results show that the total cost of the concrete, bars and formwork for two-cell box girder is less than those of the three- and four-cell box girder bridges.

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The present work reveals a problem formulation to minimize material consumption and improve efficiency of diagrids to resist equivalent wind loading. The integrated formulation includes not only sizing of structural members but also variation in geometry and topology of such a system. Particular encoding technique is offered to handle practical variation of diagrid modules. A variant of Pseudo-random Directional Search is utilized to solve this problem treating a number of three dimensional structural models. Several issues are investigated including the effect of variation in the building height, its aspect ratio and fixing or releasing diagrid angles. Consequently, especial trend of variation in diagrid angle is observed with superior structural responses with respect to sizing designs of the fixed-angle modules.

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This study is devoted to seismic collapse safety analysis of performance based optimally seismic designed steel chevron braced frame structures. An efficient meta-heuristic algorithm namely, center of mass optimization is utilized to achieve the seismic optimization process. The seismic collapse performance of the optimally designed steel chevron braced frames is assessed by performing incremental dynamic analysis and determining their adjusted collapse margin ratios. Two design examples of 5-, and 10-story chevron braced frames are illustrated. The numerical results demonstrate that all the performance-based optimal designs are of acceptable seismic collapse safety.

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This article presents numerical studies on semi-active seismic response control of structures equipped with Magneto-Rheological (MR) dampers. A multi-layer artificial neural network (ANN) was employed to mitigate the influence of time delay, This ANN was trained using data from the El-Centro earthquake. The inputs of ANN are the seismic responses of the structure in the current step, and the outputs are the MR damper voltages in the current step. The required training data for the neural controller is generated using genetic algorithm (GA). Using the El-Centro earthquake data, GA calculates the optimal damper force at each time step. The optimal voltage is obtained using the inverse model of the Bouc-Wen based on the predicted force and the corresponding velocity of the MR damper. This data is stored and used to train a multi-layer perceptron neural network. The ANN is then employed as a controller in the structure. To evaluate the efficiency of the proposed method, three- story, seven- story and twenty-story structures with a different number of MR dampers were subjected to the Kobe, Northridge, and Hachinohe earthquakes. The maximum reduction in structural drifts in the three-story structure are 13.05%, 39.90%, 15.89%, and 8.21%, for the El-Centro, Hachinohe, Kobe, and Northridge earthquakes, respectively. As the control structure is using a pre-trained neural network, the computation load in the event of an earthquake is extremely low. Additionally, as the ANN is trained on seismic pre-step data to predict the damper's current voltage, the influence of time lag is also minimized.

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Metaheuristics are considered the first choice in addressing structural optimization problems. One of the complicated structural optimization problems is the highly nonlinear dynamic truss shape and size optimization with multiple natural frequency constraints. On the other hand, natural frequency constraints are useful to control the responses of a dynamically exciting structure. In this regard, this study uses for the first time the water evaporation optimization (WEO) algorithm to address this problem. Four benchmark trusses are considered for experimental investigation of the WEO. Obtained results indicate the comparative performance of WEO to the best-known algorithms in this problem, high performance in comparison to those of different optimization techniques, and high performance in comparison to all algorithms in terms of robustness. The simulation results clearly show a good balance between the global and local exploration abilities of WEO and its potential robust efficiency for other complicated constrained engineering optimization problems.

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Despite comprehensive literature works on developing fitness-based optimization algorithms, their performance is yet challenged by constraint handling in various engineering tasks. The present study, concerns the widely-used external penalty technique for sizing design of pin-jointed structures. Observer-teacher-learner-based optimization is employed here since previously addressed by a number of investigators as a powerful meta-heuristic algorithm. Several cases of penalty handling techniques are offered and studied using either maximum or summation of constraint violations as well as their combinations. Consequently, the most successive sequence, is identified for the treated continuous and discrete structural examples. Such a dynamic constraint handling is an affordable generalized solution for structural sizing design by iterative population-based algorithms.
 

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Some structural control systems have been devised to protect structures against earthquakes, which the tuned mass damper (TMD) being one of the earliest. The effect of a tuned mass damper depends on its properties, such as mass, damping coefficient, and stiffness. The parameters of tuned mass dampers need to be tuned based on the main system and applied load. In most of the papers, the parameters of TMDs have been tuned based on the nominal parameters of structures. Also, most of the studies considered the minimization of maximum displacement of structure as the objective function of optimizing the parameters of tuned mass dampers. In this study, according to the Monte Carlo method and using the Mouth Brooding Fish algorithm, TMDs have been optimized based on the reliability of structures regarding the uncertain parameters of buildings, and their efficiency in the reduction of maximum displacement and failure probability of hundreds generated buildings with uncertain parameters, are compared with the efficiency of the displacement-based optimized TMDs. The results show that the TMDs optimized regarding uncertainty have better efficiency in reducing the maximum displacement, and failure probability of buildings than the TMDs optimized regarding nominal parameters of buildings. Also, according to the results, the displacement-based optimized TMDs regarding uncertainty show better efficiency in reducing the failure probability and displacement of the buildings than reliability-based optimized TMDs.
 

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This paper introduces a reliability-based multi-objective design method for spatial truss structures. A multi-objective optimization problem has been defined considering three conflicting objective functions including truss weight, nodal deflection, and failure probability of the entire truss structure with design variables of cross sectional area of the truss members. The failure probability of the entire truss system has been determined considering the truss structure as a series system. To this end, the uncertainties of the applied load and the resistance of the truss members have been accounted by generating a set of 50 random numbers. The limitations of members' allowable have been defined as constraints. To explain the methodology, a 25-bar benchmark spatial truss has been considered as the case study structure and has been optimally designed using the game theory concept and genetic algorithm (GA). The results show effectiveness and simplicity of the proposed method which can provide Pareto optimal solution. These optimal solutions can provide both safety and reliability for the truss structure.
 

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In this paper, a new robust metaheuristic optimization algorithm called improved time evolutionary optimization (ITEO) is applied to design reinforced concrete one-way ribbed slabs. Geometric and strength characteristics of concrete slabs are considered as design variables. The optimal design is such that in addition to achieving the minimum cost, all design constraints are satisfied under American Concrete Institute’s ACI 318-05 Standard. So, the numerical examples considered in this study have a large number of design variables and design constraints that make it complicated to converge the global optimal design. The ITEO has an excellent balance between the two phases of exploration and extraction and it has a high ability to find the optimal point of such problems. The comparison results between the ITEO and some other metaheuristic algorithms show the proposed method is competitive compared to others, and in some cases, superior to some other available metaheuristic techniques in terms of the faster convergence rate, performance, robustness of finding an optimal design solution, and needs a smaller number of function evaluations for designing considered constrained engineering problems.
 

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As a novel strategy, Quantum-behaved particles use uncertainty law and a distinct formulation obtained from solving the time-independent Schrodinger differential equation in the delta-potential-well function to update the solution candidates’ positions. In this case, the local attractors as potential solutions between the best solution and the others are introduced to explore the solution space. Also,  the difference between the average and another solution is established as a new step size. In the present paper, the quantum teacher phase is introduced to improve the performance of the current version of the teacher phase of the Teaching-Learning-Based Optimization algorithm (TLBO) by using the formulation obtained from solving the time-independent Schrodinger equation predicting the probable positions of optimal solutions. The results show that QTLBO, an acronym for the Quantum Teaching- Learning- Based Optimization, improves the stability and robustness of the TLBO by defining the quantum teacher phase. The two circulant space trusses with multiple frequency constraints are chosen to verify the quality and performance of QTLBO. Comparing the results obtained from the proposed algorithm with those of the standard version of the TLBO algorithm and other literature methods shows that QTLBO increases the chance of finding a better solution besides improving the statistical criteria compared to the current TLBO.
 

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Presently, the introduction of intelligent models to optimize structural problems has become an important issue in civil engineering and almost all other fields of engineering. Optimization models in artificial intelligence have enabled us to provide powerful and practical solutions to structural optimization problems. In this study, a novel method for optimizing structures as well as solving structure-related problems is presented. The main purpose of this paper is to present an algorithm that addresses the major drawbacks of commonly-used algorithms including the Grey Wolf Optimization Algorithm (GWO), the Gravitational Search Algorithm (GSA), and the Particle Swarm Optimization Algorithm (PSO), and at the same time benefits from a high convergence rate. Also, another advantage of the proposed CGPGC algorithm is its considerable flexibility to solve a variety of optimization problems. To this end, we were inspired by the GSA law of gravity, the GWO's top three search factors, the PSO algorithm in calculating speed, and the cellular machine theory in the realm of population segmentation. The use of cellular neighborhood reduces the likelihood of getting caught in the local optimal trap and increases the rate of convergence to the global optimal point. Achieving reasonable results in mathematical functions (CEC 2005) and spatial structures (with a large number of variables) in comparison with those from GWO, GSA, PSO, and some other common heuristic algorithms shows an enhancement in the performance of the introduced method compared to the other ones.
 

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The wind loads considerably influence lightweight spatial structures. An example of spatial structures is scallop domes that contain various configurations and forms and the wind impact on a scallop dome is more complex due to its additional curvature. In our work, the wind pressure coefficient (Cp ) on the scallop dome surface is studied numerically and experimentally. Firstly, the programming language Formian-K is used for generating the scallop dome configuration. Then, the scallop dome scale model is designed using a CAD/CAM system, and it is constructed in fiberglass. Afterward, the wind tunnel of the atmospheric boundary layer is presented, and the scale model is applied for performing the tests so that the Cp  is obtained. The scallop dome scale model was taken into account in numerical investigation. For simulation of the turbulent flow, Large Eddy Simulation (LES), Reynolds Stress Turbulence Model (RSM), the k-ε RNG, and k-omega Shear Stress Transport (k-ω SST) approaches were used. Lastly, we compared the wind pressure coefficients obtained by Computational Fluid Dynamics (CFD) with the results of the experimental investigation. As indicated by the results, the LES method, particularly, RSM model, can be applied because of lower computational costs for the analysis of other scallop dome configurations for obtaining Cp .
 

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In present study, the effects of optimization on seismic energy spectra including input energy, damping energy and yielding hysteretic energy are parametrically discussed. To this end, 12 generic steel moment-resisting frames having fundamental periods ranging from 0.3 to 3s are optimized by using uniform damage and deformation approaches subjected to a series of 40 non-pule strong ground motions. In order to obtain the optimum distribution of structural properties, an iterative optimization procedure has been adopted. In this approach, the structural properties are modified so that inefficient material is gradually shifted from strong to weak areas of a structure. This process is continued until a state of uniform damage is achieved. Then, the maximum energy demand parameters are computed for different structures designed by optimum load pattern as well as code-based pattern, and the mean energy spectra, energy-based reduction factor and the dispersion of the results are compared and discussed. Results indicate that optimum seismic load pattern can significantly affect the energy demands spectra especially in inelastic range of response. In addition, using energy-based reduction factors of optimum structures in short-period and long-period regions will result in respectively overestimation and underestimation of the required input energy demands for code-based structures, reflecting the difference dose exists in reality between the conventional forced-based methodology and energy-based seismic design approach that can more realistically incorporate the frequency content and duration of earthquake ground motions.
 

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Design optimization of structures with discrete and continuous search spaces is a complex optimization problem with lots of local optima. Metaheuristic optimization algorithms, due to not requiring gradient information of the objective function, are efficient tools for solving these problems at a reasonable computational time. In this paper, the Doppler Effect-Mean Euclidian Distance Threshold (DE-MEDT) metaheuristic algorithm is applied to solve the discrete and continuous optimization problems of the truss structures subject to multiple loading conditions and design constraints. DE-MEDT algorithm is a recently proposed metaheuristic developed based on a physical phenomenon called Doppler Effect (DE) with some idealized rules and a mechanism called Mean Euclidian Distance Threshold (MEDT). The efficiency of the DE-MEDT algorithm is evaluated by optimizing five large-scale truss structures with continuous and discrete variables. Comparing the results found by the DE-MEDT algorithm with those of other existing metaheuristics reveals that the DE-MEDT optimizer is a suitable optimization technique for discrete and continuous design optimization of large-scale truss structures.
 

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The main purpose of this paper was to use a combination of Energy-based design method and whale algorithm (WOA), hereinafter referred to as E-WOA, to optimize steel moment frames and improve the seismic performance. In E-WOA, by properly estimating the seismic input energy and determining the optimal mechanism for the structure, steel frames are designed based on the energy balance method; according to the results, in a suitable search space, optimization is performed using the WOA algorithm. The objective function of the WOA algorithm, in addition to the frame weight, is meant to improve the behavior of the structure based on the performance level criteria of the ASCE41-17 standard and the uniformity of the drift distribution at the frame height. The results show that the initial design of the Energy method reduces the computational volume of the WOA algorithm to achieve the optimal solution and the plastic hinge pattern in frame is more favorable in the E-WOA method than in the design done by the Energy method.
 

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Metaheuristic algorithms are preferred by the many researchers to reach the reliability based design optimization (RBDO) of truss structures. The cross-sectional area of the elements of a truss is considered as design variables for the size optimization under frequency constraints. The design of dome truss structures are optimized based on reliability by a popular metaheuristic optimization technique named Enhanced Vibrating Particle System (EVPS). Finite element analyses of structures and optimization process are coded in MATLAB. Large-scale dome truss of 600-bar, 1180-bar and 1410-bar are investigated in this paper and are compared with the previous studies. Also, a comparison is made between the reliability indexes of Deterministic Design Optimization (DDO) for large dome trusses and Reliability-Based Design Optimization (RBDO).
 

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A dual structural fused system consists of replaceable ductile elements (fuses) that sustain major seismic damage and leave the primary structure (PS) virtually undamaged. The seismic performance of a fused structural system is determined by the combined behavior of the individual PS and fuse components. In order to design a feasible and economic structural fuse concept, we need a procedure to choose the most efficient combination of the PS and fuse systems subject to the stringent constraints of seismic performance and minimum structural cost objectives, simultaneously. In this paper, an efficient method is developed for minimum cost design of dual fused building structures using a performance-based seismic design procedure. The method involves updating a set of reference parameters to find the most suitable combination of PS and fuse structures with satisfactory seismic performance and optimum total structural cost, concurrently. For a set of preselected reference parameters, the structural design variables including primary and fuse structural member sizes are determined through individual linear elastic design processes. Therefore, a limited number of inelastic analyses are required to evaluate seismic response of the combined fused system. The proposed method is applied to seismic design optimization of a moment resisting frame equipped with BRBs as structural fuses. The obtained results indicate that proposed design optimization procedure is sufficiently robust and reliable to design cost-effective structural fuse systems with satisfactory seismic performance.