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A new meta-heuristic algorithm is proposed for optimal design of reinforced concrete (RC) frame structures subject to combinations of gravity and lateral static loads based on ACI 318-08 design code. In the present work, artificial bee colony algorithm (ABCA) is focused and an improved ABCA (IABCA) is proposed to achieve the optimization task. The total cost of the RC frames is minimized during the optimization process subject to constraints on demand capacity ratios (DCRs) of structural members. Three benchmark design examples are tested using ABCA and IABCA and the results are compared with those of presented in the literature. The numerical results indicate that the proposed IABCA is an efficient computational tool for discrete optimization of RC frames.

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The present paper tackles the optimization problem of double layer grids considering nonlinear behaviour. In this paper, an efficient optimization algorithm is proposed to achieve the optimization task based on the newly developed grey wolf algorithm (GWA) termed as sequential GWA (SGWA). In the framework of SGWA, a sequence of optimization processes is implemented in which the initial population of each process is selected from the neighboring region of the best design found in the previous optimization process. This procedure is repeated until a termination criterion is met. Two illustrative examples are presented and optimization is performed by GWA and SGWA and two other meta-heuristics. The numerical results indicate that the proposed SGWA utperforms the other algorithms in finding optimal design of nonlinear double layer grids.

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In this study an efficient meta-heuristic is proposed for layout optimization of truss structures by combining cellular automata (CA) and firefly algorithm (FA). In the proposed meta-heuristic, called here as cellular automata firefly algorithm (CAFA), a new equation is presented for position updating of fireflies based on the concept of CA. Two benchmark examples of truss structures are presented to illustrate the efficiency of the proposed algorithm. Numerical results reveal that the proposed algorithm is a powerful optimization technique with improved convergence rate in comparison with other existing algorithms.

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The objective of the present paper is to propose a sequential enhanced colliding bodies optimization (SECBO) algorithm for implementation of seismic optimization of steel braced frames in the framework of performance-based design (PBD). In order to achieve this purpose, the ECBO is sequentially employed in a multi-stage scheme where in each stage an initial population is generated based on the information derived from the results of previous stages. The required structural seismic responses, at performance levels, are evaluated by performing nonlinear pushover analysis. Two numerical examples are presented to illustrate the efficiency of the proposed SECBO for tackling the seismic performance-based optimization problem. The numerical results demonstrate the computational advantages of the SECBO algorithm.

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This paper proposes a modified sine cosine algorithm (MSCA) for discrete sizing optimization of truss structures. The original sine cosine algorithm (SCA) is a population-based metaheuristic that fluctuates the search agents about the best solution based on sine and cosine functions. The efficiency of the original SCA in solving standard optimization problems of well-known mathematical functions has been demonstrated in literature. However, its performance in tackling the discrete optimization problems of truss structures is not competitive compared with the existing metaheuristic algorithms. In the framework of the proposed MSCA, a number of worst solutions of the current population is replaced by some variants of the global best solution found so far. Moreover, an efficient mutation operator is added to the algorithm that reduces the probability of getting stuck in local optima. The efficiency of the proposed MSCA is illustrated through multiple benchmark optimization problems of truss structures.

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The main aim of the present study is to optimize steel moment frames in the framework of performance-based design and to assess the seismic collapse capacity of the optimal structures. In the first phase of this study, four well-known metaheuristic algorithms are employed to achieve the optimization task. In the second phase, the seismic collapse safety of the obtained optimal designs is evaluated by conducting incremental dynamic analysis and generating fragility curves. Three illustrative examples including 3-, 6-, and 12-story steel moment frames are presented. The numerical results demonstrate that all the performance-based optimal designs obtained by the metahuristic algorithms are of acceptable collapse margin ratio.

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The present work is aimed at assessing the impact of strong column-weak beam (SCWB) criterion on seismic performance of optimally designed steel moment frames. To this end, different SCWB ratios are considered for steel special moment resisting frame (SMRF) structures and performance-based design optimization process is implemented with the aid of an efficient metaheuristic. The seismic collapse performance of the optimally designed SMRFs is assessed by performing incremental dynamic analysis (IDA) and determining their adjusted collapse margin ratios. Three design examples of 5-, 10-, and 15-story SMRFs are presented to illustrate the efficiency of the proposed methodology.

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Economy and safety are two important components in structural design process and stablishing a balance between them indeed results in improved structural performance specially in large-scale structures including space lattice domes. Topology optimization of geometrically nonlinear single-layer lamella, network, and geodesic lattice domes is implemented using enhanced colliding-bodies optimization algorithm for three different spans and two different dead loading conditions. Collapse reliability index of these optimal designs is evaluated to assess the safety of the structures against overall collapse using Monte-Carlo simulation method. The numerical results of this study indicate that the reliability index of most of the optimally designed nonlinear lattice domes is low and this means that the safety of these structures against overall collapse is questionable.

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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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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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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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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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The main aim of this study, is to evaluate the seismic reliability of steel concentrically braced frame (SCBF) structures optimally designed in the context of performance-based design. The Monte Carlo simulation (MCS) method and neural network (NN) techniques were utilized to conduct the reliability analysis of the optimally designed SCBFs. Multi-layer perceptron (MLP) trained by back propagation technique was used to evaluate the required structural responses and then the total exceedence probability associated with the seismic performance levels was estimated by the MCS method. Three numerical examples of 5-, 10-, and 15-story SCBFs with fixed and optimal topology of braces are presented and their probability of failure was evaluated considering the resistance characteristics and the seismic loading of the structures. The numerical results indicate that the SCBFs with optimal topology of braces were more reliable than those with fixed topology of braces.  
 

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The purpose of the current study is to design steel moment resisting frames for optimal weight in the context of performance-based design. The performance-based design optimization of steel moment frames is a highly nonlinear and complex optimization problem having many local optima. Therefore, an efficient algorithm should be used to deal with this class of structural optimization problems. In the present study, a modified Newton metaheuristic algorithm (MNMA) is proposed for the solution of the optimization problem. In fact, MNMA is the improved version of the original Newton metaheuristic algorithm (NMA), which is a multi-stage optimization technique in which an initial population is generated at each stage based on the results of the previous stages. Two illustrative examples of 5-, and 10-story steel moment frames are presented and a number of independent optimization runs are achieved by NMA and MNMA. The numerical results demonstrate the better performance of the proposed MNMA compared to the NMA in solving the performance-based optimization problem of steel moment frames.
 

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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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In this paper an enhanced ant colony optimization algorithm with a direct constraints handling strategy is proposed for the optimization of reinforced concrete frames. The construction cost of reinforced concrete frames is considered as the objective function, which should be minimized subject to geometrical and behavioral strength constraints. For this purpose, a new probabilistic function is added to the ant colony optimization algorithm to directly satisfy the geometrical constraints. Furthermore, the position of an ant in each iteration is updated if a better solution is found in terms of objective value and behavioral strength constraints satisfaction. Five benchmark design examples of planar reinforced concrete frames are presented to illustrate the efficiency of the proposed algorithm.  
 

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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 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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The main objective of this study is to predict the maximum inter-story drift ratios of steel moment-resisting frame (MRF) structures at different seismic performance levels using feed-forward back-propagation (FFBP) neural network models. FFBP neural network models with varying numbers of hidden layer neurons (5, 10, 15, 20, and 50) were trained to predict the maximum inter-story drift ratios of 5- and 10-story steel MRF structures. The numerical simulations indicate that FFBP neural network models with ten hidden layer neurons better predict the inter-story drift ratios at seismic performance levels for both 5- and 10-story steel MRFs compared to other neural network models.

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