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Many methods have been developed for structural size and configuration optimization in which cross-sectional areas are usually assumed to be continuous. In most practical structural engineering design problems, however, the design variables are discrete. This paper proposes two efficient structural optimization methods based on the harmony search (HS) heuristic algorithm that treat both discrete sizing variables and integrated discrete sizing and continuous geometric variables. The HS algorithm uses a stochastic random search instead of a gradient search so the former has a new-paradigmed derivative. Several truss examples from the literature are also presented to demonstrate the effectiveness and robustness of the new method, as compared to current optimization methods.

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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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In this paper, the discrete method of eigenvectors of covariance matrix has been used to weight minimization of steel frame structures. Eigenvectors of Covariance Matrix (ECM) algorithm is a robust and iterative method for solving optimization problems and is inspired by the CMA-ES method. Both of these methods use covariance matrix in the optimization process, but the covariance matrix calculation and new population generation in these two methods are completely different. At each stage of the ECM algorithm, successful distributions are identified and the covariance matrix of the successful distributions is formed. Subsequently, by the help of the principal component analysis (PCA), the scattering directions of these distributions will be achieved. The new population is generated by the combination of weighted directions that have a successful distribution and using random normal distribution. In the discrete ECM method, in case of succeeding in a certain number of cycles the step size is increased, otherwise the step size is reduced. In order to determine the efficiency of this method, three benchmark steel frames were optimized due to the resistance and displacement criteria specifications of the AISC-LRFD, and the results were compared to other optimization methods. Considerable outputs of this algorithm show that this method can handle the complex problems of optimizing discrete steel frames.

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This study is devoted to discrete sizing optimization of truss structures employing an efficient discrete evolutionary meta-heuristic algorithm which uses the Newton gradient-based method as its updating scheme and it is named here as Newton Meta-heuristic Algorithm (NMA). In order to enable the NMA population-based meta-heuristic to effectively explore the discrete design space, a term containing the best solution found is added to the basic updating rule of the algorithm. The efficiency of the proposed NMA metaheuristic is illustrated by presenting five benchmark discrete truss optimization problems and comparing the results with literature. The numerical results demonstrate that the NMA is a robust and powerful meta-heuristic algorithm for dealing with the discrete sizing optimization problems of steel trusses.

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The efficiency of braced structures depends significantly on structure response under seismic loads. The main design challenge for these type of structures is to select shape, number of spans, and type of connections appropriately. Therefore, introducing an optimized and cost-effective design including a certain level of safety and performance against natural hazards seems to be an inevitable necessity. The present work introduces a performance-based design for braced steel structures as well as an optimized arrangement of braces and connection types via using finite difference algorithm. The results show that the latter two factors are very important and necessary to achieve an optimized design for braced steel structures.

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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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Metaheuristic algorithms have become increasingly popular in recent years as a method for determining the optimal design of structures. Nowadays, approximate optimization methods are widely used. This study utilized the Self Adaptive Enhanced Vibrating Particle System (SA-EVPS) algorithm as an approximate optimization method, since the EVPS algorithm requires experimental parameters. As a well-known and large-scale structure, the 582-bar spatial truss structure was analyzed using the finite element method, and optimization processes were implemented using MATLAB. In order to obtain weight optimization, the self-adaptive enhanced vibration particle system (SA-EVPS) is compared with the EVPS algorithm.