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Evolution Strategies (ES) are a class of Evolutionary Algorithms based on Gaussian mutation and deterministic selection. Gaussian mutation captures pair-wise dependencies between the variables through a covariance matrix. Covariance Matrix Adaptation (CMA) is a method to update this covariance matrix. In this paper, the CMA-ES, which has found many applications in solving continuous optimization problems, is employed for size optimization of steel space trusses. Design examples reveal competitive performance of the algorithm compared to the other advanced metaheuristics.

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An efficient method for size and layout optimization of the truss structures is presented in this paper. In order to this, an efficient method by combining an improved discrete particle swarm optimization (IDPSO) and method of moving asymptotes (MMA) is proposed. In the hybrid of IDPSO and MMA, the nodal coordinates defining the layout of the structure are optimized with MMA, and afterwards the results of MMA are used in IDPSO to optimize the cross-section areas. The results show that the hybrid of IDPSO and MMA can effectively accelerate the convergence rate and can quickly reach the optimum design.

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This paper presents a design process using a course grained parallel genetic algorithm to optimize three-dimensional steel moment frames by considering the axial force and biaxial bending moments interaction in plastic hinge formation. The objective function is to minimize the total weight of the structure subjected to the reliability constraint of the structural system. System reliability analysis is performed through the proposed Modified Latin Hypercube Simulation (M-LHS) Method. For optimization, a 3DSMF-RBO program is written in CSHARP programming language. The reliability analysis results show a large decrease in the number of simulation samples and subsequently a decrease in the execution time of optimization computation. The optimization results indicate that by considering interaction of the axial force and biaxial bending moments in plastic hinge formation rather than the only bending moment, to some extent increases the total weight of the designed structure.

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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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The existence of uncertainties in engineering problems makes it essential to consider these effects at all times. Robust design optimization allows a design to be made less sensitive to uncertain input parameters. Actually, robust design optimization reduces the sensitivity of the objective function and the variations in design performance when uncertainty exists. In this study, two space trusses were optimized based on the modulus of elasticity, yield stress, and cross-sectional uncertainties in order to increase the response robustness and decrease the weight. The displacement of one node has been used as the criterion for Robust Design Optimization (RDO) of these two structures. Two trusses with 72 members and 582 members are considered, which are famous trusses in the field of structural optimization. Also, the EVPS meta-heuristic algorithm was employed which is an enhanced version of the VPS algorithm based on the single degrees of freedom of a system with viscous damping.
 

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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.
 

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Vibrating particles system (VPS) is a swarm intelligence-based optimizer inspired by free vibration with a single degree of freedom systems. VPS is one of the well-known algorithms in structural optimization problems. However, its performance can be improved to find a better solution. This study introduces an improved version of the VPS using the statistical regeneration mechanism for the optimal design of the structures with discrete variables. The improved version is named VPS-SRM, and its efficiency is tested in the three real-size optimization problems. The optimization results reveal the capability and robustness of the VPS-SRM for the optimal design of the structures with discrete sizing variables.