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This paper presents an efficient meta-heuristic algorithm for optimization of double-layer scallop domes subjected to earthquake loading. The optimization is performed by a combination of harmony search (HS) and firefly algorithm (FA). This new algorithm is called harmony search firefly algorithm (HSFA). The optimization task is achieved by taking into account geometrical and material nonlinearities. Operation of HSFA includes three phases. In the first phase, a preliminary optimization is accomplished using HS. In the second phase, an optimal initial population is produced using the first phase results. In the last phase, FA is employed to find optimum design using the produced optimal initial population. The optimum design obtained by HSFA is compared with those of HS and FA. It is demonstrated that the HSFA converges to better solution compared to the other algorithms.

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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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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 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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In recent years many researchers prefer to use metaheuristic algorithms to reach the optimum design of structures. In this study, an Enhanced Vibrating Particle System (EVPS) is applied to get the minimum weight of large-scale dome trusses under frequency constraints. Vibration frequencies are important parameters, which can be used to control the responses of a structure that is subjected to dynamic excitation. The truss structures were analyzed by finite element method and optimization processes were implemented by the computer program coded in MATLAB. The effectiveness and efficiency of the Enhanced Vibrating Particle System (EVPS) is investigated in three large-scale dome trusses 600-, 1180-, and 1410-bar to obtain the weight optimization with frequency constraints.

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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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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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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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This study presents the application of the Self-Adaptive Enhanced Vibrating Particle System (SA-EVPS) algorithm for large-scale dome truss optimization under frequency constraints. SA-EVPS incorporates self-adaptive parameter control, memory-based learning mechanisms, and statistical regeneration strategies to overcome limitations of traditional metaheuristic algorithms in structural optimization. The algorithm's performance is evaluated on three benchmark dome structures: (1) a 600-bar single-layer dome with 25 design variable groups, (2) an 1180-bar single-layer dome with 59 design variable groups, and (3) a 1410-bar double-layer dome with 47 design variable groups, all subject to natural frequency constraints. Comparative analysis against five state-of-the-art algorithms—Dynamic Particle Swarm Optimization (DPSO), Colliding Bodies Optimization (CBO), Enhanced Colliding Bodies Optimization (ECBO), Vibrating Particles System (VPS), and Enhanced Vibrating Particles System (EVPS)—demonstrates SA-EVPS's superior convergence characteristics and solution quality. Results show that SA-EVPS consistently achieves the lowest structural weights with remarkable stability across all test cases. The algorithm's self-adaptive mechanisms eliminate manual parameter tuning while the statistical regeneration mechanism prevents premature convergence in large-scale optimization problems. This research establishes SA-EVPS as a robust and efficient metaheuristic for frequency-constrained structural optimization of complex dome structures.

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This study employs Monte Carlo simulation together with a deep feedforward neural network to predict the natural frequencies of truss domes under uncertainty. Material and/or geometric properties of these structures are modeled as random variables, and their influence on the natural frequencies is examined. Monte Carlo simulation is applied to perform stochastic eigenvalue analyses of the finite element models. To reduce computational cost, a deep neural network is trained to predict natural frequencies in place of repeated eigenvalue solves, accelerating the overall simulation. Bayesian optimization is used to tune the network hyperparameters. Numerical examples show that the proposed approach substantially improves computational efficiency and predictive accuracy compared with direct Monte Carlo simulation for domes with random inputs.