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One of the main tasks of engineers is to design structural systems light and economic as possible, yet resistant enough to withstand all possible loads arising during their service life and to absorb the induced seismic energy in a controlled and predictable fashion. The traditional trial-and-error design approach is not capable to determine an economical design satisfying also the code requirements. Structural design optimization, on the other hand, provides a numerical procedure that can replace the traditional design approach with an automated one. The objective of this work is to propose a performance-based seismic design procedure, formulated as a structural design optimization problem, for designing steel and steel-concrete composite buildings subject to interstorey drift limitations. In particular a straightforward design procedure is proposed where the influence on both record and incident angle is considered. For this purpose six test examples are considered, in particular three steel and three steel-concrete composite buildings are optimally designed for minimum initial cost.

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This paper presents an improved multi-objective evolutionary algorithm (IMOEA) for the design of planar steel frames. By considering constraints as a new objective function, single objective optimization problems turned to multi objective optimization problems. To increase efficiency of IMOEA different Crossover and Mutation are employed. Also to avoid local optima dynamic interference of mutation and crossover are considered. Feasible particles called elites which are very helpful for better mutation and crossover considered as a tool to increase efficiency of proposed algorithm. The proposed evolutionary algorithm (IMOEA) is utilized to solve three well-known classical weight minimization problems of steel moment frames. In order to verify the suitability of the present method, the results of optimum design for planar steel frames are obtained by present study compared to other researches. Results indicate that, as far as the convergence, speed of the optimization process and quality of optimum design are concerned behavior, IMOEA is significantly superior to other meta-heuristic optimization algorithms with an acceptable global answer.

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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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In this article, spectral matching of ground motions is presented via the Mouth Brooding Fish (MBF) algorithm that is recently developed. It is based on mouth brooding fish life cycle. This algorithm utilizes the movements of the mouth brooding fish and their children’s struggle for survival as a pattern to find the best possible answer. For this purpose, wavelet transform is used to decompose the original ground motions to several levels and then each level is multiplied by a variable. Subsequently, this algorithm is employed to determine the variables and wavelet transform modifies the recorded accelerograms until the response spectrum gets close to a specified design spectrum. The performance of this algorithm is investigated through a numerical example and also it is compared with CBO and ECBO algorithms. The numerical results indicate that the MBF algorithm can to construct very promising results and has merits in solving challenging optimization problems.
 

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Earthquakes are random phenomena and there has been no report of similar earthquakes occurring worldwide. Therefore, traditional methods of designing buildings based on past earthquakes with inappropriate discontinuity joints are sometimes ineffective for vital structures. This may lead to collision and destruction of adjacent structures during a severe earthquake. As in the Iranian Standard No. 2800-4, this distance should be at least five-thousandths of the building height from the base level to the adjacent ground boundary for buildings up to eight stories to prevent or reduce this damage. Also, for important or/with more than eight-story buildings, this value is determined using the maximum nonlinear lateral displacement of the structures by considering the effects of the P-delta. Also, if the properties of the adjacent building are not known, this distance should be considered at least equal to 70% of the maximum nonlinear lateral displacement of the structures. The main objective of this study is to investigate the adequacy of the discontinuity joint introduced in the Iranian Standard No. 2800-4 based on the critical excitation method. This method calculates critical earthquakes for three buildings (e.g., three-, seven- and eleven-story moment frames) by considering some constraints on the energy, peak ground acceleration, Fourier amplitude, and strong ground motion duration. The results indicate that the minimum gap between two adjacent buildings derived from the existing codes is lower than those calculated using the critical excitation method. Therefore, oscillation might occur if a structure is designed according to the seismic codes and subjected to a critical earthquake.

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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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The dual steel system comprising moment-resisting frames integrated with steel shear walls represents an advanced seismic-resistant solution in structural engineering. This system synergistically combines the high ductility and energy dissipation capacity of steel frames with the substantial lateral stiffness and strength provided by steel shear walls. Proper design of such systems requires precise determination of the optimal location, thickness, and mechanical properties of the shear walls parameters that critically govern seismic performance, structural safety, material efficiency, and construction cost. To achieve an optimal balance between performance and economy, the problem is formulated as a constrained optimization task. This study employs the recently developed Puma Optimizer (PO) and introduces a novel enhanced variant, termed the Upgraded Puma Optimizer (U-PO). The key novelty of this work lies in the integration of Lévy flight distribution into the PO framework, replacing conventional Brownian motion to significantly strengthen the exploration–exploitation balance, global search capability, and convergence speed. This modification enables more effective handling of complex, high-dimensional structural optimization problems. The performance of the proposed U-PO is rigorously evaluated through the optimal design of three benchmark steel frames (1-, 10-, and 20-story) equipped with shear walls. The primary objective is to minimize the total structural weight while satisfying strength, serviceability, and seismic design requirements according to relevant building codes. Decision variables include frame member cross-sections as well as the location and thickness of shear walls. Comparative results against several established metaheuristic algorithms (HHO, AOA, and GWO) demonstrate the superiority of the U-PO, confirming that the incorporation of Lévy flights leads to markedly improved convergence behavior and solution quality. The U-PO consistently yields superior designs featuring notable reductions in structural weight through more efficient sizing and strategic placement of steel shear walls.