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In rigid plastic analysis one of the most widely applicable methods that is based on the minimum principle, is the combination of elementary mechanisms which uses the upper bound theorem. In this method a mechanism is searched which corresponds to the smallest load factor. Mathematical programming can be used to optimize this search process for simple frames, and meta-heuristic algorithms are the best choice for larger frame structures. In this paper, the Colliding Bodies Optimization (CBO) and its enhanced variant (ECBO) are employed to optimize the process of finding an upper bound for the collapse load factor of the planar frames. The efficiency of these algorithms is compared to that of the Particle Swarm Optimization (PSO) algorithm through four numerical examples form multi-bay multi-story frames and pitched roof frames.

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Natural frequencies of a structure give useful information about the structural response to dynamic loading. These frequencies should be far enough from the critical frequency range of dynamic excitations like earthquakes in order to prevent the resonance phenomenon sufficiently. Although there are many investigations on optimization of truss structures subjected to frequency constraints, just a few studies have been considered for optimal design of frame structures under these constraints. In this paper, a recently proposed metaheuristic algorithm called Adaptive Charged System Search (ACSS) is applied to optimal design of steel frame structures considering the frequency constraints. Benchmark design examples are solved with the ACSS, and optimization results are illustrated in terms of some statistical indices, convergence history and solution quality. The design examples include three planar steel frames with small to large number of design variables. Results show that the ACSS outperforms the charged system search algorithm in this sizing optimization problem.