en Optimal design Optimal design پژوهشي Research 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. plastic analysis, colliding bodies optimization, enhanced colliding bodies optimization, collapse load factor, planar frames. 479 492 http://ijoce.iust.ac.ir/browse.php?a_code=A-10-66-80&slc_lang=en&sid=1 A. Kaveh 18003194753284600872 18003194753284600872 Yes M.H. Ghafari 18003194753284600873 18003194753284600873 No