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In a structural system, the connections (i.e., between the structural elements and the structure to the ground) play an important role in the integrity and stability of the system. So, using the certain pre-defined conventional properties for these systems can stand far away from the expected optimal condition. In this regard, the current study deals with optimal design (i.e., cost and geometry parameters under different loading conditions) of the footing systems applied in the precast industrial buildings and the concrete bracket system as the privilege connection type in the RC frames. To provide a broad perspective about the optimal design of these systems, several distinct optimization models are generated and solved. For solving the proposed optimization problems, a recently developed self-adaptive and non-gradient-based method, so-called Fuzzy Differential Evolution Incorporated Virtual Mutant (FDEVM), is utilized …