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Evaluating the performance degradation of the earthquake-damaged structure and optimizing the placement of dampers is important for retrofitting post-earthquake structures. In this study, a damage evolution model is developed to evaluate the degradation of strength, stiffness, and energy dissipation capacity for earthquake-damaged structures. The proposed damage model is validated using previous experimental results based on the nonlinear finite element analysis. Then, research on the optimal design of damper parameters and quantity is carried out. Considering the optimization range of earthquake-damaged structures, a genetic algorithm with multi-objective functions is developed to determine the optimal placement of viscoelastic dampers in damaged structures. The results demonstrate that the proposed damage model can effectively describe the performance degradation of damaged structures. The control effects of the acceleration response increase exhibited a maximum enhancement of 3.38 times after accounting for the optimization range of earthquake-damaged structures. The optimization results of the multi-objective function with the optimization range are better aligned with the objectives of designers. • A damage model is developed to evaluate the degradation of strength, stiffness, and energy dissipation for structures. • Understanding of the beneficial effect of the viscoelastic damper on the seismic response for earthquake-damaged structures. • A genetic algorithm with multi-objective functions is developed to optimize the design and placement of VE dampers. • The control effects of the acceleration response increase exhibited a maximum enhancement of 3.38 times. • The optimization results of the proposed method are better aligned with the objectives of designers. [ABSTRACT FROM AUTHOR]