Buckling-restrained braces (BRBs) are one of the popular seismic-resistant structural systems. The cross-sectional area and length of the BRB is one of the most important characteristics of these braces that directly affect their cost. Since columns, beams, and connections are designed for the maximum force delivered by the brace, the decrease in cross-sectional area of the BRB causes a decrease in dimensions of the columns and beams. On the other hand, drift uniformity over the height of the structure is accounted as a structural health index and would lead in efficiency of BRB system in a seismic event. The aim of this study is then to optimize three objectives including weight of the BRB, weight of the structure, and uniformity of the drift profile over the height of structure by changing the cross-sectional area and the length of the BRB at the height of the structure using genetic algorithms and other multi-objective optimization algorithms. Optimization is based on the results of nonlinear time history analysis of 2D frames. Seven earthquake records are selected to conduct nonlinear time history analysis using OpenSees software. To this end, the desired functions and constraints were defined in the genetic algorithms, i.e., NSGA_II, MOPSO, MOEA_D, PESA_II, SPEA_II, and the initial created population was entered as the initial cross-sectional area and length of the braces in the OpenSees software. The optimization results showed that for all three objective functions, the weight of the structure, the weight of the BRB brace, and the uniformity of drift in the height of the structure can be optimized largely using a nonlinear time history analysis.