Optimum design of the structures, in other words designing the structures with minimum weight is one of the major research areas in structural engineering. The priority during optimization process is to ensure whether the necessary conditions are satisfied or not. In this study, the optimization of steel frame systems is carried out for traditional and dynamic constraints by using a genetic algorithm that mimics the biological processes. The stress constraints are determined according to TS648-Turkish code for design and construction of steel structures. Furthermore, displacement constrains are considered in the optimization procedure. In addition, natural frequencies are incorporated as dynamic constraints. Optimum design of multi-story plane frames is obtained and comparisons with the results of previous studies are made. The same design processes are repeated for the case of frames with composite beams. A program is coded in MATLAB to carry out all these applications. Results obtained in the study for the frame systems are also verified by SAP2000. It is concluded that the weight of the frames with composite beams are fewer and the dynamic constraints affect the design.