||The impressive numerical research investigations and remarkable computational capability arising in the last fifty years have fostered considerable developments in the design optimization of structural engineering. Although composite steel and concrete structures have generally been recognized as one of the effective ways to minimize the costs in tall building construction, additional savings in material cost may be further obtained via a systematic goal-oriented optimal design process. Due to the complex nature of composite tall building design, an automatic resizing approach accounting for full or partial composite interaction is still lacking in the view of the current iterative and cumbersome "trial-and-error" design method. The purpose of this research study is to devise a numerical optimization approach towards achieving minimum cost design for lateral resisting composite frameworks subject to top and interstorey drift as well as fabrication sizing constraints. Application of the algorithm implementing the aforementioned approach is demonstrated through designing both two- and three-dimensional composite frameworks in accordance with the design provisions and fabrication requirements. The first phase of this research study involves a comprehensive review of elastic interaction theories and development of design specifications and recommendations for composite structures, aiming at a well-defined design problem formulation for the optimization procedure. An assessment of the design provisions and available formulae on effective flexural and axial stiffness of composite beams and columns is made in this review and the most preferable selection is adopted. Applying effective sectional properties for composite elements and the principle of virtual energy, the lateral stiffness optimization problem for composite structures can be expressed explicitly in terms of basic sizing variables. Then a rigorously derived Optimality Criteria (OC) method is developed to find the optimum solution wherein the satisfaction of both the drift and sizing constraints are assured. Associated with the solution process is the discussion of some optimization techniques, such as scaling and reciprocal approximation. They have been shown useful and efficient in improving the convergence performance of the optimization problem. Illustrative examples of composite frames ranging from 4-bay 1-storey academic frame building to 3-bay multiple storey large planar framework are presented. In addition, a l-bay 12-storey academic composite frame structure is designed for comparison purposes with the same pure steel frame structure model as found in other literature.