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This paper presents results of extensive computational experiments in which evolutionary multiobjective algorithms were used to find Pareto-optimal solutions to a complex structural design problem. In particular, Strength-Pareto Evolutionary Algorithm 2 (SPEA2) was combined with a mathematical programming method to find optimal designs of steel structural systems in tall buildings with respect to two objectives (both minimized): the total weight and the maximum horizontal displacement of a tall building. SPEA2 was employed to determine Pareto-optimal topologies of structural members (topology optimization) whose cross-sections were subsequently optimized by the mathematical programming method (sizing optimization). The paper also presents the shape of the Pareto front in this two-dimensional objective space and discusses its dependence on the building's aspect ratio. The results reported provide both qualitative and quantitative knowledge regarding the relationship between the two objectives. They also show the trade-offs involved in the process of conceptual and detailed design of complex structural systems in tall buildings.