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One of the main tasks of engineers is to design structural systems light and economic as possible, yet resistant enough to withstand all possible loads arising during their service life and to absorb the induced seismic energy in a controlled and predictable fashion. The traditional trial-and-error design approach is not capable to determine an economical design satisfying also the code requirements. Structural design optimization, on the other hand, provides a numerical procedure that can replace the traditional design approach with an automated one. The objective of this work is to propose a performance-based seismic design procedure, formulated as a structural design optimization problem, for designing steel and steel-concrete composite buildings subject to interstorey drift limitations. In particular a straightforward design procedure is proposed where the influence on both record and incident angle is considered. For this purpose six test examples are considered, in particular three steel and three steel-concrete composite buildings are optimally designed for minimum initial cost.