An　improved　formula　to　determine　the　equivalent　viscous　damping　ratio　of　a　single-degree-of-freedom　(SDOF)　bilinear　oscillator　is　proposed　in　this　paper,　which　simultaneously　considers　the　influence　of　the　initial　period,　ductility　ratio,　and　strain　hardening　ratio.　A　large　number　of　parameters　are　considered　in　order　to　present　comprehensive　results.　Based　on　the　assumption　of　secant　stiffness,　several　equivalent　linearization　approaches　are　evaluated　through　parametric　analyses.　Then,　optimization　analyses　are　performed　using　a　genetic　algorithm　to　identify　the　variation　trend　of　optimal　damping　ratios.　A　new　formula　of　an　equivalent　viscous　damping　ratio　is　proposed　by　nonlinear　regression　analyses　of　the　optimal　damping　ratios.　Finally,　the　proposed　approach　is　validated　and　the　results　show　that　the　proposed　approach　leads　to　better　estimates　of　maximum　inelastic　displacement　response　in　the　entire　parameter　space　considered　in　this　study　when　compared　with　other　equivalent　linearization　approaches.　(C)　2015　American　Society　of　Civil　Engineers.