Offshore　structures　are　critical　infrastructure　in　the　field　of　ocean　engineering,　which　may　under　the　threat　of　earthquake　shaking,　especially　when　they　are　located　in　the　high-risk　seismic　zones.　This　paper　proposes　using　an　innovative　inerter-based　damping　isolation　system　(IDIS)　for　the　seismic　protection　of　offshore　platforms.　The　concept　of　IDIS　is　firstly　proposed　by　integrating　the　conventional　bearings　with　inerter-based　dampers　(IDs).　An　analytical　model　of　the　system　is　established,　and　the　corresponding　equilibrium　equations　of　motion　are　derived.　Without　loss　of　generality,　the　deck　acceleration,　displacement　on　the　jacket　cap,　and　isolating　layer　deformation　are　chosen　as　the　performance　objectives,　and　parametric　analyses　are　performed　to　investigate　the　influences　of　the　key　parameters　of　IDIS　on　each　performance　objective.　A　performance-based　multi-objective　optimization　framework　is　then　developed　for　determining　the　optimal　parameters　of　IDIS.　The　control　effectiveness　of　IDIS　is　demonstrated　in　the　frequency　domain　and　compared　to　that　of　the　traditional　damping　isolation　system　(DIS).　Finally,　case　studies　are　performed　to　further　investigate　the　performance　of　IDIS　subjected　to　natural　seabed　ground　motions.　The　results　show　that　properly　optimized　IDIS　is　more　effective　than　the　conventional　DIS　in　terms　of　not　only　the　structural　responses　but　also　the　deformation　of　the　isolating　layer.　The　proposed　IDIS　can　be　an　attractive　and　effective　alternative　to　the　conventional　DIS　in　the　vibration　control　of　offshore　platforms.　©　2023　Elsevier　Ltd