In　this　paper,　a　multi-objective　optimization　of　a　single　tuned　mass　damper　is　proposed　at　the　aim　to　control　vibrations　induced　in　building　structures　under　low-moderate　earthquakes.　The　optimum　design　is　carried　out　by　considering　both　economic　and　performance　criteria.　The　cost　of　the　device　is　the　economic　objective　that　is　assumed　directly　related　to　its　mechanical　parameters.　At　the　aim　to　control　the　damage　level　and　the　behaviour　of　components　and　equipment,　the　ratio　between　the　absolute　accelerations　of　the　protected　structure　and　the　unprotected　one　is　assumed　as　the　device　performance.　A　multi-objective　optimization　is　then　formulated,　and　Pareto　optimum　solutions　are　achieved　by　the　Non-dominated　Sorting　Genetic　Algorithm　in　its　second　version.　Finally,　a　sensitivity　analysis　of　the　optimum　solution　with　respect　to　some　input　data　is　carried　out.　Copyright　©　2016　John　Wiley　&　Sons,　Ltd.　Copyright　©　2016　John　Wiley　&　Sons,　Ltd.