As　a　structural　optimization　technique,　topology　optimization　is　an　important　tool　for　helping　designers　to　determine　the　most　suitable　shape　of　a　structure.　With　this　powerful　tool,　designers　can　define　families　of　candidate　solutions　by　modifying　the　input　volume　reduction　(VR)　ratio,　reducing　the　structural　weight　as　much　as　possible.　However,　finding　the　best　compromise　between　material　savings　and　structural　performance　among　these　candidate　solutions　is　a　critical　issue　for　designers.　To　deal　with　this　issue,　an　optimization　index　(OI)　is　presented　in　this　paper.　It　provides　a　mathematical　procedure　that　highlights　the　best　choice　among　several　candidate　solutions　obtained　by　the　optimization　procedure.　The　index　was　originally　defined　in　a　previous　study　on　the　structural　optimization　of　composite　steel-concrete　bridges.　In　this　paper,　a　generalized　version　of　the　original　optimization　index　is　introduced　and　used　to　investigate　a　particular　aspect　related　to　concrete　shell-supported　bridges.　Starting　from　three　shell-supported　footbridges,　the　shapes　of　which　are　the　final　result　of　form-finding　optimization　procedures,　different　starting　models　are　defined,　and　each　is　characterized　by　different　edge-stiffening　conditions.　Despite　using　an　anticlastic　shell　shape,　unavoidable　tensile　stresses　occur　because　of　the　thickness　of　the　shell,　variations　in　the　material,　the　loading　of　the　deck,　and　other　factors.　For　each　starting　model,　a　finite-element　topological　optimization　conducted　with　the　solid　isotropic　material　with　penalization　(SIMP)　method　is　performed　to　minimize　the　weight　(i.e.,　volume)　of　the　shell　by　a　certain　percentage.　According　to　the　results　obtained　from　topology　optimization,　the　proposed　generalized　optimization　index　(OI*)　analytical　formulation　is　discussed　in　detail,　and　its　effectiveness　is　validated.