Ranked　keyword　search　has　gained　Ranked　keyword　search　has　gained　traction　due　to　its　attractive　properties　such　as　flexibility　and　accessibility.　However,　most　existing　ranked　keyword　search　schemes　ignore　the　semantic　associations　between　the　documents　and　queries.　To　solve　this　challenging　issue　in　cloud-assisted　edge　computing,　we　first　design　the　Semantic-aware　Ranked　Multi-keyword　Search　(SRMS)　scheme　by　adopting　the　Latent　Dirichlet　Allocation　(LDA)　topic　model　and　the　Chinese　Remainder　Theorem　(CRT)-based　secret　sharing　mechanism.　Considering　that　the　cloud　server　may　be　malicious,　we　implement　a　basic　verification　mechanism　in　SRMS　to　verify　the　correctness　and　completeness　of　search　results　and　extend　this　verification　mechanism　in　cloud-assisted　edge　computing　scenarios.　Formal　security　analysis　proves　that　SRMS　and　extended　result　verification　mechanisms　are　secure　in　both　the　known　ciphertext　model　and　the　known　background　model.　Extensive　experiments　using　the　real-world　dataset　demonstrate　that　SRMS　is　efficient　and　practical.