Nowadays,　Internet　of　Things　Devices　(IOTDs)　support　numerous　applications　that　require　extensive　computational　resources　and　are　sensitive　to　delays.　Nevertheless,　IOTDs　are　constrained　by　limited　computational　power　and　battery　life,　preventing　them　from　processing　all　tasks　in　real-time.　Computation　offloading　provides　a　solution　to　these　problems　where　IOTDs　can　offload　part　of　their　tasks　to　edge　servers　for　execution.　Small　Base　Stations　(SBSs)　are　located　closer　to　IOTDs,　which　act　as　edge　servers.　However,　SBSs　have　limited　computing　resources　compared　with　a　Cloud　Data　Center　(CDC).　Therefore,　a　heterogeneous　edge-cloud　system　is　often　deployed　in　urban　areas　for　computation　offloading.　In　addition,　attaining　the　lowest　cost　in　such　a　system　while　satisfying　the　delay　requirements　of　tasks　presents　a　significant　challenge.　In　this　work,　a　computation　offloading　strategy　aimed　at　minimizing　the　overall　system　cost　is　proposed.　Initially,　an　optimization　problem　with　real-world　constraints　is　defined,　leveraging　the　hybrid　architecture　as　its　basis.　Then,　a　novel　swarm　optimization　algorithm　named　Grey　wolf　optimization　embedded　with　Simulated　annealing　and　Genetic　learning　(GSG)　is　proposed　to　solve　this　optimization　problem.　GSG　optimizes　resource　allocation　and　task　offloading　among　IOTDs,　SBSs,　and　CDC.　Simulation　experiments　involving　real-life　tasks　demonstrate　that　GSG　achieves　a　significantly　lower　system　cost　than　its　existing　peers.　©　2024　IEEE.