With　the　rapidly　development　of　mobile　cloud　computing　(MCC),　the　Internet　of　Things　(IoT),　and　artificial　intelligence　(AI),　user　equipment　(UEs)　are　facing　explosive　growth.　In　order　to　effectively　solve　the　problem　that　UEs　may　face　with　insufficient　capacity　when　dealing　with　computationally　intensive　and　delay　sensitive　applications,　we　take　Mobile　Edge　Computing　(MEC)　of　the　IoT　as　the　starting　point　and　study　the　computation　offloading　strategy　of　UEs.　First,　we　model　the　application　generated　by　UEs　as　a　directed　acyclic　graph　(DAG)　to　achieve　fine-grained　task　offloading　scheduling,　which　makes　the　parallel　processing　of　tasks　possible　and　speeds　up　the　execution　efficiency.　Then,　we　propose　a　multi-population　cooperative　elite　algorithm　(MCE-GA)　based　on　the　standard　genetic　algorithm,　which　can　solve　the　offloading　problem　for　tasks　with　dependency　in　MEC　to　minimize　the　execution　delay　and　energy　consumption　of　applications.　Experimental　results　show　that　MCE-GA　has　better　performance　compared　to　the　baseline　algorithms.　To　be　specific,　the　overhead　reduction　by　MCE-GA　can　be　up　to　72.4%,　38.6%,　and　19.3%,　respectively,　which　proves　the　effectiveness　and　reliability　of　MCE-GA.　©　2021　by　the　authors.　Licensee　MDPI,　Basel,　Switzerland.