The　sudden　surge　of　various　applications　poses　great　challenges　to　the　computation　capability　of　mobile　devices.　To　address　this　issue,　computation　offloading　to　multi-access　edge　computing　(MEC)　was　proposed　as　a　promising　paradigm.　This　paper　studies　partial　computation　offloading　scenario　by　considering　time　delay　and　energy　consumption,　where　the　task　can　be　splitted　into　several　blocks　and　computed　both　in　local　devices　and　MEC,　respectively.　Since　the　formulated　problem　is　a　nonconvex　problem,　this　paper　proposes　an　ant　colony-based　algorithm　to　achieve　the　suboptimal　solution.　Specifically,　the　proposed　method　first　establish　a　multi-user　one-　MEC　scenario,　in　which　user　devices　are　able　to　offload　some　part　of　the　task　to　MEC　server.　Then,　it　develops　an　ant　colony-based　algorithm　to　decide　the　offloading　parts　and　allocation　strategy　of　MEC　resources　to　minimize　system　cost.　Finally,　simulation　results　show　the　effectiveness　of　the　proposed　algorithm　in　terms　of　system　cost　and　demonstrate　that　it　outperforms　other　existing　methods.　©　2023,　Beijing　University　of　Posts　and　Telecommunications.　All　rights　reserved.