With　continuous　emergence　of　the　new　mobile　applications,　multi-access　edge　computing　(MEC)　is　generally　regarded　as　a　promising　technology　to　enable　the　computing-intensive　and　delay-sensitive　services　at　the　mobile　devices　by　pushing　more　computing　resources　to　the　network　edge.　However,　computation　offloading,　which　has　been　a　hot　topic　for　MEC　networks,　is　still　facing　the　challenges　due　to　the　diversified　task　characteristics　of　the　new　mobile　applications　and　the　multidimensional　resource　conditions　of　the　MEC　networks.　In　this　paper,　we　take　the　time-dependent　logic　characteristics　of　the　tasks　into　consideration　and　propose　a　more　flexible　computation　offloading　and　task　scheduling　strategy　based　on　the　multi-connectivity　technology　to　further　minimize　the　MEC　network　cost.　We　model　our　problem　as　a　multi-objective　optimization　problem　and　propose　a　genetic　algorithm-based　flexible　computation　offloading　and　task　scheduling　algorithm　(GA-FCOTS)　to　search　for　the　optimal　solution　iteratively.　Simulation　results　verify　the　convergence　of　the　proposed　algorithm,　and　show　that　the　proposed　algorithm　can　balance　multiple　performances　and　reduce　the　network　cost　effectively　compared　with　the　other　baseline　schemes.