Nowadays,　multi-access　edge　computing　(MEC)　has　been　widely　recognized　as　a　promising　technology　that　can　support　a　wide　range　of　new　applications　for　the　Internet　of　Things　(IoT).　In　dynamic　MEC　networks,　the　heterogeneous　computation　capacities　of　the　edge　servers　and　the　diversified　requirements　of　the　IoT　applications　are　both　asymmetric,　where　and　when　to　offload　and　schedule　the　time-dependent　tasks　of　IoT　applications　remains　a　challenge.　In　this　paper,　we　propose　a　flexible　offloading　and　task　scheduling　scheme　(FLOATS)　to　adaptively　optimize　the　computation　of　offloading　decisions　and　scheduling　priority　sequences　for　time-dependent　tasks　in　dynamic　networks.　We　model　the　dynamic　optimization　problem　as　a　multi-objective　combinatorial　optimization　problem　in　an　infinite　time　horizon,　which　is　intractable　to　solve.　To　address　this,　a　rolling-horizon-based　optimization　mechanism　is　designed　to　decompose　the　dynamic　optimization　problem　into　a　series　of　static　sub-problems.　A　genetic　algorithm　(GA)-based　computation　offloading　and　task　scheduling　algorithm　is　proposed　for　each　static　sub-problem.　This　algorithm　encodes　feasible　solutions　into　two-layer　chromosomes,　and　the　optimal　solution　can　be　obtained　through　chromosome　selection,　crossover　and　mutation　operations.　The　simulation　results　demonstrate　that　the　proposed　scheme　can　effectively　reduce　network　costs　in　comparison　to　other　reference　schemes.