Current　mobile　edge　computing　(MEC)　owns　cloud　resources　at　the　network　edge,　which　enables　low-latency　mobile　services.　In　addition　to　fixed　MEC　servers,　MEC　proxy　servers　with　certain　mobility　and　limited　computing,　e.g.,　flying　unmanned　aerial　vehicles　(UAVs),　and　vehicles,　have　emerged　as　competitors　in　providing　services.　In　this　work,　aiming　at　a　task　offloading　problem　of　a　UAV-assisted　MEC　system,　a　hybrid　network　environment　with　multiple　mobile　devices　(MDs)　and　multiple　UAVs　is　established.　A　constrained　mixed　integer　nonlinear　program　of　the　UAV-assisted　hybrid　cloud-edge　system　is　formulated.　A　novel　hybrid　metaheuristic　algorithm　called　Genetic　Simulated　annealing-based　Particle　Swarm　Optimization　(GSPSO)　is　presented　to　solve　the　program.　Then,　a　task　offloading　and　resource　scheduling　method　is　designed　to　intelligently　minimize　the　total　energy　consumption　of　the　hybrid　system.　Simulation　results　verify　superiority　of　GSPSO　over　its　three　benchmark　algorithms,　thus　demonstrating　the　proposed　method　significantly　improves　the　energy　efficiency　of　the　UAV-enabled　hybrid　system.　©　2023　IEEE.