A　collaborative　system　that　includes　mobile　devices　(MDs),　edge　nodes　(ENs),　and　the　cloud　is　needed　where　ENs　at　the　network　edge　can　run　offloaded　tasks　of　MDs　with　limited　resources　and　energy　for　timely　processing　for　latency-sensitive　applications.　Unlike　existing　studies,　we　formulate　a　total　cost　minimization　problem　for　the　system　for　applications,　which　can　be　divided　into　several　interdependent　subtasks.　Each　subtask　can　be　executed　in　MDs,　ENs,　and　the　cloud.　This　work　formulates　a　mixed-integer　nonlinear　program　to　minimize　the　total　system　cost.　To　address　it,　a　novel　meta-heuristic　optimization　algorithm　called　Genetic　Simulated-annealing-based　Particle　swarm　optimization　with　Auto-Encoder　(GSPAE)　is　proposed,　which　innovatively　combines　feature　extraction　of　deep　learning　and　global　search　of　meta-heuristic　optimization.　Genetic　operations　provide　diverse　solutions,　the　Metropolis　acceptance　of　annealing　offers　a　robust　global　search,　and　autoencoders　(AEs)　extract　distribution　characteristics　of　particles　toward　high-quality　regions　for　fast　convergence.　Thus,　GSPAE　optimizes　the　associations　between　ENs　and　MDs　and　the　scheduling　of　subtasks　among　MDs,　ENs,　and　the　cloud.　Experiments　with　large-scale　Google　cluster　datasets　show　that　compared　to　state-of-the-art　benchmark　methods,　GSPAE　reduces　the　total　cost　by　at　least　17%　while　strictly　meeting　limits　of　application　latency,　available　energy,　computing,　and　communication　resources　of　ENs　and　MDs.