Mobile　edge　computing　(MEC)　is　an　emerging　architecture　that　supports　computing,　storage,　and　networking　resources　to　users＇　mobile　devices　(MDs).　MDs　have　limited　resources　and　energy　capacity,　and　they　have　to　offload　some　tasks　of　computational/delay-intensive　applications　to　their　nearby　small　base　station　(SBS),　which　is　a　paradigm　of　MEC.　Although　task　offloading　decreases　energy　consumed　by　MDs,　it　brings　additional　transmission　delay　among　MDs　and　SBS/cloud　data　center　(CDC),　and　processing　delay　in　SBS　and　CDC.　It　is　challenging　to　minimize　the　total　cost　of　a　heterogeneous　system　including　MDs,　an　SBS　and　a　CDC　while　strictly　guaranteeing　delay　limits　of　tasks.　This　work　adopts　different　queuing　systems　to　analyze　the　performance　of　MDs,　the　SBS　and　the　CDC　in　the　heterogeneous　MEC　system.　Then,　this　work　formulates　a　constrained　optimization　problem　to　minimize　the　total　cost　of　the　system.　To　solve　it,　we　design　a　hybrid　method　named　Genetic　Simulated-annealing-based　Particle　swarm　optimization　(GSP)　integrating　genetic　operations　of　genetic　algorithm　and　the　Metropolis　acceptance　rule　of　simulated　annealing　into　particle　swarm　optimization.　Real-life　data-based　simulation　results　demonstrate　that　GSP＇s　solution　outperforms　several　state-of-the-art　algorithms　in　terms　of　total　cost.