Nowadays,　numerous　mobile　devices　(MDs)　provide　nearly　anytime　and　anywhere　services,　running　on　top　of　various　computation-intensive　applications.　However,　bearing　limited　battery,　bandwidth,　computing,　and　storage　resources,　MDs　cannot　completely　execute　all　tasks　of　such　applications　in　real-time.　Cloud　data　centers　(CDCs)　possess　enormous　resources　and　energy,　which　can　help　execute　tasks　offloaded　from　MDs.　Nonetheless,　CDCs　reside　in　remote　sites,　thereby　leading　to　long　transmission　latency.　In　recent　years,　small　base　stations　(SBSs)　have　emerged　to　offer　close　proximity,　high　bandwidth,　and　low　latency　services　to　their　nearby　and　limited　MDs.　However,　it　becomes　a　new　challenge　to　minimize　the　total　system　cost　in　a　complex　and　heterogeneous　architecture.　To　address　it,　this　work　proposes　an　energy-minimized　partial　computation　offloading　technique.　First,　a　limited　optimization　problem　of　cost　minimization　for　the　system　is　formulated.　Afterward,　an　improved　hybrid　meta-heuristic　algorithm　is　developed,　which　synergistically　combines　a　Metropolis　acceptance　criterion　of　simulated　annealing　and　genetic　operations.　One　uniqueness　of　the　proposed　algorithm　is　that　it　simultaneously　determines　task　allocation　among　MDs,　an　SBS,　and　a　CDC,　the　transmission　power　of　MDs,　and　bandwidth　allocation　of　wireless　channels　between　MDs　and　SBS.　Experiments　with　real-life　tasks　from　Google　data　centers　have　shown　that　the　proposed　Genetic　Simulated-annealing-based　Particle　swarm　optimization　(GSP)　significantly　achieves　lower　system　cost　and　faster　convergence　speed　than　benchmark　peers.　©　2024　Elsevier　Ltd