Currently,　a　cloud-edge　collaborative　system　combines　almost　unlimited　storage　and　computing　resources　where　tasks　can　be　migrated　to　high-performance　servers　in　edge　servers　or　the　cloud.　However,　resource　allocation　and　task　offloading　present　big　challenges　due　to　the　competition　among　mobile　devices　(MDs)　for　communication　and　computing　resources　of　edge　servers.　Therefore,　it　is　significant　to　properly　offload　MDs＇　tasks　to　edge　servers　or　the　cloud.　This　work　proposes　a　collaborative　edge-cloud　architecture,　including　a　centralized　cloud,　edge　servers,　and　MDs.　Then,　this　work　jointly　considers　computing　power,　task　sizes,　computing　resources,　transmission　power　of　MDs,　transmission　rates,　computing　power,　transmission　power,　computing　resource　of　edge　servers,　and　computing　resource　of　the　cloud.　Considering　the　abovementioned　factors,　this　work　designs　a　mixed-integer　non-linear　programming　problem.　To　solve　it,　a　Genetic　Simulated　annealing-based　Particle　Swarm　Optimization　(GSPSO)　algorithm　is　proposed　to　obtain　the　best　solution.　Building　upon　it,　this　work　proposes　an　energy-minimized　task　offloading　and　resource　allocation　strategy,　thereby　minimizing　the　system＇s　energy　consumption　while　ensuring　strict　task　response　time　limits.　Experimental　results　show　that　GSPSO　reduces　the　system＇s　energy　by　66.34%,　34.65%,　and　4.95%　more　than　particle　swarm　optimization　(PSO),　self-adaptive　PSO,　and　Tyrannosaurus　optimization.　©　2024　IEEE.