Recent　years　have　seen　a　surge　in　Internet　of　Things　(IoT)　technologies,　with　billions　of　mobile　devices　(MDs)　straining　limited　computing　and　networking　resources.　Mobile　edge　computing　offloads　tasks　from　MDs　to　edge　servers,　saving　energy　and　reducing　network　pressure.　Edge　servers　provide　closer　services　yet　have　fewer　resources　than　cloud　servers.　A　new　heterogeneous　edge　and　cloud　computing　paradigm　combines　the　benefits　of　both.　Edge　servers　provide　close　proximity　services　to　MDs,　while　the　cloud　owns　enough　resources.　The　existence　of　mobile　IoT　devices　makes　it　more　practical　to　consider　mobility　when　allocating　resources　of　edge　servers　to　decrease　the　energy　consumption　of　the　heterogeneous　edge　and　cloud　while　meeting　the　latency　needs　of　tasks.　This　work　formulate　a　constrained　energy　consumption　optimization　problem　and　design　a　hybrid　algorithm　named　Genetic　Simulated-annealing-based　particle　swarm　optimization　(PSO)　to　yield　a　near-optimal　solution.　Simulation　results　prove　that　compared　to　genetic　algorithm,　PSO,　simulated-annealing-based　PSO,　and　Trex,　GSPSO　reduces　the　total　energy　consumption　by　38.64%,　54.63%,　45.94%,　and　36.21%,　respectively.　©　2024　IEEE.