Smart　mobile　devices　(SMDs)　can　meet　users＇　high　expectations　by　executing　computational　intensive　applications　but　they　only　have　limited　resources,　including　CPU,　memory,　battery　power,　and　wireless　medium.　To　tackle　this　limitation,　partial　computation　offloading　can　be　used　as　a　promising　method　to　schedule　some　tasks　of　applications　from　resource-limited　SMDs　to　high-performance　edge　servers.　However,　it　brings　communication　overhead　issues　caused　by　limited　bandwidth　and　inevitably　increases　the　latency　of　tasks　offloaded　to　edge　servers.　Therefore,　it　is　highly　challenging　to　achieve　a　balance　between　high-resource　consumption　in　SMDs　and　high　communication　cost　for　providing　energy-efficient　and　latency-low　services　to　users.　This　work　proposes　a　partial　computation　offloading　method　to　minimize　the　total　energy　consumed　by　SMDs　and　edge　servers　by　jointly　optimizing　the　offloading　ratio　of　tasks,　CPU　speeds　of　SMDs,　allocated　bandwidth　of　available　channels,　and　transmission　power　of　each　SMD　in　each　time　slot.　It　jointly　considers　the　execution　time　of　tasks　performed　in　SMDs　and　edge　servers,　and　transmission　time　of　data.　It　also　jointly　considers　latency　limits,　CPU　speeds,　transmission　power　limits,　available　energy　of　SMDs,　and　the　maximum　number　of　CPU　cycles　and　memories　in　edge　servers.　Considering　these　factors,　a　nonlinear　constrained　optimization　problem　is　formulated　and　solved　by　a　novel　hybrid　metaheuristic　algorithm　named　genetic　simulated　annealing-based　particle　swarm　optimization　(GSP)　to　produce　a　close-to-optimal　solution.　GSP　achieves　joint　optimization　of　computation　offloading　between　a　cloud　data　center　and　the　edge,　and　resource　allocation　in　the　data　center.　Real-life　data-based　experimental　results　prove　that　it　achieves　lower　energy　consumption　in　less　convergence　time　than　its　three　typical　peers.