With　the　advantages　of　real-time　data　processing　and　flexible　deployment,　unmanned　aerial　vehicle　(UAV)-assisted　mobile　edge　computing　systems　are　widely　used　in　both　civil　and　military　fields.　However,　due　to　limited　energy,　it　is　usually　difficult　for　UAVs　to　stay　in　the　air　for　long　periods　and　to　perform　computational　tasks.　In　this　paper,　we　propose　a　full-duplex　air-to-air　communication　system　(A2ACS)　model　combining　mobile　edge　computing　and　wireless　power　transfer　technologies,　aiming　to　effectively　reduce　the　computational　latency　and　energy　consumption　of　UAVs,　while　ensuring　that　the　UAVs　do　not　interrupt　the　mission　or　leave　the　work　area　due　to　insufficient　energy.　In　this　system,　UAVs　collect　energy　from　external　air-edge　energy　servers　(AEESs)　to　power　onboard　batteries　and　offload　computational　tasks　to　AEESs　to　reduce　latency.　To　optimize　the　system＇s　performance　and　balance　the　four　objectives,　including　the　system　throughput,　the　number　of　low-power　alarms　of　UAVs,　the　total　energy　received　by　UAVs　and　the　energy　consumption　of　AEESs,　we　develop　a　multi-objective　optimization　framework.　Considering　that　AEESs　require　rapid　decision-making　in　a　dynamic　environment,　an　algorithm　based　on　multi-agent　deep　deterministic　policy　gradient　(MADDPG)　is　proposed,　to　optimize　the　AEESs＇　service　location　and　to　control　the　power　of　energy　transfer.　While　training,　the　agents　learn　the　optimal　policy　given　the　optimization　weight　conditions.　Furthermore,　we　adopt　the　K-means　algorithm　to　determine　the　association　between　AEESs　and　UAVs　to　ensure　fairness.　Simulated　experiment　results　show　that　the　proposed　MODDPG　(multi-objective　DDPG)　algorithm　has　better　performance　than　the　baseline　algorithms,　such　as　the　genetic　algorithm　and　other　deep　reinforcement　learning　algorithms.