Due to the flexibility and high line-of-sight (LoS) probability, unmanned aerial vehicles (UAVs) can play an important role in 5G/6G networks. In this work, we study a novel air-to-air (A2A) communication scheme, in which two UAV swarms perform two UAV-enabled virtual antenna arrays (UVAAs) for exchanging data by using collaborative beamforming (CB). In order to improve the transmission efficiency and save the energy consumptions of the UAVs, we formulate an A2A communication multi-objective optimization problem (A2ACMOP) to simultaneously enhance the duplex transmission rates and reduce the total energy consumptions of the UAV swarms by deploying the UAVs and adjusting their excitation current weights. Due to the complexity and NP-hardness of the formulated A2ACMOP, we propose an improved non-dominated sorting genetic algorithm-III (INSGA-III) with opposition-based learning solution initialization and hybrid solution update operators to solve the problem. Simulation results verify that the proposed INSGA-III can effectively solve the formulated A2ACMOP and it has better performance than some other benchmark strategies.