The　air　ground　integrated　networks　can　leverage　unmanned　aerial　vehicle　(UAV)　communications　to　tackle　the　ever-increasing　and　unbalanced　traffic　load　in　future　communication　systems.　This　paper　investigates　the　UAV　enabled　traffic　offloading　problem　in　air　ground　integrated　networks　with　mixed　user　traffic.　The　problem　jointly　maximizes　the　system　load　balance　and　the　total　UAV　reward,　which　can　be　formulated　under　a　two-layer　network　graph　model.　In　the　cellular　network　graph,　the　association　between　the　delay-sensitive　users　and　the　access　points　(APs)　as　well　as　the　association　between　the　UAVs　and　the　APs　are　formulated.　In　the　UAV　network　graph,　the　association　between　the　delay-insensitive　users　and　the　UAVs　is　formulated.　By　observing　the　coupling　relationship　of　the　decision　variables,　we　decouple　the　problem　into　three　sub-problems　and　solve　the　first　two　sub-problems　with　reduced　complexity.　Then,　we　devise　a　Deep　Neural　Network　(DNN)　empowered　genetic　algorithm　to　solve　the　last　sub-problem.　The　DNN　can　be　leveraged　to　filter　out　the　non-optimal　solutions　in　the　initialization　operator　of　the　genetic　algorithm　for　improving　the　efficiency.　Performance　comparisons　are　provided　between　the　proposed　traffic　offloading　scheme　and　the　existing　ones,　which　validate　the　advantages　of　the　DNN　empowered　genetic　algorithm　regarding　its　convergence,　accuracy,　and　robustness.