In the context of Industry 5.0, artificial intelligence (AI)-based logistics Unmanned Aerial Vehicles (UAVs) have been widely applied in intelligent transportation systems due to their advantages of faster speed, lower cost, more environment-friendly, and less manpower needed. Whereas, most of the existing logistics UAV delivery models have not taken the energy consumption of the logistics UAVs and mixed time windows of the customers, which leads to their models cannot be applied in practical transportation systems. Therefore, we propose to minimize the total energy cost of multiple logistics UAVs during the customized products delivery period for a smart transportation system. Taking the energy consumption variation of the logistics UAVs, mixed time windows of the customers, as well as simultaneous delivery and pick up into consideration, we formulate a cooperative path planning problem via jointly optimizing the route of the logistics UAVs and the service allocation. To solve this large-scale integer programming problem, we employ the Large Neighborhood Search Algorithm (LNS) to accelerate the convergence rate of Genetic Algorithm (GA), and then develop an improved GA based cooperative path planning algorithm (IGCPA). The optimization procedure of the proposed algorithm IGCPA is divided into two phases, using the GA crossover operator and variational operator in the global search phase and LNS operator in the local search phase, and validating the integer programming model and the effectiveness of the solution algorithm based on different scale cases. Finally, abundant simulation results show that the energy cost of IGCPA is reduced by 17.35%, 15.18% and 9.99% compared with GA, LNS and Particle Swarm Optimization (PSO), respectively. Furthermore, the IGCPA is validated using Solomn standard data, which further verifies that the IGCPA can enhance the convergence rate of GA as well as obtain a lower delivery cost. Sensitivity analysis of the maximum UAV load and battery capacity reveals that the distribution cost tends to decrease and then increase as the increase of maximum load and battery capacity.