## 1 Introduction
Based on the above analysis, this paper constructs a multi-objective optimization for multi-UAV aided power and information transmission in order to maximize the energy utilization of the UAVs and minimize the time delay of information collection. The UAV's energy efficiency is defined as the ratio of the energy received by SDs to the energy consumption of the UAV, which is most affected by the flight trajectory and is independent of the hover time. Therefore, the trajectory of each UAV can be assigned first, so as to minimize the cost of the UAV's flight. Moreover, this is a typical multiple traveling salesman problem, which is NP-complete and difficult to be solved by traditional optimization methods. For this reason, the MAC-NSGA II (multiple ant colony-nondominated sorting genetic algorithm II) is proposed here to minimize the total trajectory of the UAVs, while minimizing their maximum trajectory to balance the flight load. On this basis, the Pareto optimal solution set of energy efficiency and information collection delay is obtained by NSGA II. The multi-UAV aided wireless power and information transfer is a hybrid dynamic system, where the power transfer is continuous, and the information collection can be regarded as a discrete event due to its instantaneous completion. As a powerful visual mathematical tool, Petri net has the ability to represent concurrent and synchronous behavior. Moreover, the dynamic process triggered by the transition is not affected by the system parameters and network topology. Consequently, the wireless power and information transfer can be modeled and analyzed by Petri net [21; 22]. The main contributions of the article are concentrated in the following three aspects:  
1. The HCCPNS (hybrid colored cyber Petri net system) is proposed for the first time to model the multi-UAV aided wireless power and information transfer system. The place represents the status of the UAV or SD, where the continuous part is the energy, and the discrete part is information. The variation of a marking or a token corresponds to the continuous transition and the discrete transition, respectively. To the best of our knowledge, this is the first time that Petri net is employed to express the energy flow, control flow, and information flow simultaneously. 2. The multi-UAV aided wireless power and information transfer is constructed as a multi-objective optimization problem. On the one hand, we hoped that the UAV can replenish more energy for SDs, thus improving energy efficiency. Since the wireless charging power is constant, this inevitably results in a longer hovering time. On the other hand, when an SD sends out the request for information transmission, it expects a UAV to arrive at the corresponding position to receive data as soon as possible, that is, the time delay of information collection should be minimal. It is not difficult to see that the two targets are in conflict and a trade-off needs to be found. 3. Under the premise of one-to-one service, the strategy of trajectory assignment and hover of multiple UAVs is designed. The MAC-NSGA II is proposed in order to optimize the energy utilization and average delay of information simultaneously based on the optimal trajectory of multiple UAVs. Numerical simulation results demonstrate that the proposed algorithm has excellent performance, especially for large scale networks. The rest of the paper is organized as follows. Section 2 reviews the work related to wireless power transfer and Petri nets. The specification of multi-UAV wireless power and information transfer based on HCCPNS is proposed, and the multi-objective optimization problem is formulated in Section 3. Section 4 presents the MSC-NSGA II. Section 5 demonstrates and analyzes the simulation results. Section 6 summarizes the paper and looks into the future research.