Time-dependent hydrogen fuel cell vehicle routing problem with drones and variable drone speeds

This paper proposes a novel problem called the time-dependent hydrogen fuel cell vehicle routing problem with drones and variable drone speeds (TDHFCVRP-D-VDS). In this problem, a fleet of hydrogen fuel cell vehicles (HFCVs) are equipped with multiple unmanned aerial vehicles (UAVs) to perform delivery and pickup services within the customers' time windows. The UAV is capable of performing pickup operations after the delivery service, as long as it does not exceed its energy capacity. The HFCV can launch and retrieve the UAV multiple times as needed throughout the routing process. We establish a mixed integer programming model to simultaneously minimize the total cost and makespan, and verify its accuracy by Gurobi. To tackle larger-scale instances, we propose a non-dominated sorting genetic algorithm III with intelligent selection (NSGA-III-IS). The initial population is generated using four distinct approaches aimed at enhancing both diversity and quality. Considering the customers' time windows, we factor in the temporal-spatial distances between customers when generating the initial population. Our approach employs a two-phase algorithm for developing initial solutions. In the first phase, the algorithm focuses on generating UAV trips, while in the second phase, it creates joint delivery routes for both the HFCV and the UAV. To enhance the optimization process, we have developed four strategies for optimizing UAV speed. These strategies dynamically adjust the UAV's speed in response to the customers' time windows and the HFCVs' arrival times. Additionally, we have integrated an intelligent selection mechanism to optimize the execution probabilities of both general and problem-specific operators. The experimental results demonstrate the following: (1) The proposed NSGA-III-IS outperforms other variant algorithms and two benchmark algorithms; (2) UAVs significantly benefit from variable flight speeds, resulting in reduced costs and improved efficiency; (3) The HFCV with UAV joint delivery pattern is superior for reducing carbon emissions compared to other joint delivery patterns; (4) Longer customer time windows and optimized UAV speed strategies are effective in reducing the total cost, makespan, and total UAV hover waiting time; (5) Finally, a method that combines multi-attribute decision-making with principal component analysis is utilized to aid decision-makers in selecting satisfactory solutions.