Ensemble multi-objective optimization approach for heterogeneous drone delivery problem

Recently, driven by advancements in the payload capacity and endurance of drones, the logistics industry has shown significant interest in drone Last-Mile logistics. Efficient routing are crucial scientific challenges in drone delivery problems. In this study, we address the routing problem in heterogeneous drone delivery, which involves a large drone transporting multiple small drones to sub-regions for parcel delivery, aiming to both reduce the drones' distance costs and improve customer satisfaction, termed HDDPBO To tackle the HDDPBO problem effectively, we propose a voting-based ensemble multi-objective genetic approach, named VEMOGA, in which an improved clustering algorithm is developed to divide customers into K clusters, enabling each drone to handle multiple parcel deliveries within a sub-region. In this way, it reduces the complexity of HDDPBO by transforming it into multiple sub-problems. Secondly, a multi-objective genetic approach with heuristic operators is proposed to explore high-quality solutions, in which customized crossover and mutation operators are designed in the genetic approach, and a voting-based ensemble algorithm is designed to robustly select the Pareto frontier with high-quality convergence and diversity. Extensive experiments are conducted on synthetic instances to evaluate the proposed algorithm, and the experimental results demonstrate superior performance compared to three other baselines. Additionally, a real-world instance has been scrutinized to ascertain the applicability of Last-Mile logistics, and sensitivity analyses of pivotal factors have been conducted and several managerial insights pertinent are given to the drone-based Last-Mile logistics.