A humanitarian vehicle routing problem synchronized with drones in time-varying weather conditions

This paper applies the cooperative delivery mode of trucks synchronized with drones to humanitarian logistics (HVRP-SD), considers the impact of time-varying weather conditions on the synchronous delivery from two dimensions (HVRP-SD-TVW): drone safety and drone delivery efficiency, and investigate a multi-objective optimization problem. This issue concerns not only the delivery timeliness of relief supplies, but also the fairness of supplies allocation. First, we establish a basic multi-objective mixed integer programming model for HVRP-SD, and then establish an extended mathematical model for HVRP-SD-TVW. To solve the multi-objective optimization problem, we develop a hybrid multi-objective evolutionary algorithm (HMOEA). According to the characteristics of HVRP-SD-TVW, HMOEA designs a variable-length two-dimensional array encoding method, fitness evaluation rules, multimodal mutation, and specialized local search operators. A set of numerical experiments prove that HMOEAS is highly competitive, and both the multimodal mutation and local search have significant effects on improving the quality of solutions. Further, taking the emergency supplies distribution in flood-stricken areas of Gongyi City, China in 2021 as a sample case, we prove that weather conditions play an important role in the truck-drone synchronized delivery decision by comparing the results of the basic model and extended model. In addition, we respectively analyze the variation in solutions under different weather scenarios, departure times, and drone risk resilience to guide decision-making.