Optimized Scheduling for Multi-Drop Vehicle–Drone Collaboration with Delivery Constraints Using Large Language Models and Genetic Algorithms with Symmetry Principles

With the rapid development of e-commerce and globalization, logistics distribution systems have become integral to modern economies, directly impacting transportation efficiency, resource utilization, and supply chain flexibility. However, solving the Vehicle and Multi-Drone Cooperative Delivery Problem with Delivery Restrictions is challenging due to complex constraints, including limited payloads, short endurance, regional restrictions, and multi-objective optimization. Traditional optimization methods, particularly genetic algorithms, struggle to address these complexities, often relying on static rules or single-objective optimization that fails to balance exploration and exploitation, resulting in local optima and slow convergence. The concept of symmetry plays a crucial role in optimizing the scheduling process, as many logistics problems inherently possess symmetrical properties. By exploiting these symmetries, we can reduce the problem’s complexity and improve solution efficiency. This study proposes a novel and scalable scheduling approach to address the Vehicle and Multi-Drone Cooperative Delivery Problem with Delivery Restrictions, tackling its high complexity, constraint handling, and real-world applicability. Specifically, we propose a logistics scheduling method called Loegised, which integrates large language models with genetic algorithms while incorporating symmetry principles to enhance the optimization process. Loegised includes three innovative modules: a cognitive initialization module to accelerate convergence by generating high-quality initial solutions, a dynamic operator parameter adjustment module to optimize crossover and mutation rates in real-time for better global search, and a local optimum escape mechanism to prevent stagnation and improve solution diversity. The experimental results on benchmark datasets show that Loegised achieves an average delivery time of 14.80, significantly outperforming six state-of-the-art baseline methods, with improvements confirmed by Wilcoxon signed-rank tests (p<0.001). In large-scale scenarios, Loegised reduces delivery time by over 20% compared to conventional methods, demonstrating strong scalability and practical applicability. These findings validate the effectiveness and real-world potential of symmetry-enhanced, language model-guided optimization for advanced logistics scheduling.