Multi-objective optimization of multimodal logistics paths: a decomposition-based approach for coordinating trucks and UAVs within the cyber-physical internet framework

This study investigates the multi-objective optimisation of multimodal logistics paths within the Cyber-Physical Internet (CPI), focusing on the coordinated use of trucks and unmanned aerial vehicles (UAVs). A decomposition-based evolutionary algorithm is developed, which integrates a hierarchical k-shortest path enumeration as a preprocessing stage. Differential evolution operators and a polynomial mutation mechanism are then applied to efficiently explore the reduced decision space. Numerical experiments on large-scale real-world networks demonstrate that the proposed approach captures trade-offs between transportation time and cost across multiple origin–destination pairs and generates stable and diverse Pareto-optimal solutions. Sensitivity analyses reveal diminishing marginal benefits from increasing candidate paths, highlight the existence of an optimal UAV deployment scale that balances time efficiency and operational cost, and demonstrate a synergistic interaction between UAV maximum range and payload capacity in enhancing transportation efficiency. The results offer practical recommendations for coordinated routing and resource allocation, supporting scalable and adaptive decision-making in CPI-enabled multimodal logistics systems.