Multi-objective optimization of dynamic truck–multi-drone cooperative delivery based on an improved non-dominated sorting genetic algorithm-II

This study proposes a truck-multi-drone cooperative delivery framework integrating trucks, direct-flight drones and truck-mounted drones to address last-mile logistics challenges. A mixed-integer linear programming model is formulated with distance-based noise attenuation, dynamic launch–recovery synchronization and soft time-window constraints to minimize total cost, maximum delivery completion time and service delay. To efficiently solve this problem, an improved non-dominated sorting genetic algorithm-II (NSGA-II) featuring structured heuristic initialization and problem-oriented evolutionary mechanisms is developed. Computational experiments on Solomon benchmark instances demonstrate the effectiveness of the framework. The proposed algorithm achieves superior Pareto-front coverage and stronger service-delay control than baseline heuristics, while remaining close to exact benchmarks in small-scale cases. Furthermore, the full cooperative mode attains the lowest average cost among zero-delay modes while maintaining competitive timeliness. The proposed framework provides effective decision support for multi-resource last-mile operations.