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<p>The Vehicle Routing Problem (VRP) remains a cornerstone of operational research, challenging researchers with its practical and diverse extensions. Among these, the Vehicle Routing Problem with Drones (VRPD) combines conventional vehicles and unmanned aerial vehicles (UAVs), presenting unique opportunities to optimize logistics. This study introduces a novel hybrid algorithm, ICA-VNS, which synergizes the Imperialist Competitive Algorithm (ICA) with Variable Neighborhood Search (VNS) to solve the VRPD. The algorithm begins with ICA for global optimization, followed by VNS for precise local search, and incorporates a heuristic greedy operator for drone assignment. By leveraging these techniques, the algorithm minimizes delivery times while maintaining feasible routes for trucks and drones. Experimental results on benchmark datasets demonstrate that ICA-VNS achieves up to 22% improvement in specific cases and an average improvement of 3.15% over state-of-the-art methods. This research highlights the transformative potential of hybrid metaheuristic approaches in addressing modern logistics challenges, particularly in last-mile delivery scenarios.</p>

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A Hybrid Metaheuristic Algorithm for Solving Vehicle Routing Problem with Drone (VRPD)

  • 期刊论文

  • 发表日期：

    2025年10月7日

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  • Ahmad Rahimi Denjkolaei,
  • Rasul Enayatifar,
  • Mahdi Golsorkhtabaramiri,
  • Kamal Jadidy aval

摘要

The Vehicle Routing Problem (VRP) remains a cornerstone of operational research, challenging researchers with its practical and diverse extensions. Among these, the Vehicle Routing Problem with Drones (VRPD) combines conventional vehicles and unmanned aerial vehicles (UAVs), presenting unique opportunities to optimize logistics. This study introduces a novel hybrid algorithm, ICA-VNS, which synergizes the Imperialist Competitive Algorithm (ICA) with Variable Neighborhood Search (VNS) to solve the VRPD. The algorithm begins with ICA for global optimization, followed by VNS for precise local search, and incorporates a heuristic greedy operator for drone assignment. By leveraging these techniques, the algorithm minimizes delivery times while maintaining feasible routes for trucks and drones. Experimental results on benchmark datasets demonstrate that ICA-VNS achieves up to 22% improvement in specific cases and an average improvement of 3.15% over state-of-the-art methods. This research highlights the transformative potential of hybrid metaheuristic approaches in addressing modern logistics challenges, particularly in last-mile delivery scenarios.