Optimization of Transportation Routes with Multiple Drones: A Proposal Using Machine Learning, Metaheuristics, and Exact Solutions
Abstract
The increasing utilization of drones for last-mile deliveries, motivated by the reduction of delivery time and maintenance costs, as well as by the mitigation of CO2 emissions, demands robust solutions for the multiple drone transport route optimization problem (Covering Salesman Problem with Multiple Drones – CSPMD). This article proposes a multilayer solution to this problem, in an approach that integrates Machine Learning (ML), metaheuristic, and dynamic programming. The obtained results indicate that the use of specific metaheuristics, in the context of this multilayer framework, constitutes a promising strategy for solving the CSPMD. The performance evaluation of these metaheuristics indicated that the Genetic Algorithm outperformed in small instances, achieving a cost up to 0.49% lower, while Simulated Annealing proved superior in large instances, with a cost up to 1.93% lower.
References
Avrim, B., Chen, D., and Saeed, S. (2021). Learning complexity of simulated annealing. Accessed on: 2025-11-13.
Bezdek, J. C., Ehrlich, R., and Full, W. (1984). Fcm: The fuzzy c-means clustering algorithm. Computers & Geosciences. Accessed on: 2025-08-21.
Kaufman, L. and Rousseeuw, P. J. (1987). Clustering by means of medoids. Journal of Computational and Applied Mathematics. Accessed on: 2025-08-20.
ONU (2018). Transporte sustentável é destaque na conferência do clima da onu. Technical report. Accessed on: 2025-11-13.
Paul, B., Niels, A., and Marie, S. (2018). Dynamic programming approaches for the traveling salesman problem with drone. Accessed on: 2025-11-13.
Pratik, S. T., Rohit, K. V., and Rakesh, T. (2024). Analysis of time complexity of k-means and fuzzy c-means clustering algorithm. Engineering Mathematics Letters. Accessed on: 2025-11-13.
Song, H., Jingi, A. M., and Yang, X. (2022). Drone-assisted last-mile delivery problem by covering salesman problem with nodes and segments. SSRN Electronic Journal. Accessed on: 2024-04-14.
Toaza, B. and Esztergár-Kiss, D. (2023). A review of metaheuristic algorithms for solving tsp-based scheduling optimization problems. Applied Soft Computing. Accessed on: 2025-08-20.
Wen, X. and Wu, G. (2022). Heterogenous multi-drone routing problem for parcel delivery. Computers & Operations Research. Accessed on: 2025-02-01.
Yoo, W., Yu, E., and Jung, J. (2018). Drone delivery: Factors affecting the public’s attitude and intention to adopt. Telematics and Informatics. Accessed on: 2024-04-14.
