A Novel Framework for Solving the Optimal Path Problem in Collaborative Consignment Delivery Systems Using Drones

Shibu Kumar K. B.1,2, Philip Samuel3
1Department of Computer Science and Engineering, Rajiv Gandhi Institute of Technology, Kottayam, India
2Department of Computer Science and Engineering, College of Engineering Trivandrum, Thiruvananthapuram, India
3Department of Computer Science, Cochin University of Science and Technology, Kochi, India

Tóm tắt

Drone based consignment delivery system is considered to be the future of retail marketing where unmanned aerial vehicles are employed for door delivery of items. This results in a fast, efficient and accurate delivery system which is not affected by geographic conditions and can be used for delivery of items to areas where human reachability is difficult. Also, it can ensure that the customers avoid close contact with strangers, especially in the era of a pandemic like COVID 19. However, the system poses a number of challenges too, the most important of them being the limited battery life of drones. Though newer batteries provide better flight times, the battery discharges faster with increased number of landings and take-offs. Hence the flight of the drone has to be kept optimal for efficient delivery of consignments. In this paper, we propose a delivery system using drones where both the delivery agency and the customers collaborate together to distribute the consignments and model a novel framework for finding the optimal path of delivery drones. We employ unsupervised learning approaches to find the landing locations for drones, based on the concentration of customers. We use a nature inspired optimization algorithm using the fundamental principles of particle physics to get rid of the practical limitations of k-means, a widely used centroid based clustering technique. Besides, we address the case where the customers are spread in such a way that their partitions are not well-separated. Finally, we model, experiment and evaluate our methods on two different datasets.

Tài liệu tham khảo

Agatz, N., Campbell, A.M., Fleischmann, M., Savels, M.: Challenges and opportunities in attended home delivery. The Vehicle Routing Problem: Latest Advances and New Challenges - Operations Research/Computer Science Interfaces 43, 379–96 (2008) Ahmadyfard, A., Modares, H.: Combining pso and k-means to enhance data clustering. In: 2008 international symposium on telecommunications, pp. 688–91 (2008). https://doi.org/10.1109/ISTEL.2008.4651388 Ahmed, M., Seraj, R., Islam, S.M.S.: The k-means algorithm: A comprehensive survey and performance evaluation. Electronics 9(8) (2020). https://doi.org/10.3390/electronics9081295. https://www.mdpi.com/2079-9292/9/8/1295 Akeb, H., Bouchakhchoukha, A., Hifi, M.: A three-stage heuristic for the capacitated vehicle routing problem with time windows, pp. 1–19. Springer International Publishing, Cham (2015). https://doi.org/10.1007/978-3-319-12631-9_1 Applegate, D., Bixby, R., Chvatal, V., Cook, W.: Concorde tsp solver. online. http://www.math.uwaterloo.ca/tsp/concorde/index.html Armano, G., Farmani, M.R.: Multiobjective clustering analysis using particle swarm optimization. Expert Systems with Applications 55, 184–193 (2016). https://doi.org/10.1016/j.eswa.2016.02.009. https://www.sciencedirect.com/science/article/pii/S0957417416 30032X Arthur, D., Vassilvitskii, S.: k-means++: the advantages of careful seeding. In: SODA ’07: Proceedings of the eighteenth annual ACM-SIAM symposium on Discrete algorithms, pp. 1027–1035. Society for Industrial and Applied Mathematics, Philadelphia, PA, USA (2007) Barnhart, C., Laporte, G.: Handbooks in operations research & management science: Transportation. Transportation 14 (2007) Battarra, M., Erdogan, G., Vigo, D.: Exact algorithms for the clustered vehicle routing problem. Operations Research 62, 58–71 (2014). https://doi.org/10.1287/opre.2013.1227 Bent, R., Hentenryck, P.V.: A two-stage hybrid local search for the vehicle routing problem with time windows. Department of Computer Science, Brown University, Tech. rep. (2001) Bradley, P.S., Fayyad, U.M.: Refining initial points for K-Means clustering. In: Proc. 15th international Conf. on machine learning, pp. 91–99. Morgan Kaufmann, San Francisco, CA (1998) Budka, M.: Clustering as an example of optimizing arbitrarily chosen objective functions. Advanced Methods for Computational Collective Intelligence 457, 177–86 (2013) Chen, R.M., Hsieh, F.R., Wu, D.S.: Heuristics based ant colony optimization for vehicle routing problem. In: 2012 7th IEEE conference on industrial electronics and applications (ICIEA), pp. 1039–1043 (2012). https://doi.org/10.1109/ICIEA.2012.6360876 Chen, S.M., Chien, C.Y.: A new method for solving the traveling salesman problem based on the genetic simulated annealing ant colony system with particle swarm optimization techniques. In: 2010 international conference on machine learning and cybernetics, vol. 5, pp. 2477–2482 (2010). https://doi.org/10.1109/ICMLC.2010.5580809 Cheng, D., Zhu, Q., Huang, J., Wu, Q., Yang, L.: A novel cluster validity index based on local cores. IEEE Trans. Neural Netw. Learn. Syst. 30(4), 985–999 (2019). https://doi.org/10.1109/TNNLS.2018.2853710 Chiang, W.C., Li, Y., Shang, J., Urban, T.L.: Impact of drone delivery on sustainability and cost: Realizing the uav potential through vehicle routing optimization. Appl. Energy 242, 1164–1175 (2019). https://doi.org/10.1016/j.apenergy.2019.03.117. https://www.sciencedirect.com/science/article/pii/S0306261919 305252 Cosma, O., Pop, P., Sitar, C.: A two-level based genetic algorithm for solving the soft-clustered vehicle routing problem. Carpathian Journal of Mathematics 38, 117–128 (2021). https://doi.org/10.37193/CJM.2022.01.09 Dalatu, P.I.: Time complexity of k-means and k-medians clustering algorithms in outliers detection. Global J. Pure Appl. Math. 12(5), 4405–4418 (2016) Dantzig, G., Fulkerson, R., Johnson, S.: Solution of a large-scale traveling-salesman problem. Operations Research 2, 393–410 (1954) Delin, L., Lixiao, Z., Zhihui, X.: Heuristic simulated annealing genetic algorithm for traveling salesman problem. In: 2011 6th international conference on computer science education (ICCSE), pp. 260–264 (2011). https://doi.org/10.1109/ICCSE.2011.6028630 Dorling, K., Heinrichs, J., Messier, G.G., Magierowski, S.: Vehicle routing problems for drone delivery. IEEE Trans. Syst. Man Cybern. Syst. 47(1), 70–85 (2017). https://doi.org/10.1109/TSMC.2016.2582745 Duvvada, H.P., Naidu, G.D.R., Sri, V.D.: K-means cluster analysis of cities based on their inter-distances. Int. J. Eng. Develop. Res. 5(4), 1356–1363 (2017) Expósito-Izquierdo, C., Rossi, A., Sevaux, M.: A two-level solution approach to solve the clustered capacitated vehicle routing problem. Comput. Indust. Eng. 91, 274–289 (2016). https://doi.org/10.1016/j.cie.2015.11.022. https://www.sciencedirect.com/science/article/pii/S0360835215004684 Fränti, P., Sieranoja, S.: How much can k-means be improved by using better initialization and repeats? Pattern Recogn. 93, 95–112 (2019) Gatteschi, V., Lamberti, F., Paravati, G., Sanna, A., Demartini, C., Lisanti, A., Venezia, G.: New frontiers of delivery services using drones: A prototype system exploiting a quadcopter for autonomous drug shipments. In: 2015 IEEE 39th annual computer software and applications conference, vol. 2, pp. 920–927 (2015). https://doi.org/10.1109/COMPSAC.2015.52 Goodchildand, A., Toy, J.: Delivery by drone: An evaluation of unmanned aerial vehicle technology in reducing co2 emissions in the delivery service industry. Transportation Research Part D: Transport and Environment 61(A), 58–67 (2018) Gordon-Spears, D.F., Spears, W.M.: Analysis of a phase transition in a physics-based multiagent system. In: Formal approaches to agent-based systems, pp. 193–207. Springer, Berlin (2003) Hamerly, G., Elkan, C.: Alternatives to the k-means algorithm that find better clusterings. In: CIKM ’02: Proceedings of the eleventh international conference on Information and knowledge management, pp. 600–607. ACM, New York (2002). https://doi.org/10.1145/584792.584890 Hamerly, G., Elkan, C.: Alternatives to the k-means algorithm that find better clusterings. In: CIKM ’02: Proceedings of the eleventh international conference on Information and knowledge management, pp. 600–607. ACM, New York (2002). https://doi.org/10.1145/584792.584890. https://portal.acm.org/citation.cfm?id=584890 Hu, W., Liang, H., Peng, C., Du, B., Hu, Q.: A hybrid chaos-particle swarm optimization algorithm for the vehicle routing problem with time window. Entropy 15(4), 1247–1270 (2013). https://doi.org/10.3390/e15041247. https://www.mdpi.com/1099-4300/15/4/1247 Johannessen, K.A.: A conceptual approach to time savings and cost competitiveness assessments for drone transport of biologic samples with unmanned aerial systems (drones). Drones 6(3) (2022). https://doi.org/10.3390/drones6030062. https://www.mdpi.com/2504-446X/6/3/62 Kennedy, J., Eberhart, R.: Particle swarm optimization. In: Proceedings of ICNN’95 - international conference on neural networks, vol. 4, pp. 1942–1948 (1995). https://doi.org/10.1109/ICNN.1995.488968 Khan, S.S., Ahmad, A.: Cluster center initialization algorithm for k-means algorithm. Pattern Recogn. Lett. 25(11), 1293–1302 (2004) Kim, S., Kwon, Y., Choi, S., Lee, J., Ko, S., Chung, B., Moon, I., Ko, C.: Development of mathematical models for parcel delivery service network design. Journal of the Korean Institute of Industrial Engineers 45, 203–212 (2019) Kitjacharoenchai, P., Ventresca, M., Moshref-Javadi, M., Lee, S., Tanchoco, J.M., Brunese, P.A.: Multiple traveling salesman problem with drones: Mathematical model and heuristic approach. Computers & Industrial Engineering 129, 14–30 (2019). https://doi.org/10.1016/j.cie.2019.01.020. https://www.sciencedirect.com/science/article/pii/S0360835219 300245 Kyriakakis, N.A., Stamadianos, T., Marinaki, M., Marinakis, Y.: The electric vehicle routing problem with drones: An energy minimization approach for aerial deliveries. Cleaner Logistics and Supply Chain 4, 100041 (2022). https://doi.org/10.1016/j.clscn.2022.100041. https://www.sciencedirect.com/science/article/pii/S2772390922 000142 Lawler, E.L.: The Travelling Salesman Problem: A Guided Tour of Combinatorial Optimization. John Wiley & sons (1985) Li, L., Wang, W., Xu, X.: Multi-objective particle swarm optimization based on global margin ranking. Inform. Sci. 375, 30–47 (2017). https://doi.org/10.1016/j.ins.2016.08.043. https://www.sciencedirect.com/science/article/pii/S0020025516 306156 Liu, F., Deng, Y.: Determine the number of unknown targets in open world based on elbow method. IEEE Trans. Fuzzy Syst. 29(5), 986–995 (2021). https://doi.org/10.1109/TFUZZ.2020.2966182 Liu, X., Zhang, B., Du, F.: Integrating relative coordinates with simulated annealing to solve a traveling salesman problem. In: 2014 Seventh international joint conference on computational sciences and optimization, pp. 177–180 (2014). https://doi.org/10.1109/CSO.2014.39 Lloyd, S.P.: Least squares quantization in pcm. IEEE Trans. Inform. Theory 28(2), 129–137 (1982) Marc, A.H., Fuksz, L., Pop, P.C., Dănciulescu, D.: A novel hybrid algorithm for solving the clustered vehicle routing problem. In: Onieva, E., Santos, I., Osaba, E., Quintián, H., Corchado, E. (eds.) Hybrid artificial intelligent systems, pp. 679–689. Springer International Publishing, Cham (2015) van der Merwe, D., Engelbrecht, A.: Data clustering using particle swarm optimization. In: The 2003 congress on evolutionary computation, 2003. CEC ’03., vol. 1, pp. 215–220 (2003). https://doi.org/10.1109/CEC.2003.1299577 Moshref-Javadi, M., Hemmati, A., Winkenbach, M.: A truck and drones model for last-mile delivery: A mathematical model and heuristic approach. Appl. Math. Model. 80, 290–318 (2020). https://doi.org/10.1016/j.apm.2019.11.020. https://www.sciencedirect.com/science/article/pii/S0307904X19 306936 Murray, C.C., Chu, A.G.: The flying sidekick traveling salesman problem: Optimization of drone-assisted parcel delivery. Transportation Research Part C: Emerging Technologies 54, 86–109 (2015). https://doi.org/10.1016/j.trc.2015.03.005 Nagata, Y., Bräysy, O., Dullaert, W.: A penalty-based edge assembly memetic algorithm for the vehicle routing problem with time windows. Comput. Operat. Res. 37(4), 724–737 (2010). https://doi.org/10.1016/j.cor.2009.06.022. https://www.sciencedirect.com/science/article/pii/S0305054809 001762 Ochieng, W.O., Ye, T., Scheel, C., Lor, A., Saindon, J., Yee, S.L., Meltzer, M.I., Kapil, V., Karem, K.: Uncrewed aircraft systems versus motorcycles to deliver laboratory samples in west africa: a comparative economic study. Lancet Global Health 8(1) (2020). https://doi.org/10.1016/S2214-109X(19)30464-4 Pe\(\widetilde{n}\)a, J.M., Lozano, J.A., Larra\(\widetilde{n}\)aga, P.: An empirical comparison of four initialization methods for the k-means algorithm. Pattern Recogn. Lett. 20(10), 1027–1040 (1999). https://doi.org/10.1016/S0167-8655(99)00069-0 Pop, P., Chira, C.: A hybrid approach based on genetic algorithms for solving the clustered vehicle routing problem. In: 2014 IEEE congress on evolutionary computation (CEC), pp. 1421–1426 (2014). https://doi.org/10.1109/CEC.2014.6900422 Raykov, Y.P., Boukouvalas, A., Baig, F., Little, M.A.: What to do when k-means clustering fails: A simple yet principled alternative algorithm. PLOS ONE 11(9), 1–28 (2016). https://doi.org/10.1371/journal.pone.0162259 Rizkallah, L., Farouk, M., Darwish, N.: A clustering algorithm for solving the vehicle routing assignment problem in polynomial time. Int. J. Eng. Technol. 9 (2019). https://doi.org/10.14419/ijet.v9i1.22231 Rubin, S.H., Bouabana-Tebibel, T., Hoadjli, Y., Ghalem, Z.: Reusing the np-hard traveling-salesman problem to demonstrate that p np (invited paper). In: 2016 IEEE 17th international conference on information reuse and integration (IRI), pp. 574–581 (2016). https://doi.org/10.1109/IRI.2016.84 Sevaux, M., Sörensen, K.: Hamiltonian paths in large clustered routing problems. In: Proceedings of the EU/MEeting 2008 workshop on metaheuristics for logistics and vehicle routing, EU/ME (2008) Sunny, C., kumar K. B., S.: Refined pso clustering for not well-separated data. Journal of Experimental & Theoretical Artificial Intelligence pp. 1–17 (2021). https://doi.org/10.1080/0952813X.2021.1970238 Vidal, T., Battarra, M., Subramanian, A., Erdoğan, G.: Hybrid metaheuristics for the clustered vehicle routing problem. Comput. Operat. Res. 58, 87–99 (2015). https://doi.org/10.1016/j.cor.2014.10.019. https://www.sciencedirect.com/science/article/pii/S0305054814 002767 Xie, L., Zeng, J., Cui, Z.: General framework of artificial physics optimization algorithm. In: 2009 World congress on nature biologically inspired computing (NaBIC), pp. 1321–1326 (2009). https://doi.org/10.1109/NABIC.2009.5393736 Xu, X., Li, J., Zhou, M., Xu, J., Cao, J.: Accelerated two-stage particle swarm optimization for clustering not-well-separated data. IEEE Trans. Syst. Man Cybern. Syst. 50(11), 4212–4223 (2020). https://doi.org/10.1109/TSMC.2018.2839618 Yadav, V., Narasimhamurthy, A.: A heuristics based approach for optimizing delivery schedule of an unmanned aerial vehicle (drone) based delivery system. In: \(9^{th}\) international conference on advances in pattern recognition (ICAPR), vol. 2, pp. 920–927 (2015) Yan, H., Chen, Y., Yang, S.H.: Uav-enabled wireless power transfer with base station charging and uav power consumption. IEEE Trans. Vehicular Technol. 69(11), 12883–12896 (2020). https://doi.org/10.1109/TVT.2020.3015246 Yijun, W.: Distribution route optimization of logistics enterprise based on genetic algorithm. In: World automation congress 2012, pp. 1–4 (2012) Yoo, H.D., Chankov, S.M.: Drone-delivery using autonomous mobility: An innovative approach to future last-mile delivery problems. In: 2018 IEEE International Conference on Industrial Engineering and Engineering Management (IEEM), pp. 1216–1220 (2018). https://doi.org/10.1109/IEEM.2018.8607829 Zailani, M.A.H., Sabudin, R.Z.A.R., Rahman, R.A., Saiboon, I.M., Ismail, A., Mahdy, Z.A.: Drone for medical products transportation in maternal healthcare: A systematic review and framework for future research. Medicine 99(36) (2020). https://doi.org/10.1097/MD.0000000000021967 Zhang, Y., He, Y., Jin, Y., Qin, H., Azhar, M., Huang, J.Z.: A robust k-means clustering algorithm based on observation point mechanism. Complexity 2020 (2020). https://doi.org/10.1155/2020/3650926 Zhou, Y., Chen, L., Yang, Y., Li, Y., Cheng, G., Fu, Y., Zhu, C., Liu, Y., Mao, H.: Electric vehicle routing problem: Model and algorithm. In: 2020 12th international conference on measuring technology and mechatronics automation (ICMTMA), pp. 1049–1054 (2020). https://doi.org/10.1109/ICMTMA50254.2020.00225 Zhou, Y., Kou, Y., Zhou, M.: Bilevel memetic search approach to the soft-clustered vehicle routing problem. Trans. Sci. (2022). https://doi.org/10.1287/trsc.2022.1186