Abstract
The problem of modeling real logistics systems arranged in a hierarchical manner is considered. Clusters of lower level consumers are formed that meet the time window (TW) constraints for each consumer and the cluster as a whole. In each such cluster, a traveling salesman’s route is constructed and the vertex closest to the central node, which is the vertex of reloading goods from heavy vehicles (Vs) to light Vs serving consumer clusters, is selected. The transshipment vertices, in turn, are combined into higher level traveling salesmen’s routes, taking into account TWs for routes of this level. The software implementation is tested on well-known networks. The technique is applicable for the synthesis of the central distribution center and system distribution centers of the lower level, as well as for calculating the required number of vehicles (agents).
Similar content being viewed by others
REFERENCES
F. Liu, Ch. Lu, L. Gui, Q. Zhang, X. Tong, and M. Yuan, “Heuristics for vehicle routing problem: A survey and recent advance,” 2023. https://doi.org/10.48550/arXiv.2303.04147
S.-Y. Tan and W.-C. Yen, “The vehicle routing problem: State-of-the-art classification and review,” Appl. Sci. 11 (21), 10295 (2021). https://doi.org/10.3390/app112110295
H. Li, H. Wang, J. Chen, and M. Bai, “Two-echelon vehicle routing problem with satellite bi-synchronization,” Eur. J. Oper. Res. 288 (3) (2020). https://doi.org/10.1016/j.ejor.2020.06.019
R. Baldacci, A. Mingozzi, R. Roberti, and R. Clavo, “An exact algorithm for the two-echelon capacitated vehicle routing problem,” Oper. Res. 61 (2), 298–314 (2013). https://doi.org/10.1287/opre.1120.1153
G. Xiaobing, Y. Wang, Sh. Li, and B. Niu, “Vehicle routing problem with time windows and simultaneous delivery and pick-up service based on MCPSO,” Math. Probl. Eng. 2 (2012). https://doi.org/10.1155/2012/104279
M. L. Fisher, “Optimal solution of vehicle routing problems using minimum K-trees,” Oper. Res. 42 (2), 626–642 (1994).
B. Kallehauge, J. Larsen, O. Madsen, and M. Solomon, “Vehicle routing problem with time windows,” in Column Generation (Springer, 2006), pp. 67–98. https://doi.org/10.1007/0-387-25486-2_3
R. Macedo, C. Alves, J. Carvalho, F. Clautiaux, and S. Hanafi, “Solving the vehicle routing problem with time windows and multiple routes exactly using a pseudo-polynomial model,” Eur. J. Oper. Res. 214 (3), 536–545 (2011). https://doi.org/10.1016/j.ejor.2011.04.037
W. Zhang, D. Yang, G. Zhang, and M. Gen, “Hybrid multiobjective evolutionary algorithm with fast sampling strategy-based global search and route sequence difference-based local search for VRPTW,” Expert Syst. Appl. 145 (2020). https://doi.org/10.1016/j.eswa.2019.113151
M. Mahmoud and A.-R. Hedar, “Three strategies tabu search for vehicle routing problem with time windows,” Comput. Sci. Inf. Technol. 2 (2), 108–119 (2014). https://doi.org/10.13189/csit.2014.020208
Solomon benchmark. https://www.sintef.no/projectweb/top/vrptw/solomon-benchmark/.
Z. Zhou, X. Ma, Z. Liang, and Z. Zhu, “Multi-objective multi-factorial memetic algorithm based on bone route and large neighborhood local search for VRPTW,” in IEEE Congress on Evolutionary Computation (CEC) (Glasgow, 2020). https://doi.org/10.1109/CEC48606.2020.9185528.
H. Shu, H. Zhou, Z. He, and X. Hu, “Two-stage multi-objective evolutionary algorithm based on classified population for tri-objective VRPTW,” Int. J. Unconv. Comput. 16 (2–3), 141–171 (2021).
W. Xu, X. Wang, and Q. Guo, “Gathering strength, gathering storms: knowledge transfer via selection for VRPTW,” Mathematics 10 (16) (2022). https://doi.org/10.3390/math10162888
H. Fan, X. Ren, and Y. Zhang, “A chaotic genetic algorithm with variable neighborhood search for solving time-dependent green VRPTW with fuzzy demand,” Symmetry 14 (10) (2022). https://doi.org/10.3390/sym14102115
M. Nasri, I. Hafidi, and A. Metrane, “Multithreading parallel robust approach for the VRPTW with uncertain service and travel times,” Symmetry 13 (1) (2020). https://doi.org/10.3390/sym13010036
A. F. Kummer, L. S. Buriol, and O. C. B. de Araújo, “A biased random key genetic algorithm applied to the VRPTW with skill requirements and synchronization constraints,” in GECCO'20: Genetic and Evolutionary Computation Conference (Cancun, Mexico, 2020). https://doi.org/10.1145/3377930.3390209
A. Jungwirth, M. Frey, and R. Kolisch, The vehicle routing problem with time windows, flexible service locations and time-dependent location capacity (2020). https://www.semanticscholar.org/paper/The-vehicle-routing-problem-with-time-windows%2C-and-Jungwirth-Frey/22db87ca3cba4ea33561667c190f0443a93925bf.
J. Poullet, Leveraging machine learning to solve the vehicle routing problem with time windows (2020). https://hdl.handle.net/1721.1/127285.
M. A. Figliozzi, “An iterative construction and improvement algorithm for the vehicle routing problem with soft time windows,” Transp. Res. P. C. Emerg. Technol. 18 (5) (2010). https://doi.org/10.1016/j.proeng.2016.07.236
A. N. Melnikov, I. I. Lyubimov, and K. I. Manayev, “Improvement of the Vehicles Fleet Structure of a Specialized Motor Transport Enterprise,” Proc. Eng 150, 1200–1208 (2016). https://doi.org/10.1016/j.proeng.2016.07.236
M.S. Germanchuk, M.G. Kozlova, and V.A. Luk’yanenko, “Models of generalized traveling salesman problems in the intellectualization of decision support for geoinformation systems,” in Geographical and Geoecological Research in Ukraine and Adjacent Territories: Collection of Scientific Papers, Ed. by B. A. Vakhrushev (DIAIPI, Simferopol, 2013), Vol. 1, pp. 413–415 [in Russian].
A. Rakhmangulov, A. Kolga, and N. Osintsev, “Mathematical model of optimal empty rail car distribution at railway transport nodes,” Transp. Probl. 9 (3), 19–32 (2014).
R. Uthayakumar and S. Prlyan, “Pharmaceutical supply chain and inventory management strategies: Optimization for a pharmaceutical company and a hospital,” Oper. Res. Heal Care 2 (3), 52–64 (2013). https://doi.org/10.1016/j.orhc.2013.08.001
A. Azzi, A. Persona, F. Sgarbossa, and M. Bonin, “Drug inventory management and distribution: Outsourcing logistics to third-party providers,” Strategic Outsourcing: Int. J. 6 (1), 48–64 (2013). https://doi.org/10.1108/17538291311316063
Ch. French, E. W. Smykay, D. J. Bowersox, and F. H. Mossman, “Physical distribution management,” Am. J. Agric. Econ. 43 (3), 728–30 (1961).
M. Dorigo and L. M. Gambardella, “Ant colony system: A cooperative learning approach to the traveling salesman problem,” IEEE Trans. Neural Networks 1 (1), 53–66 (1997). https://doi.org/10.1109/4235.585892
M. Dorigo and L. M. Gambardella, “Ant colonies for the traveling salesman problem,” BioSystems 43, 73–81 (1997). https://doi.org/10.1016/S0303-2647(97)01708-5
T. Stützle, “Local search algorithms for combinatorial problems : Analysis, improvements, and new applications,” Dr. rer. nat. Dissertation (Darmstadt Technological University, Germany, 1998). https://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.71.1869&rep=rep1&type=pdf.
N. Kohl, J. Desrosiers, O. B. G. Madsen, M. M. Solomon, and F. Soumis, “2-path cuts for the vehicle routing problem with time windows,” Transp. Sci. 33, 101–116 (1999). https://doi.org/10.1287/trsc.33.1.101
É. D. Taillard, “FANT: Fast Ant System,” Tech. Rep. Istituto Dalle Molle di Studi sull’Intelligenza Artificiale (Lugano, 1998).
P. Badeau, M. Gendreau, F. Guertin, J.-Y. Potvin, and É. D. Taillard, “A parallel tabu search heuristic for the vehicle routing problem with time windows,” Transp. Res. P. C. Emerg. Technol. 1 (2), 109–122 (1997). https://doi.org/10.1016/S0968-090X(97)00005-3
É. D. Taillard, P. Badeau, M. Gendreau, F. Guertin, and J.-Y. Potvin, “A tabu search heuristic for the vehicle routing problem with soft time windows,” Transp. Sci. 31, 170–186 (1997).
P. Kilby, P. Prosser, and P. Shaw, “Guided local search for the vehicle routing problem with time windows,” in Meta-Heuristics: Advances and Trends in Local Search Paradigms for Optimization (Springer, Boston, Mass., 1999), pp. 473–486. https://doi.org/10.1007/978-1-4615-5775-3_32
P. Shaw, “Using constraint programming and local search methods to solve vehicle routing problems,” in Fourth Int. Conf. on Principles and Practice of Constraint Programming (Springer, 1998), pp. 417–431.
M. Dorigo, V. Maniezzo, and A. Colorni, “Positive feedback as a search strategy,” Dipartimento di Elettronica, Politecnico di Milano, Italy, Tech. Rep. 91-016 (1991). https://citeseerx.ist.psu.edu/viewdoc/download?doi=10.1.1.52.6342&rep=rep1&type=pdf.
M. Dorigo, V. Maniezzo, and A. Colorni, “The ant system: Optimization by a colony of cooperating agents,” IEEE Trans. Syst. Man Cybern. 26 (1), 29–41 (1996). https://doi.org/10.1109/3477.484436
M. M. Flood, “The traveling salesman problem,” Oper. Res. 4, 61–75 (1956).
M. S. Germanchuk, D. V. Lemtyuzhnikova, and V. A. Lukianenko, “Metaheuristic algorithms for multiagent routing problems,” Autom. Remote Control (Engl. Transl.) 82 (10), 1787–1801 (2021). https://doi.org/10.1134/S0005117921100155
Scipy. https://scipy.org/.
Concorde TSP Solver. https://www.math.uwaterloo.ca/tsp/concorde.html.
PyConcorde. https://github.com/jvkersch/pyconcorde.
Funding
The research results presented in Section 1 were supported by the Russian Science Foundation, project no. 22-71-10131. The research results presented in Sections 2, 3 were supported by the Ministry of Science and Higher Education of the Russian Federation, project no. 075-02-2023-1799.
Author information
Authors and Affiliations
Corresponding authors
Ethics declarations
The authors declare that they have no conflicts of interest.
Additional information
Publisher’s Note.
Pleiades Publishing remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Rights and permissions
About this article
Cite this article
Kozlova, M.G., Lemtyuzhnikova, D.V., Luk’yanenko, V.A. et al. Models and Algorithms for Multiagent Hierarchical Routing with Time Windows. J. Comput. Syst. Sci. Int. 62, 862–883 (2023). https://doi.org/10.1134/S106423072305009X
Received:
Revised:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1134/S106423072305009X