Skip to main content
Log in

Models and Algorithms for Multiagent Hierarchical Routing with Time Windows

  • SYSTEM ANALYSIS AND OPERATIONS RESEARCH
  • Published:
Journal of Computer and Systems Sciences International Aims and scope

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).

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Fig. 1.
Fig. 2.
Fig. 3.
Fig. 4.
Fig. 5.
Fig. 6.
Fig. 7.
Fig. 8.
Fig. 9.
Fig. 10.
Fig. 11.
Fig. 12.
Fig. 13.
Fig. 14.
Fig. 15.
Fig. 16.
Fig. 17.
Fig. 18.

Similar content being viewed by others

REFERENCES

  1. 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

  2. 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

    Article  Google Scholar 

  3. 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

  4. 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

    Article  MathSciNet  Google Scholar 

  5. 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

  6. M. L. Fisher, “Optimal solution of vehicle routing problems using minimum K-trees,” Oper. Res. 42 (2), 626–642 (1994).

    Article  MathSciNet  Google Scholar 

  7. 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

    Book  Google Scholar 

  8. 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

    Article  MathSciNet  Google Scholar 

  9. 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

  10. 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

    Article  Google Scholar 

  11. Solomon benchmark. https://www.sintef.no/projectweb/top/vrptw/solomon-benchmark/.

  12. 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.

  13. 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).

    Google Scholar 

  14. 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

  15. 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

  16. 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

  17. 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

    Book  Google Scholar 

  18. 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.

  19. J. Poullet, Leveraging machine learning to solve the vehicle routing problem with time windows (2020). https://hdl.handle.net/1721.1/127285.

  20. 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

  21. 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

    Article  Google Scholar 

  22. 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].

    Google Scholar 

  23. 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).

    Google Scholar 

  24. 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

    Article  Google Scholar 

  25. 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

    Article  Google Scholar 

  26. Ch. French, E. W. Smykay, D. J. Bowersox, and F. H. Mossman, “Physical distribution management,” Am. J. Agric. Econ. 43 (3), 728–30 (1961).

    Google Scholar 

  27. 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

    Article  Google Scholar 

  28. 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

    Article  Google Scholar 

  29. 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.

    Google Scholar 

  30. 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

    Article  Google Scholar 

  31. É. D. Taillard, “FANT: Fast Ant System,” Tech. Rep. Istituto Dalle Molle di Studi sull’Intelligenza Artificiale (Lugano, 1998).

  32. 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

    Article  Google Scholar 

  33. 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).

    Article  Google Scholar 

  34. 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

    Book  Google Scholar 

  35. 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.

  36. 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.

  37. 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

    Article  Google Scholar 

  38. M. M. Flood, “The traveling salesman problem,” Oper. Res. 4, 61–75 (1956).

    Article  Google Scholar 

  39. 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

  40. Scipy. https://scipy.org/.

  41. Concorde TSP Solver. https://www.math.uwaterloo.ca/tsp/concorde.html.

  42. PyConcorde. https://github.com/jvkersch/pyconcorde.

Download references

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

Authors

Corresponding authors

Correspondence to M. G. Kozlova, D. V. Lemtyuzhnikova, V. A. Luk’yanenko or O. O. Makarov.

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

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

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

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1134/S106423072305009X

Navigation