Abstract
This paper considers the multi-depot vehicle routing problem with object alternation. We propose a formal statement of the problem with two types of objects and a mathematical model with two blocks of Boolean variables. First, the model is studied without gathering vehicles (mobile objects). Then, a special object (a single collection point) is introduced in the model. We show additional constraints of the mathematical model with this object. Special attention is paid to the condition of no subcycles. This condition is considered based on the adjacency matrix. Five greedy algorithms are proposed for solving the problem, two of which are iterative. One of the greedy algorithms is given a probabilistic modification based on the randomization of variables (an adaptive algorithm). Finally, the proposed algorithms are compared in terms of the average value of the objective function and the running time in a computational experiment. Also, the results of another experiment—the parametric tuning of the adaptive algorithm—are presented.
REFERENCES
Benediktovich, V.I., Demidenko, V.M., Dymkov, M.P., and Brilevskii, A.O., Vehicle Routing Models and Their Application in Logistic Supply Chains of Commodity Distribution Networks, in Ekonomika, modelirovanie, prognozirovanie (Economics. Modeling. Forecasting), 2012, vol. 6, pp. 94–106.
Litvinchev, I.S., Cedillo, G., and Velarde, M., Integrating Territory Design and Routing Problems, J. Comput. Syst. Sci. Int., 2017, vol. 56, no. 6, pp. 969–974. https://doi.org/10.1134/S1064230717060120
Kosonogova, L.G., Koroleva, A.A., and Dubasov, A.V., Analysis of the Optimal Traffic Flow Distribution When Routing the Number of Vehicles, Vestnik: Nauchnyi Zhurnal, 2021, no. 6(48), pp. 81–85.
Yusupova, N.I. and Valeev, R.S., A Routing Problem for the Delivery of a Homogeneous Product to Various Clients by Motor Vehicles, Modern High Technologies, 2020, no. 4, pp. 84–88.
Zhou, Y., Li, W., Wang, X., Qiu, Y., and Shen, W., Adaptive Gradient Descent Enabled Ant Colony Optimization for Routing Problems, Swarm and Evolutionary Computation, 2022, vol. 70(3), art. no. 101046. https://doi.org/10.1016/j.swevo.2022.101046
Ramalingam, A. and Vivekanandan, K., Genetic Algorithm Based Solution Model for Multi-depot Vehicle Routing Problem with Time Windows, International Journal of Advanced Research in Computer and Communication Engineering, 2014, vol. 3, no. 11, pp. 8433–8439.
Mazidi, A., Fakhrahmad, M., and Sadreddini, M., A Meta-heuristic Approach to CVRP Problem: Local Search Optimization Based on GA and Ant Colony, Journal of Advances in Computer Research, 2016, vol. 7, no. 1, pp. 1–22.
Medvedev, S.N., Medvedeva, O.A., Zueva, Y.R., and Chernyshova, G.D., Formulation and Algorithmization of the Interleaved Vehicle Routing Problem, Journal of Physics: Conference Series, 2019, vol. 1203, p. 012053. https://doi.org/10.1088/1742-6596/1203/1/012053
Medvedev, S., Sorokina, A., and Medvedeva, O., The Vehicle Routing Problem for Several Agents among the Objects of Two Types, Proc. 2019 XXI International Conference “Complex Systems: Control and Modeling Problems” (CSCMP), Samara, 2019, pp. 535–540.
Medvedev, S.N., A Mathematical Model and an Algorithm for Solving a Multi-Depot Vehicle Routing Problem with a Single End Point, Proceedings of Voronezh State University. Series: Systems Analysis and Information Technologies, 2021, no. 1, pp. 21–32. https://doi.org/10.17308/sait.2021.1/3368
Kenzin, M.Y., Bychkov, I.V., and Maksimkin, N.N., Rich Vehicle Routing Problem for the Multi-robot Environmental Monitoring, Izvestiya SFedU. Engineering Sciences, 2019, no. 7, pp. 82–92.
Christofides, N., Graph Theory. An Algorithmic Approach, Academic, 1975.
Gol’shtein, E.G. and Yudin, D.B., Zadachi lineinogo programmirovaniya transportnogo tipa (Transportation Linear Programming Problems), Moscow: Nauka, 1969.
Medvedev, S.N. and Medvedeva, O.A., An Adaptive Algorithm for Solving the Axial Three-Index Assignment Problem, Autom. Remote Control, 2019, vol. 80, no. 4, pp. 718–732.
Medvedev, S.N., On the Optimal Solution of the Vehicle Routing Problem with Object Alternation and a Single Collection Point, Trudy Vserossiiskoi nauchnoi konferentsii “Sovremennye metody prikladnoi matematiki, teorii upravleniya i komp’yuternykh tekhnologii” (PMTUKT-2021) (Proc. All-Russian Sci. Conf. “Modern Methods of Applied Mathematics, Control Theory and Computer Technolgies” (AMCTCT-2021)), Voronezh, 2021, pp. 97–101.
Author information
Authors and Affiliations
Corresponding author
Additional information
This paper was recommended for publication by A.A. Lazarev, a member of the Editorial Board
Rights and permissions
About this article
Cite this article
Medvedev, S.N. Greedy and Adaptive Algorithms for Multi-Depot Vehicle Routing with Object Alternation. Autom Remote Control 84, 305–325 (2023). https://doi.org/10.1134/S0005117923030086
Received:
Revised:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1134/S0005117923030086