Transactions on Data Analysis in Social Science

Transactions on Data Analysis in Social Science

Optimization Methods for Vehicle Routing in Transportation Planning and Logistics: A Structured Review and Algorithm-Selection Framework

Author
Department of Logistics and Supply Chain Management, Faculty of Management, Vietnam National University, Ho Chi Minh City, Vietnam
10.22034/tdas.2025.255657
Abstract
Vehicle routing lies at the core of transportation planning and logistics, and a large body of Operations Research (OR) methods has been developed to solve it. This paper presents a structured narrative review of optimization methods for the capacitated vehicle routing problem (CVRP) and its principal extensions. The review covers mixed-integer programming formulations, exact branch-and-cut and branch-and-price algorithms, classical construction heuristics, modern metaheuristics (tabu search, simulated annealing, genetic algorithms, ant colony optimization, particle swarm optimization, adaptive large neighborhood search and hybrid genetic search), matheuristics and learning-based approaches, using a compact mixed-integer linear programming (MILP) model as a common reference formulation. We propose a classification framework that organizes methods by solution guarantee, search paradigm and suitability for different problem scales, and derive practical guidelines for algorithm selection based on instance size, constraint structure, uncertainty and available computing time. We also summarize standards for fair computational comparison, as inconsistent benchmarking is a recurrent weakness of the applied metaheuristic literature. No single method dominates: exact methods remain indispensable for small or well-structured instances and for computing bounds, whereas well-engineered hybrid metaheuristics are preferred at scale, and several population-based algorithms popular in applied studies are generally less competitive than neighborhood-search-based methods on standard benchmarks. Open research directions include integrating machine learning with optimization, dynamic and stochastic routing, and reproducible benchmarking.
Keywords

[1]      Dantzig, G. B., & Ramser, J. H. (1959). The truck dispatching problem. Management Science, 6(1), 80–91. https://doi.org/10.1287/mnsc.6.1.80
[2]      Laporte, G. (2009). Fifty years of vehicle routing. Transportation Science, 43(4), 408–416. https://doi.org/10.1287/trsc.1090.0301
[3]      Toth, P., & Vigo, D. (Eds.). (2014). Vehicle routing: Problems, methods, and applications (2nd ed.). SIAM. https://doi.org/10.1137/1.9781611973594
[4]      Dantzig, G. B. (1963). Linear programming and extensions. Princeton University Press. https://doi.org/10.1515/9781400884179
[5]      Ahuja, R. K., Magnanti, T. L., & Orlin, J. B. (1993). Network flows: Theory, algorithms, and applications. Prentice Hall.
[6]      Lenstra, J. K., & Rinnooy Kan, A. H. G. (1981). Complexity of vehicle routing and scheduling problems. Networks, 11(2), 221–227. https://doi.org/10.1002/net.3230110211
[7]      Cordeau, J.-F., Gendreau, M., Laporte, G., Potvin, J.-Y., & Semet, F. (2002). A guide to vehicle routing heuristics. Journal of the Operational Research Society, 53(5), 512–522. https://doi.org/10.1057/palgrave.jors.2601319
[8]      Vidal, T., Crainic, T. G., Gendreau, M., & Prins, C. (2013). Heuristics for multi-attribute vehicle routing problems: A survey and synthesis. European Journal of Operational Research, 231(1), 1–21. https://doi.org/10.1016/j.ejor.2013.02.053
[9]      Braekers, K., Ramaekers, K., & Van Nieuwenhuyse, I. (2016). The vehicle routing problem: State of the art classification and review. Computers & Industrial Engineering, 99, 300–313. https://doi.org/10.1016/j.cie.2015.12.007
[10]   Hooker, J. N. (1995). Testing heuristics: We have it all wrong. Journal of Heuristics, 1(1), 33–42. https://doi.org/10.1007/BF02430364
[11]   Sörensen, K. (2015). Metaheuristics—the metaphor exposed. International Transactions in Operational Research, 22(1), 3–18. https://doi.org/10.1111/itor.12001
[12]   Kantorovich, L. V. (1960). Mathematical methods of organizing and planning production. Management Science, 6(4), 366–422. https://doi.org/10.1287/mnsc.6.4.366
[13]   Karmarkar, N. (1984). A new polynomial-time algorithm for linear programming. Combinatorica, 4(4), 373–395. https://doi.org/10.1007/BF02579150
[14]   Bixby, R. E. (2012). A brief history of linear and mixed-integer programming computation. Documenta Mathematica, Extra Volume ISMP, 107–121. https://doi.org/10.4171/dms/6/16
[15]   Nocedal, J., & Wright, S. J. (2006). Numerical optimization (2nd ed.). Springer. https://doi.org/10.1007/978-0-387-40065-5
[16]   Miller, C. E., Tucker, A. W., & Zemlin, R. A. (1960). Integer programming formulation of traveling salesman problems. Journal of the ACM, 7(4), 326–329. https://doi.org/10.1145/321043.321046
[17]   Baldacci, R., Mingozzi, A., & Roberti, R. (2012). Recent exact algorithms for solving the vehicle routing problem under capacity and time window constraints. European Journal of Operational Research, 218(1), 1–6. https://doi.org/10.1016/j.ejor.2011.07.037
[18]   Pecin, D., Pessoa, A., Poggi, M., & Uchoa, E. (2017). Improved branch-cut-and-price for capacitated vehicle routing. Mathematical Programming Computation, 9(1), 61–100. https://doi.org/10.1007/s12532-016-0108-8
[19]   Solomon, M. M. (1987). Algorithms for the vehicle routing and scheduling problems with time window constraints. Operations Research, 35(2), 254–265. https://doi.org/10.1287/opre.35.2.254
[20]   Gendreau, M., Laporte, G., & Séguin, R. (1996). Stochastic vehicle routing. European Journal of Operational Research, 88(1), 3–12. https://doi.org/10.1016/0377-2217(95)00050-X
[21]   Pillac, V., Gendreau, M., Guéret, C., & Medaglia, A. L. (2013). A review of dynamic vehicle routing problems. European Journal of Operational Research, 225(1), 1–11. https://doi.org/10.1016/j.ejor.2012.08.015
[22]   Clarke, G., & Wright, J. W. (1964). Scheduling of vehicles from a central depot to a number of delivery points. Operations Research, 12(4), 568–581. https://doi.org/10.1287/opre.12.4.568
[23]   Gillett, B. E., & Miller, L. R. (1974). A heuristic algorithm for the vehicle-dispatch problem. Operations Research, 22(2), 340–349. https://doi.org/10.1287/opre.22.2.340
[24]   Blum, C., & Roli, A. (2003). Metaheuristics in combinatorial optimization: Overview and conceptual comparison. ACM Computing Surveys, 35(3), 268–308. https://doi.org/10.1145/937503.937505
[25]   Gendreau, M., Hertz, A., & Laporte, G. (1994). A tabu search heuristic for the vehicle routing problem. Management Science, 40(10), 1276–1290. https://doi.org/10.1287/mnsc.40.10.1276
[26]   Kirkpatrick, S., Gelatt, C. D., & Vecchi, M. P. (1983). Optimization by simulated annealing. Science, 220(4598), 671–680. https://doi.org/10.1126/science.220.4598.671
[27]   Ropke, S., & Pisinger, D. (2006). An adaptive large neighborhood search heuristic for the pickup and delivery problem with time windows. Transportation Science, 40(4), 455–472. https://doi.org/10.1287/trsc.1050.0135
[28]   Holland, J. H. (1975). Adaptation in natural and artificial systems. University of Michigan Press.
[29]   Prins, C. (2004). A simple and effective evolutionary algorithm for the vehicle routing problem. Computers & Operations Research, 31(12), 1985–2002. https://doi.org/10.1016/S0305-0548(03)00158-8
[30]   Vidal, T., Crainic, T. G., Gendreau, M., Lahrichi, N., & Rei, W. (2012). A hybrid genetic algorithm for multidepot and periodic vehicle routing problems. Operations Research, 60(3), 611–624. https://doi.org/10.1287/opre.1120.1048
[31]   Vidal, T. (2022). Hybrid genetic search for the CVRP: Open-source implementation and SWAP* neighborhood. Computers & Operations Research, 140, 105643. https://doi.org/10.1016/j.cor.2021.105643
[32]   Dorigo, M., Maniezzo, V., & Colorni, A. (1996). Ant system: Optimization by a colony of cooperating agents. IEEE Transactions on Systems, Man, and Cybernetics—Part B: Cybernetics, 26(1), 29–41. https://doi.org/10.1109/3477.484436
[33]   Bullnheimer, B., Hartl, R. F., & Strauss, C. (1999). An improved ant system algorithm for the vehicle routing problem. Annals of Operations Research, 89, 319–328. https://doi.org/10.1023/A:1018940026670
[34]   Kennedy, J., & Eberhart, R. (1995). Particle swarm optimization. In Proceedings of the IEEE International Conference on Neural Networks (Vol. 4, pp. 1942–1948). IEEE. https://doi.org/10.1109/ICNN.1995.488968
[35]   Accorsi, L., & Vigo, D. (2021). A fast and scalable heuristic for the solution of large-scale capacitated vehicle routing problems. Transportation Science, 55(4), 832–856. https://doi.org/10.1287/trsc.2021.1059
[36]   Bengio, Y., Lodi, A., & Prouvost, A. (2021). Machine learning for combinatorial optimization: A methodological tour d’horizon. European Journal of Operational Research, 290(2), 405–421. https://doi.org/10.1016/j.ejor.2020.07.063
[37]   Nazari, M., Oroojlooy, A., Snyder, L., & Takáč, M. (2018). Reinforcement learning for solving the vehicle routing problem. Advances in Neural Information Processing Systems, 31.
[38]   Kool, W., van Hoof, H., & Welling, M. (2019). Attention, learn to solve routing problems! In International Conference on Learning Representations.
[39]   Barr, R. S., Golden, B. L., Kelly, J. P., Resende, M. G. C., & Stewart, W. R. (1995). Designing and reporting on computational experiments with heuristic methods. Journal of Heuristics, 1(1), 9–32. https://doi.org/10.1007/BF02430363
[40]   Uchoa, E., Pecin, D., Pessoa, A., Poggi, M., Vidal, T., & Subramanian, A. (2017). New benchmark instances for the capacitated vehicle routing problem. European Journal of Operational Research, 257(3), 845–858. https://doi.org/10.1016/j.ejor.2016.08.012
[41]   López-Ibáñez, M., Dubois-Lacoste, J., Pérez Cáceres, L., Birattari, M., & Stützle, T. (2016). The irace package: Iterated racing for automatic algorithm configuration. Operations Research Perspectives, 3, 43–58. https://doi.org/10.1016/j.orp.2016.09.002
Volume 7, Issue 3
Summer 2025
Pages 209-219

  • Receive Date 15 March 2025
  • Revise Date 09 June 2025
  • Accept Date 11 July 2025