should be a list of longitude and latitude pairs separated by commas within the pairs and by semicolons between different pairs. You can also specify sources and destinations in the table request, which is useful in case the complete table is too large to handle in a single request.Besides doing precise routing calculations, visualization can be an important tool. The Python library folium can be quite useful to do it. It is definitely worth taking a look at it.Earlier in this article we implemented an exact MIP model for the CVRP, which is not suitable for moderate-size instances. However, algorithms that combine column generation to Branch and Cut have been successful in solving instances with up to a few hundred customers. It is worth taking a look at the research papers of Fukasawa et al. (2006) and Pecin et al. (2017).Those interested in a previous introduction to column generation might find it in my previous Medium article.Regarding meta-heuristics, the papers of Vidal et al. (2012) and Vidal (2022) are fantastic. Both are also available in the form of technical reports, with links available in the HGS-CVRP repository.In this article, two approaches for solving the Capacitated Vehicle Routing Problem (CVRP) were presented: Mixed-Integer Programming and (Meta)Heuristics. The first alternative was used to solve a small instance in which it has been successful, although it is not able to handle moderate-size or large instances. The second approach was used to solve a challenging problem from the literature with 150 customers to which the solver found a good quality solution with a 1.2% gap to the known optimal within 300s.Bynum, M. L. et al., 2021. Pyomo-optimization modeling in python. Springer.Dantzig, G. B., & Ramser, J. H., 1959. The truck dispatching problem. Management science, 6(1), 80–91.Fukasawa, R., Longo, H., Lysgaard, J., Aragão, M. P. D., Reis, M., Uchoa, E., & Werneck, R. F., 2006. Robust branch-and-cut-and-price for the capacitated vehicle routing problem. Mathematical programming, 106, 491–511.Pecin, D., Pessoa, A., Poggi, M., & Uchoa, E., 2017. Improved branch-cut-and-price for capacitated vehicle routing. Mathematical Programming Computation, 9, 61–100.Rochat, Y., & Taillard, É. D., 1995. Probabilistic diversification and intensification in local search for vehicle routing. Journal of heuristics, 1, 147–167.Toth, P., & Vigo, D., 2002. An overview of vehicle routing problems. The vehicle routing problem, 1–26.Vidal, T., 2022. Hybrid genetic search for the CVRP: Open-source implementation and SWAP* neighborhood. Computers & Operations Research, 140, 105643.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.----Towards Data ScienceChemical Engineer, Researcher, Optimization Enthusiast, and Data Scientist passionate about describing phenomena using mathematical models.Bruno Scalia C. F. LeiteinTowards Data Science--3Dominik PolzerinTowards Data Science--34Leonie MonigattiinTowards Data Science--21Bruno Scalia C. F. LeiteinTowards Data Science--Hennie de HarderinTowards Data Science--4Egor HowellinTowards Data Science--1Hennie de HarderinTowards Data Science--4Hennie de HarderinTowards Data Science--7Dominik PolzerinTowards Data Science--34Hennie de HarderinTowards Data Science--7HelpStatusWritersBlogCareersPrivacyTermsAboutText to speechTeams