The Capacitated Vehicle Routing Problem (CVRP) consists of generating a customer route for each vehicle in which the sum of the customer demands does not exceed the vehicle’s capacity. Each vehicle must start from the depot, and when it finishes visiting the last customer, it must return to the depot, thus managing to visit all customers only once by any of the vehicles and have a route solution where the sum of the distances of all the routes is the minimum. This research addressed different algorithms to give a feasible solution with an approximation concerning the best known. Fifty benchmark instances were used, which allowed us to define that the best algorithm to use is Tabu Search, achieving in these fifty instances an approximation close to the optimal, which leads us to conclude that the Tabu Search metaheuristic is easy to adapt for routing problems, allowing to obtain satisfactory results. This research proposed using the randomness and exchange method for an initial solution with a good neighborhood. Work is done with the Tabu Search algorithm to explore the solution space and obtain a global solution, and finally, an intensification process is carried out that improves the solution. This research shows that the proposed algorithms give feasible solutions with an approximation of no more than 10% difference, and in some cases, the best-known solution is obtained.