Nowadays, the vehicle routing problem is one of the most important combinational optimization problems and it has received much attention because of its real application in industrial and service-related contexts. It is considered an important topic in the logistics industry and in the field of operations research. This paper focuses on the comparison between two metaheuristics namely the Genetic Algorithm (GA) and the Discrete Artificial Bee Colony (DABC) algorithm in order to solve the vehicle routing problem with a capacity constraint. In the first step, an initial population with good solutions is created, and in the second step, the routing problem is solved by employing the genetic algorithm which incorporates genetic operators and the discrete artificial bee colony algorithm which incorporates neighbourhood operators which are used for improving the obtained solutions. Experimental tests were performed on a set of 14 instances from the literature in the case of which the related number of customers ranges typically from 50 to 200, in order to assess the effectiveness of the two employed approaches. The computational results showed that the DABC algorithm obtained good solutions and a lower computational time in comparison with the GA algorithm. They also indicated that the DABC outperformed the state-of-the-art algorithms in the context of vehicle routing for certain instances.