Combinatorial optimization problems are usually modeled in a static fashion. In this kind of problems, all data are known in advance, i.e. before the optimization process has started. However, in practice, many problems are dynamic, and change while the optimization is in progress. For example, in the dynamic vehicle routing problem (DVRP), new orders arrive when the working day plan is in progress. In this case, routes must be reconfigured dynamically while executing the current simulation. The DVRP is an extension of a conventional routing problem, its main interest being the connection to many real word applications (repair services, courier mail services, dial-a-ride services, etc.). In this article, a DVRP is examined, and solving methods based on particle swarm optimization and variable neighborhood search paradigms are proposed. The performance of both approaches is evaluated using a new set of benchmarks that we introduce here as well as existing benchmarks in the literature. Finally, we measure the behavior of both methods in terms of dynamic adaptation.