Abstract: The Vehicle Routing Problem (VRP) can be described as the problem of designing optimal delivery or collection routes from one or several depots to a number of geographically scattered cities or customers, subject to side constraints. The dynamic case of this problem where the information is not completely known in advance has not received enough consideration. In our research, we consider this case which new requests are received along the day. Hence, they must be serviced at their locations by a set of vehicles in real time minimizing two objectives simultaneously: the total travel distance and the response time of customers. The main goal of this research is to propose a mathematic model and to find a solution for our problem using an improved evolutionary algorithm. The experimental results show that the proposed approach proved to be successful on a variety of benchmark instances in terms of solution quality.