In the light of the impact of transportation management and logistics on the economy and extending the efficiency in the systems of production, the well-timed supply of materials and products is a momentous prerequisite for economic and environmental extension.  In addition, since the optimality usage of communication networks and detecting optimal routes to decrease traffic volume and travel time in the logistics network by discovering optimal routes for vehicles to attain the destination, is an fundamental challenge and a goal in the smart transportation system,  hence, in this paper, we accomplish a new model targeted to minimize the costs of customer service for a dynamic transport network in a safe solution in regard to monitor the dynamic production process and achieve the instantaneous information dependent upon the traffic situation of an advanced evolutionary genetic algorithm.  Besides, the Logit function is used to obtain probability and assign routes in the model.  Eventually, So that to evaluate the proficiency and feasibility of the suggested model, a number of numerical examples accompanied with sensitivity analysis are demonstrated.