Using the Genetic Algorithm for the Optimization of Dynamic School Bus Routing Problem-Figure 1. Example of a VRP solution

VRP is widely described as the process where the distribution vehicles deliver goods in a depot to the clients found in geographically dispersed locations and then return to the depot on the optimum route. The VRP, first introduced by Dantzig and Ramser in 1959, aims to minimize the total distance to be covered during the routing of the vehicles in a centrally-located depot (Dantzig & Ramser, 1959). The routing process is operated by taking the vehicle capacities into consideration so as to ensure that each client located on the routing plan is visited only once. The depot, vehicle, and goods concepts mentioned in the general description of VRP can be re-adapted as school, student and bus stop, based on different sectors that the problem applies to. Figure 1 shows a scheme indicating the VRP solution applied to a distribution system, where the clientele network is dispersed over three different zones.