A metaheuristic for solving large instances of the School Bus Routing Problem

This research is motivated by a real-life school bus routing problem (SBRP). In the Flemish region (Belgium), transport of children to their school is organized by the Flemish transportation company. Each pupil having the right to be transported to its school, also has the right to a bus stop located at a distance less than 750 metres from its residence. To efficiently design the routes, a set of potential stops is determined, so that each pupil has at least one stop he/she can walk to. Routes are then determined for the school buses so that all students are picked up at a stop they are allowed to use, while making sure that the capacity of the buses is not exceeded. Flemish transportation company are faced with problems where up to 3000 students have to be picked up and brought to 7 different schools. The basic SBRP as described in [3] is a generalization of the basic vehicle routing problem (VRP) and therefore also NP-hard. In general, the VRP defines an optimization problem where allocation of stops to vehicles and the optimal sequence of stops with corresponding demands have to be determined without violating vehicle capacities. Different constraints can be envisaged such as maximum distance constraint and time windows. The total distance covered by all vehicles acts as a criterion has to be minimized [4]. In contrast with the basic VRP, total demand for each stop is not known beforehand. We only know whether a student is allowed to walk to a stop or not. This gives us the possibility to incur potential savings (e.g. not have to visit a stop), since we can assign students to stops ourselves. However, introducing these extra assignment decisions makes the problem much more difficult to solve. Figure 1 shows an example of such a SBRP. In this figure, dots represent students, the small squares represent potential stops, the large square