A metaheuristic for solving large instances of the school bus routing problem

The school bus routing problem discussed in this paper, is similar to the standard vehicle routing problem, but has several interesting additional features. In the standard VRP all stops to visit are given. In our school bus routing problem, we assume that a set of potential stops is given, as well as a set of students that can walk to one or more stops. The school buses used to pick up the students and transport them to their schools have a finite capacity. The goal of this routing problem is to select a subset of stops that will actually be visited by the buses, determine which stop each student should walk to and develop a set of tours that minimize the total distance travelled by all buses. The focus in this paper lies on understanding the problem in its simple form and on building a powerful meta-heuristic to solve large instances quickly. Our solution method starts with a GRASP-like savings algorithm, after which a Variable Neigbourhood Search algorithm is used to improve the initial solution. A modified version of the well-known transportation problem helps the meta-heuristic to quickly assign students to stops.