The Clustered Dial-a-Ride Problem
We study a variant of the classical dial-a-ride problem, with an application to public transport planning in rural areas. In the classical dial-a-ride problem, n users each specify a pickup and a delivery location, and the aim is to plan the least cost route to cater all requests. This can be modeled as a traveling salesmen problem in a complete graph with precedence constraints (pick-ups need to happen before deliveries). In this paper, we consider the clustered dial-a-ride problem, where we do not operate on a complete graph but on a graph composed of serially numbered cliques where each clique is connected to the next one via a single edge. This setting is inspired by door-to-door transportation for people from remote villages who want to get to another village or the next city by a bus which operates on demand. We argue that in case the optimal route exhibits certain structural properties, it can be computed significantly faster. To make use of this observation, we devise a classification algorithm which can decide whether the optimal route exhibits these structural properties before computing it. Extensive experiments on artificial and real-world instances reveal that the majority of optimal routes indeed have the desired properties and that our classifier is an efficient tool to recognize the respective instances.