The optimal route and stops for a group of users in a road network

The rise of innovative transportation services and the recent breakthrough in the development of autonomous vehicles have stimulated the research on collective travel planning problems such as ride-sharing, carpooling, and on-demand vehicle routing in recent years. In this paper, we introduce several optimization problems to recommend a suitable route and stops of a vehicle, in a road network, for a group of users intending to travel collectively. The goal of each problem is to minimize the aggregate cost of the individual travelers’ paths and the shared route under various constraints. First, we introduce the optimal end-stops (OES) query that finds a pair of pick-up-and-drop-off locations such that the sum of the distance between these locations and the total distance traveled by the travelers from their start locations to the pick-up location and from the drop-off location to their end locations is minimized. We propose a polynomial-time fast algorithm for the OES query by utilizing the path-coherence property of road networks. Second, we formulate the optimal route and intermediate stops (ORIS) query to find a set of intermediate stops for the vehicle such that the sum of the total distance traveled by the vehicle and the total distance traveled by the travelers from their start locations to one of the stops and to their end locations from one of the stops is minimized. We propose a novel near-optimal polynomial-time-and-space heuristic algorithm for the ORIS query that performs reasonably well in practice. We also analyze several variants of this problem. Finally, we perform extensive experiments to demonstrate the efficiency and efficacy of our algorithms.