ADMM-Based Distributed Routing and Rebalancing for Autonomous Mobility on Demand Systems

This paper addresses decision making for networked autonomous vehicles in mobility on demand (MoD) systems. An optimization formulation, termed Pick-up, Delivery, and Rebalancing Problem with Time Windows (PDRPTW), that simultaneously account for the scheduling of the vehicles in response to existing service requests and the rebalancing of them for future requests is presented in the node-based graph with the vehicle working states. Then, the alternating direction method of multipliers (ADMM) decompose the PDRPTW problem into each vehicle's routing. The ADMM framework allows for decomposition of the problem into minimization of total vehicle routing cost and minimization of idle vehicles' waiting cost; the method leads to consensus upon the routing and waiting plans of the vehicles. Numerical examples demonstrate the efficacy and the benefits of the proposed distributed algorithm on instances of Solomon benchmark and rebalancing scenario.