Max-sum with Quadtrees for Continuous DCOPs with Application to Lane-Free Autonomous Driving

In this paper we put forward a novel extension of the classic Max-Sum algorithm to the framework of Continuous Distributed Constrained Optimization Problems (Continuous DCOPs), in which we model the exchanged messages by means of a popular geometric algorithm, Quadtrees. As such, the discretization process is dynamic and embedded in the internal Max-Sum operations (addition and marginal maximization). We apply our Max-Sum with Quadtrees approach to Lane-Free Autonomous Driving in a highway populated with vehicles. Our experimental evaluation verifies the efficiency of our approach in this challenging dynamic coordination domain, demonstrating its superior performance with respect to the standard Max-Sum algorithm.