Optimal Routing of Modular Agents on a Graph

TL;DR

This paper introduces a heuristic algorithm for optimally routing two modular agents on a graph, considering joining and separating actions to minimize resource costs, with applications in autonomous modular vehicles.

Contribution

It presents a polynomial-time heuristic algorithm that uses graph centrality and nearest neighbor methods for optimal modular agent routing, a novel approach in this context.

Findings

Algorithm performs better than 85% of benchmarks in simulations.

Uses graph centrality to decide joining points for modules.

Efficiently estimates routing costs for joined and separated modules.

Abstract

Motivated by an emerging framework of Autonomous Modular Vehicles, we consider the abstract problem of optimally routing two modules, i.e., vehicles that can attach to or detach from each other in motion on a graph. The modules' objective is to reach a preset set of nodes while incurring minimum resource costs. We assume that the resource cost incurred by an agent formed by joining two modules is the same as that of a single module. Such a cost formulation simplistically models the benefits of joining two modules, such as passenger redistribution between the modules, less traffic congestion, and higher fuel efficiency. To find an optimal plan, we propose a heuristic algorithm that uses the notion of graph centrality to determine when and where to join the modules. Additionally, we use the nearest neighbor approach to estimate the cost routing for joined or separated modules. Based on this estimated cost, the algorithm determines the subsequent nodes for both modules. The proposed algorithm is polynomial time: the worst-case number of calculations scale as the eighth power of the number of the total nodes in the graph. To validate its benefits, we simulate the proposed algorithm on a large number of pseudo-random graphs, motivated by real transportation scenario where it performs better than the most relevant benchmark, an adapted nearest neighbor algorithm for two separate agents, more than 85 percent of the time.