Algorithms for smooth, safe and quick routing on sensor-equipped grid networks

Automation plays an important role in modern transportation and handling systems, e.g., to control the routes of aircraft and ground service equipment in airport aprons, automated guided vehicles in port terminals or in public transportation, handling robots in automated factories, drones in warehouse picking operations, etc. Information technology provides hardware and software (e.g., collision detection sensors, routing and collision avoidance logic) that contribute to safe and efficient operations, with relevant social benefits in terms of improved system performance and reduced accident rates. In this context, we address the design of efficient collision-free routes in a minimum-size routing network. We consider a grid and a set of vehicles, each moving from the bottom of the origin column to the top of the destination column. Smooth nonstop paths are required, without collisions nor deviations from shortest paths, and we investigate the minimum number of horizontal lanes allowing for such routing. The problem is known as fleet quickest routing problem on grids. We propose a mathematical formulation solved, for small instances, through standard solvers. For larger instances, we devise heuristics that, based on known combinatorial properties, define priorities, and design collision-free routes. Experiments on random instances show that our algorithms are able to quickly provide good quality solutions.