Aggregating Robots Compute: An Adaptive Heuristic for the Euclidean Steiner Tree Problem

It is becoming state-of-the-art to form large-scale multi-agent systems or artificial swarms showing adaptive behavior by constructing high numbers of cooperating, embodied, mobile agents (robots). For the sake of space- and cost-efficiency such robots are typically miniaturized and equipped with only few sensors and actuators resulting in rather simple devices. In order to overcome these constraints, bio-inspired concepts of self-organization and emergent properties are applied. Thus, accuracy is usually not a trait of such systems, but robustness and fault tolerance are. It turns out that they are applicable to even hard problems and reliably deliver approximated solutions. Based on these principles we present a heuristic for the Euclidean Steiner tree problem which is NP-hard. Basically, it is the problem of connecting objects in a plane efficiently. The proposed system is investigated from two different viewpoints: computationally and behaviorally. While the performance is, as expected, clearly suboptimal but still reasonably well, the system is adaptive and robust.