Abstract
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.
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References
Aaronson, S.: NP-complete problems and physical reality. ACM SIGACT News 36(1), 30–52 (2005)
Bonabeau, E., Dorigo, M., Theraulaz, G.: Swarm Intelligence: From Natural to Artificial Systems. Oxford Univ. Press, Oxford (1999)
Chlebík, M., Chlebíková, J.: Approximation hardness of the Steiner Tree problem on graphs. In: Penttonen, M., Schmidt, E.M. (eds.) SWAT 2002. LNCS, vol. 2368, pp. 170–179. Springer, Heidelberg (2002)
Dorigo, M., Caro, G.D.: Ant Colony Optimization: A new meta-heuristic. In: Angeline, P.J., Michalewicz, Z., Schoenauer, M., Yao, X., Zalzala, A. (eds.) Proceedings of the 1999 Congress on Evolutionary Computation (CEC 1999), Piscataway, NJ, pp. 1470–1477. IEEE Press, Los Alamitos (1999)
Garey, M.R., Graham, R.L., Johnson, D.S.: Some NP-complete geometric problems. In: Annual ACM Symp. on Theory of Computing, pp. 10–22 (1976)
Hales, T.C.: The honeycomb conjecture. Discrete and Computational Geometry 25(1), 1–22 (2001)
Hamann, H.: Modeling and investigation of robot swarms. Master’s thesis, University of Stuttgart, Germany (2006)
Hamann, H., Wörn, H.: Embodied computation. Parallel Processing Letters 17(3), 287–298 (2007)
Hofstadter, D.R.: Gödel, Escher, Bach. Basic Books (1979)
Hwang, F.K., Richards, D.S., Winter, P.: The Steiner Tree Problem. North-Holland, Amsterdam (1992)
Kolb, M., Herrmann, H.J.: The sol-gel transition modelled by irreversible aggregation of clusters. J. Physics A 18(8), L435–L441 (1985)
LaValle, S.M., Kuffner, J.J.: Rapidly-exploring random trees: Progress and prospects. In: Donald, B.R., Lynch, K.M., Rus, D. (eds.) Algorithmic and Computational Robotics, Wellesley, MA, USA, pp. 293–308. A. K. Peters (2001)
Litus, Y., Zebrowski, P., Vaughan, R.: Energy-efficient multi-robot rendezvous: Parallel solutions by embodied approximation. In: Workshop on Algorithmic equivalencies between biological and robotic swarms, Atlanta, USA (June 2007)
Payton, D., Daily, M., Estowski, R., Howard, M., Lee, C.: Pheromone robotics. Autonomous Robots 11(3), 319–324 (2001)
Robins, G., Zelikovsky, A.: Improved Steiner Tree approximation in graphs. In: 11th ACM-SIAM Symposium on Discrete Algorithms, pp. 770–779 (2000)
Seyfried, J., Szymanski, M., Bender, N., Estaña, R., Thiel, M., Wörn, H.: The I-SWARM project. In: Şahin, E., Spears, W.M. (eds.) Swarm Robotics Workshop, pp. 70–83. Springer, Heidelberg (2005)
Tom, J., Witten, A., Sander, L.M.: Diffusion-limited aggregation, a kinetic critical phenomenon. Phys. Rev. Lett. 19, 1400–1403 (1981)
Warme, D., Winter, P., Zachariasen, M.: Geosteiner homepage, http://www.diku.dk/geosteiner/
Zachariasen, M., Winter, P.: Concatenation-based greedy heuristics for the Steiner tree problem in the Euclidean plane. Algorithmica 25, 418–437 (1999)
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Hamann, H., Wörn, H. (2008). Aggregating Robots Compute: An Adaptive Heuristic for the Euclidean Steiner Tree Problem. In: Asada, M., Hallam, J.C.T., Meyer, JA., Tani, J. (eds) From Animals to Animats 10. SAB 2008. Lecture Notes in Computer Science(), vol 5040. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-69134-1_44
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DOI: https://doi.org/10.1007/978-3-540-69134-1_44
Publisher Name: Springer, Berlin, Heidelberg
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