Fractals2019: Combinatorial Optimisation with Dynamic Constraint Annealing

  • Mikhail ProkopenkoEmail author
  • Peter Wang
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 11531)


Fractals2019 started as a new experimental entry in the RoboCup Soccer 2D Simulation League, based on Gliders2d code base, and advanced to become a RoboCup-2019 champion. We employ combinatorial optimisation methods, within the framework of Guided Self-Organisation, with the search guided by local constraints. We present examples of several tactical tasks based on the Gliders2d code (version v2), including the search for an optimal assignment of heterogeneous player types, as well as blocking behaviours, offside trap, and attacking formations. We propose a new method, Dynamic Constraint Annealing, for solving dynamic constraint satisfaction problems, and apply it to optimise thermodynamic potential of collective behaviours, under dynamically induced constraints.



We thank HELIOS team for their excellent code base of agent2d, as well as several members of Gliders team contributing during 2012–2016: David Budden, Oliver Cliff, Victor Jauregui and Oliver Obst.


  1. 1.
    Akiyama, H., Nakashima, T.: HELIOS base: an open source package for the RoboCup soccer 2D simulation. In: Behnke, S., Veloso, M., Visser, A., Xiong, R. (eds.) RoboCup 2013. LNCS (LNAI), vol. 8371, pp. 528–535. Springer, Heidelberg (2014). Scholar
  2. 2.
    Akiyama, H., Nakashima, T., Fukushima, T., Suzuki, Y., Ohori, A.: Helios 2019: team description paper. In: RoboCup 2019 Symposium and Competitions, Sydney, Australia (2019)Google Scholar
  3. 3.
    Akiyama, H., Noda, I.: Multi-agent positioning mechanism in the dynamic environment. In: Visser, U., Ribeiro, F., Ohashi, T., Dellaert, F. (eds.) RoboCup 2007. LNCS (LNAI), vol. 5001, pp. 377–384. Springer, Heidelberg (2008). Scholar
  4. 4.
    Ay, N., Bertschinger, N., Der, R., Guttler, F., Olbrich, E.: Predictive information and explorative behavior of autonomous robots. Eur. Phys. J. B 63, 329–339(11) (2008)MathSciNetCrossRefGoogle Scholar
  5. 5.
    Bai, A., Wu, F., Chen, X.: Online planning for large Markov decision processes with hierarchical decomposition. ACM Trans. Intell. Syst. Technol. 6(4), 45:1–45:28 (2015)CrossRefGoogle Scholar
  6. 6.
    Balduzzi, D., Tuyls, K., Perolat, J., Graepel, T.: Re-evaluating evaluation. In: Proceedings of the 32nd International Conference on Neural Information Processing Systems, USA, pp. 3272–3283 (2018)Google Scholar
  7. 7.
    Budden, D.M., Wang, P., Obst, O., Prokopenko, M.: RoboCup simulation leagues: enabling replicable and robust investigation of complex robotic systems. IEEE Trans. Robot. Autom. 22(3), 140–146 (2015)CrossRefGoogle Scholar
  8. 8.
    Černý, V.: Thermodynamical approach to the traveling salesman problem: an efficient simulation algorithm. J. Optimiz. Theory App. 45(1), 41–51 (1985)MathSciNetCrossRefGoogle Scholar
  9. 9.
    Cheng, Z., et al.: YuShan2018 team description paper for RoboCup2018. In: RoboCup 2018 Symposium and Competitions, Montreal, Canada (2018)Google Scholar
  10. 10.
    Cioppa, T.M., Lucas, T.W.: Efficient nearly orthogonal and space-filling Latin hypercubes. Technometrics 49(1), 45–55 (2007)MathSciNetCrossRefGoogle Scholar
  11. 11.
    Cliff, O.M., Lizier, J.T., Wang, X.R., Wang, P., Obst, O., Prokopenko, M.: Towards quantifying interaction networks in a football match. In: Behnke, S., Veloso, M., Visser, A., Xiong, R. (eds.) RoboCup 2013. LNCS (LNAI), vol. 8371, pp. 1–12. Springer, Heidelberg (2014). Scholar
  12. 12.
    Cliff, O., Lizier, J., Wang, X.R., Wang, P., Obst, O., Prokopenko, M.: Quantifying long-range interactions and coherent structure in multi-agent dynamics. Artif. Life 23(1), 34–57 (2017)CrossRefGoogle Scholar
  13. 13.
    Crosato, E., Spinney, R.E., Nigmatullin, R., Lizier, J.T., Prokopenko, M.: Thermodynamics and computation during collective motion near criticality. Phys. Rev. E 97, 012120 (2018)CrossRefGoogle Scholar
  14. 14.
    DeepMind: AlphaStar: Mastering the Real-Time Strategy Game StarCraft II (2019).
  15. 15.
    Der, R., Martius, G.: The Playful Machine – Theoretical Foundation and Practical Realization of Self-Organizing Robots. Springer, Heidelberg (2012). Scholar
  16. 16.
    Eglese, R.W.: Simulated annealing: a tool for operational research. Eur. J. Oper. Res. 46(3), 271–281 (1990)MathSciNetCrossRefGoogle Scholar
  17. 17.
    Gabel, T., Klöppner, P., Godehardt, E., Tharwat, A.: Communication in soccer simulation: on the use of wiretapping opponent teams. In: Holz, D., Genter, K., Saad, M., von Stryk, O. (eds.) RoboCup 2018. LNCS (LNAI), vol. 11374, pp. 3–15. Springer, Cham (2019). Scholar
  18. 18.
    Hamann, H., et al.: Hybrid societies: challenges and perspectives in the design of collective behavior in self-organizing systems. Front. Robot. AI 3, 14 (2016)CrossRefGoogle Scholar
  19. 19.
    Kim, P., Nakamura, S., Kurabayashi, D.: Hill-climbing for a noisy potential field using information entropy. Paladyn 2(2), 94–99 (2011)Google Scholar
  20. 20.
    Klyubin, A., Polani, D., Nehaniv, C.: Representations of space and time in the maximization of information flow in the perception-action loop. Neural Comput. 19(9), 2387–2432 (2007)MathSciNetCrossRefGoogle Scholar
  21. 21.
    Knuth, D.E.: The Art of Computer Programming, vol. 3. Addison-Wesley, Boston (1997)zbMATHGoogle Scholar
  22. 22.
    Kok, J.R., Vlassis, N., Groen, F.: UvA Trilearn 2003 team description. In: Polani, D., Browning, B., Bonarini, A., Yoshida, K. (eds.) Proceedings of the CD RoboCup 2003. Springer, Heidelberg (2003)Google Scholar
  23. 23.
    Kosorukoff, A.: Human based genetic algorithm. In: 2001 IEEE International Conference on Systems, Man, and Cybernetics, vol. 5, pp. 3464–3469. IEEE (2001)Google Scholar
  24. 24.
    Kropaczek, D.J., Walden, R.: Constraint annealing method for solution of multiconstrained nuclear fuel cycle optimization problems. Nucl. Sci. Eng. 193(5), 506–522 (2019)CrossRefGoogle Scholar
  25. 25.
    Laarhoven, P.J.M., Aarts, E.H.L. (eds.): Simulated Annealing: Theory and Applications. Kluwer Academic Publishers, Norwell (1987)zbMATHGoogle Scholar
  26. 26.
    Martius, G., Herrmann, J.M., Der, R.: Guided self-organisation for autonomous robot development. In: Almeida e Costa, F., Rocha, L.M., Costa, E., Harvey, I., Coutinho, A. (eds.) ECAL 2007. LNCS (LNAI), vol. 4648, pp. 766–775. Springer, Heidelberg (2007). Scholar
  27. 27.
    Nakashima, T., Akiyama, H., Suzuki, Y., Ohori, A., Fukushima, T.: HELIOS2018: team description paper. In: RoboCup 2018 Symposium and Competitions, Montreal, Canada (2018)Google Scholar
  28. 28.
    Nehaniv, C., Polani, D., Olsson, L., Klyubin, A.: Evolutionary information-theoretic foundations of sensory ecology: channels of organism-specific meaningful information. In: Modeling Biology: Structures, Behaviour, Evolution, pp. 9–11 (2005)Google Scholar
  29. 29.
    Noda, I., Stone, P.: The RoboCup soccer server and cmunited clients: implemented infrastructure for MAS research. Auton. Agents Multi-Agent Syst. 7(1–2), 101–120 (2003)CrossRefGoogle Scholar
  30. 30.
    Prokopenko, M., Gerasimov, V., Tanev, I.: Evolving spatiotemporal coordination in a modular robotic system. In: Nolfi, S., et al. (eds.) SAB 2006. LNCS (LNAI), vol. 4095, pp. 558–569. Springer, Heidelberg (2006). Scholar
  31. 31.
    Prokopenko, M., Gerasimov, V., Tanev, I.: Measuring spatiotemporal coordination in a modular robotic system. In: Rocha, L., Yaeger, L., Bedau, M., Floreano, D., Goldstone, R., Vespignani, A. (eds.) Artificial Life X: Proceedings of The 10th International Conference on the Simulation and Synthesis of Living Systems, Bloomington IN, USA, pp. 185–191 (2006)Google Scholar
  32. 32.
    Prokopenko, M., Obst, O., Wang, P., Budden, D., Cliff, O.M.: Gliders 2013: tactical analysis with information dynamics. In: RoboCup 2013 Symposium and Competitions, Eindhoven, The Netherlands (2013)Google Scholar
  33. 33.
    Prokopenko, M., Wang, P., Obst, O., Jaurgeui, V.: Gliders 2016: integrating multi-agent approaches to tactical diversity. In: RoboCup 2016 Symposium and Competitions, Leipzig, Germany (2016)Google Scholar
  34. 34.
    Prokopenko, M.: Guided self-organization. HFSP J. 3(5), 287–289 (2009)CrossRefGoogle Scholar
  35. 35.
    Prokopenko, M. (ed.): Guided Self-Organization: Inception. ECC, vol. 9. Springer, Heidelberg (2014). Scholar
  36. 36.
    Prokopenko, M., Einav, I.: Information thermodynamics of near-equilibrium computation. Phys. Rev. E 91, 062143 (2015)MathSciNetCrossRefGoogle Scholar
  37. 37.
    Prokopenko, M., Wang, P.: Evaluating team performance at the edge of chaos. In: Polani, D., Browning, B., Bonarini, A., Yoshida, K. (eds.) RoboCup 2003. LNCS (LNAI), vol. 3020, pp. 89–101. Springer, Heidelberg (2004). Scholar
  38. 38.
    Prokopenko, M., Wang, P.: Disruptive innovations in RoboCup 2D soccer simulation league: from Cyberoos’98 to Gliders2016. In: Behnke, S., Sheh, R., Sarıel, S., Lee, D.D. (eds.) RoboCup 2016. LNCS (LNAI), vol. 9776, pp. 529–541. Springer, Cham (2017). Scholar
  39. 39.
    Prokopenko, M., Wang, P.: Fractals 2019: guiding self-organisation of intelligent agents. In: RoboCup 2019 Symposium and Competitions, Sydney, Australia (2019)Google Scholar
  40. 40.
    Prokopenko, M., Wang, P.: Gliders2d: source code base for RoboCup 2D soccer simulation league. In: Chalup, S., Niemueller, T., Suthakorn, J., Williams, M.-A. (eds.) RoboCup 2019. LNCS (LNAI), vol. 11531, pp. 418–428. Springer, Cham (2019).
  41. 41.
    Prokopenko, M., Wang, P., Marian, S., Bai, A., Li, X., Chen, X.: RoboCup 2D soccer simulation league: evaluation challenges. In: Akiyama, H., Obst, O., Sammut, C., Tonidandel, F. (eds.) RoboCup 2017. LNCS (LNAI), vol. 11175, pp. 325–337. Springer, Cham (2018). Scholar
  42. 42.
    Reis, L.P., Lau, N., Oliveira, E.C.: Situation based strategic positioning for coordinating a team of homogeneous agents. BRSDMAS 2000. LNCS (LNAI), vol. 2103, pp. 175–197. Springer, Heidelberg (2001). Scholar
  43. 43.
    Riedmiller, M., Gabel, T., Trost, F., Schwegmann, T.: Brainstormers 2D - team description 2008. In: RoboCup 2008 (2008)Google Scholar
  44. 44.
    Russell, S.J., Norvig, P.: Artificial Intelligence: A Modern Approach. Prentice Hall, New Jersey (2003)zbMATHGoogle Scholar
  45. 45.
    Stone, P., Riley, P., Veloso, M.: The CMUnited-99 champion simulator team. In: Veloso, M., Pagello, E., Kitano, H. (eds.) RoboCup 1999. LNCS (LNAI), vol. 1856, pp. 35–48. Springer, Heidelberg (2000). Scholar
  46. 46.
    Stone, P., Veloso, M.: Task decomposition, dynamic role assignment, and low-bandwidth communication for real-time strategic teamwork. Artif. Intell. 110(2), 241–273 (1999)CrossRefGoogle Scholar
  47. 47.
    Tavafi, A., Nozari, N., Vatani, R., Yousefi, M.R., Rahmatinia, S., Pirdir, P.: MarliK 2012 soccer 2D simulation team description paper. In: RoboCup 2012 Symposium and Competitions, Mexico City, Mexico (2012)Google Scholar
  48. 48.
    Verfaillie, G., Schiex, T.: Solution reuse in dynamic constraint satisfaction problems. In: Proceedings of the Twelfth National Conference on Artificial Intelligence, AAAI 1994, vol. 1, pp. 307–312. American Association for Artificial Intelligence, Menlo Park (1994)Google Scholar
  49. 49.
    Yang, Z., et al.: MT2018: team description paper. In: RoboCup 2018 Symposium and Competitions, Montreal, Canada (2018)Google Scholar
  50. 50.
    Zuparic, M., Jauregui, V., Prokopenko, M., Yue, Y.: Quantifying the impact of communication on performance in multi-agent teams. Artif. Life Robot. 22(3), 357–373 (2017)CrossRefGoogle Scholar

Copyright information

© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.Complex Systems Research Group, Faculty of EngineeringThe University of SydneyCamperdownAustralia
  2. 2.Data MiningCSIRO Data61EppingAustralia

Personalised recommendations