Evolving Systems

, 2:189 | Cite as

Quantifying the role of complexity in a system’s performance

Original Paper


In this work we studied the relationship between a system’s complexity and its performances in solving a given task. Although complexity is generally assumed to play a key role in an agent’s performance, its influence has not been deeply investigated in the past. To this aim we analysed a predator–prey scenario where a prey had to develop several strategies to counter an increasingly skilled predator. The predator has several advantages over the prey, thus requiring the prey to develop more and more complex strategies. The prey is driven by a fully recurrent neural network trained using genetic algorithms.We conducted several experiments measuring the prey’s complexity using Kolmogorov algorithmic complexity. Our finding is that, in accordance to what was believed in literature, complexity is indeed necessary to solve non-trivial tasks. The main contribution of this work lies in having proved the necessity of complexity to solve non-trivial tasks. This has been made possible by blending together a goal oriented system with a complex one. An experiment is provided to distinguish between the complexity of a chaotic system and the complexity of a random one.


Complexity Genetic algorithms Neural networks Chaotic systems 



Dr. Riano is supported by InvestNI and the Northern Ireland Integrated Development Fund under the Centre of Excellence in Intelligent Systems project.


  1. Ashby W (1956) An introduction to cybernetics. University paperbacks. Wiley, New YorkGoogle Scholar
  2. Ashby W (1958) Requisite variety and its implications for the control of complex systems. Cybernetica 1(2):83–99MathSciNetMATHGoogle Scholar
  3. Beer RD, Gallagher JC (1992) Evolving dynamical neural networks for adaptive behavior. Adapt Behav 1(1):91–122CrossRefGoogle Scholar
  4. Bongard J (2008) Behavior chaining: incremental behavior integration for evolutionary robotics. Artif Life 11:64Google Scholar
  5. Dauce E, Quoy M, Cessac B, Doyon B, Samuelides M (1998) Self-organization and dynamics reduction in recurrent networks: stimulus presentation and learning. Neural Networks 11(3):521–533CrossRefGoogle Scholar
  6. Daw C, Finney C, Tracy E (2003) A review of symbolic analysis of experimental data. Rev Sci Instrum 74:915CrossRefGoogle Scholar
  7. Falcioni M, Loreto V, Vulpiani A (2003) Kolmogorov’s legacy about entropy, chaos, and complexity. In: The Kolmogorov legacy in physics, pp 85–108Google Scholar
  8. Floreano D, Dürr P, Mattiussi C (2008) Neuroevolution: from architectures to learning. Evol Intell 1(1):47–62CrossRefGoogle Scholar
  9. Gell-Mann M, Lloyd S (1996) Information measures, effective complexity, and total information. Complexity 2(1):44–52MathSciNetCrossRefGoogle Scholar
  10. Gomez F, Miikkulainen R (1997) Incremental evolution of complex general behavior. Adapt Behav 5(3-4):317CrossRefGoogle Scholar
  11. Grassberger P (1989) Problems in quantifying self-generated complexity. Helv Phys Acta 62(5):489–511MathSciNetGoogle Scholar
  12. Harvey I, Di Paolo E, Wood R, Quinn M, Tuci E (2005) Evolutionary robotics: a new scientific tool for studying cognition. Artif Life 11(1–2):79–98CrossRefGoogle Scholar
  13. Hülse M, Wischmann S, Pasemann F (2004) Structure and function of evolvedneuro-controllers for autonomous robots. Connect Sci 16(4):249–266CrossRefGoogle Scholar
  14. Izquierdo E, Harvey I, Beer RD (2008) Associative learning on a continuum in evolved dynamical neural networks. Adapt Behav 16(6):361–384CrossRefGoogle Scholar
  15. Kaspar F, Schuster HG (1987) Easily calculable measure for the complexity of spatiotemporal patterns. Phys Rev A 36(2):842–848MathSciNetCrossRefGoogle Scholar
  16. Khalatur P, Novikov V, Khokhlov A (2003) Conformation-dependent evolution of copolymer sequences. Phys Rev E 67(5):51901CrossRefGoogle Scholar
  17. Kolmogorov AN (1965) Three approaches to the concept of the amount of information. Prob Info Trans 1(1):1–7MathSciNetGoogle Scholar
  18. Kuusela T, Jartti T, Tahvanainen K, Kaila T (2002) Nonlinear methods of biosignal analysis in assessing terbutaline-induced heart rate and blood pressure changes. Am J Physiol-Heart Circ Physiol 282(2):H773Google Scholar
  19. Lenski RE, Ofria C, Pennock RT, Adami C (2003) The evolutionary origin of complex features. Nature 423(6936):139–144. doi: 10.1038/nature01568 Google Scholar
  20. Nelson AL, Barlow GJ, Doitsidis L (2009) Fitness functions in evolutionary robotics: a survey and analysis. Robot Auton Syst 57(4):345–370CrossRefGoogle Scholar
  21. Nolfi S, Floreano D (1998) Coevolving predator and prey robots: do “arms race” arise in artificial evolution? Artif Life 4(4):311–335CrossRefGoogle Scholar
  22. Nolfi S, Floreano D (1999) Learning and evolution. Auton Robots 7(1):89–113CrossRefGoogle Scholar
  23. Paine RW, Tani J (2004) Motor primitive and sequence self-organization in a hierarchical recurrent neural network. Neural Netw 17(8–9):1291–1309CrossRefGoogle Scholar
  24. Perone CS (2009) Pyevolve: a Python open-source framework for genetic algorithms. SIGEVOlution 4(1):12–20CrossRefGoogle Scholar
  25. Riano L, McGinnity TM (2010) On the emergence of novel behaviours from complex non linear systems. In: Proceeding of BICA 2010. International conference on biological inspired cognitive architectures. IOS PressGoogle Scholar
  26. Stanley KO, Miikkulainen R (2004) Competitive coevolution through evolutionary complexification. J Artif Intell Res 21(1):63–100Google Scholar
  27. Urzelai J, Floreano D (2001) Evolution of adaptive synapses: robots with fast adaptive behavior in new environments. Evol Comput 9(4):495–524CrossRefGoogle Scholar
  28. Walker J, Garrett S, Wilson M (2003) Evolving controllers for real robots: a survey of the literature. Adapt Behav 11:179–203CrossRefGoogle Scholar
  29. Werbos P (1990) Backpropagation through time: what it does and how to do it. Proc IEEE 78(10):1550–1560Google Scholar

Copyright information

© Springer-Verlag 2011

Authors and Affiliations

  1. 1.Intelligent Systems Research Centre, School of Computing and Intelligent SystemsUniversity of UlsterLondonderryUK

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