Evolutionary Intelligence

, Volume 12, Issue 1, pp 83–95 | Cite as

Robustness, evolvability and phenotypic complexity: insights from evolving digital circuits

  • Nicola MilanoEmail author
  • Paolo Pagliuca
  • Stefano Nolfi
Research Paper


We analyze the relation between robustness to mutations, phenotypic complexity, and evolvability in the context of artificial circuits evolved for the ability to solve a parity problem. We demonstrate that whether robustness to mutations enhances or diminishes phenotypic variability and evolvability depends on whether robustness is achieved through the development of parsimonious (phenotypically simple) solutions, that minimize the number of genes playing functional roles, or through phenotypically more complex solutions, capable of buffering the effect of mutations. We show that the characteristics of the selection process strongly influence the robustness and the performance of the evolving candidate solutions. Finally, we propose a new evolutionary method that outperforms evolutionary algorithms commonly used in this domain.


Evolvability Robustness Phenotypic variability Phenotypic complexity Evolutionary stagnation 



  1. Abdelhalim L, Blachon S, Selbig J, Nikolosky Z (2011) Robustness of metabolic networks: a review of existing definitions. Biosystems 106(1):1–8Google Scholar
  2. Adami C (2002) Sequence complexity in Darwinian evolution. Complexity 8:49–57Google Scholar
  3. Ancel LW, Fontana W (2000) Plasticity, evolvability, and modularity in RNA. J Exp Zool Part B Mol Dev Evol 288:242–283Google Scholar
  4. Back T (1994) Selective pressure in evolutionary algorithms: a characterization of selection mechanisms. In: Proceedings of 1st IEEE conference evolutionary computation, Jun. 27–29, 1994, pp 57–62Google Scholar
  5. Bäck T, Hammel U (1994) Evolution strategies applied to perturbed objective functions. In Proceedings of the international conference on evolutionary computation. pp 40–45Google Scholar
  6. Balch M (2003) Complete digital design. McGraw-Hill, New YorkGoogle Scholar
  7. Bedau MA, Packard NH (2003) Evolution of evolvability via adaptation of mutation rates. Biosystems 69:143–162Google Scholar
  8. Beyer HG, Schwefel HP (2002) Evolution strategies—a comprehensive introduction. Nat Comput 1(1):3–52MathSciNetzbMATHGoogle Scholar
  9. Carlson JM, Doyle J (2002) Complexity and robustness. PNAS 99:2538–2545Google Scholar
  10. Crutchfield JP, Görnerup O (2006) Objects that make objects: the population dynamics of structural complexity. J R Soc Interface 3:345–349Google Scholar
  11. De Visser JA et al (2003) Perspective: evolution and detection of genetic robustness. Evolution 57(9):1959–1972Google Scholar
  12. Earl DJ, Deem MW (2004) Evolvability is a selectable trait. PNAS 101:11531–11536Google Scholar
  13. Edelman GM, Gally JA (2001) Degeneracy and complexity in biological systems. Proc Natl Acad Sci USA, 98(13):763–768Google Scholar
  14. Frei R, Whitacre J (2012) Degeneracy and networked buffering: principles for supporting emergent evolvability in agile manufacturing systems. Nat Comput 11(3):417–430MathSciNetGoogle Scholar
  15. Hartmann M, Haddow P (2004) Evolution of fault tolerant and noise-robust digital designs. IEE Proc Comput Digit Tech 151:287–294Google Scholar
  16. Hazen RM, Griffin PL, Carothers JM, Szostak JW (2007) Functional information and the emergence of biocomplexity. Proc Natl Acad Sci 104:8574–8581Google Scholar
  17. Houle D (1992) Comparing evolvability and variability of quantitative traits. Genetics 130:195–204Google Scholar
  18. Hu T, Payne JL, Banzhaf W, Moore JH (2012) Evolutionary dynamics on multiple scales: a quantitative analysis of the interplay between genotype, phenotype, and fitness in linear genetic programming. Genet Program Evolvable Mach 13(3):305–337Google Scholar
  19. Jin Y, Branke K (2005) Evolutionary optimization in uncertain environments: a survey. IEEE Trans Evol Comput 9(3):303–317Google Scholar
  20. Kirschner M, Gerhart J (1998) Evolvability PNAS 95:8420–8427Google Scholar
  21. Levitan B, Kauffman S (1994) Adaptive walks with noisy fitness measurements. Mol Divers 1(1):53–68Google Scholar
  22. Macia J, Solé RV (2009) Distributed robustness in cellular networks: insights from synthetic evolved circuits. J R Soc Interface 6(33):393–400Google Scholar
  23. Masel J, Trotter MV (2010) Robustness and evolvability. Trends Genet 26(9):406–414Google Scholar
  24. Milano N, Nolfi S (2016) Robustness to faults promotes evolvability: insights from evolving digital circuits. PLoS ONE 11(7):e0158627Google Scholar
  25. Miller J, Hartmann M (2001) Evolving messy gate for fault tolerance: some preliminary findings. In: Proceedings 3rd NASA workshop on evolvable hardware. pp 116–123Google Scholar
  26. Miller JF, Thomson P (2000) Cartesian genetic programming. In: Poli R, Banzhaf W, Langdon WB, Miller J, Nordin P, Fogarty TC (eds) Lecture Notes in Computer Science 1802 Genetic programming. Springer, HeidelbergGoogle Scholar
  27. Miller JF, Job D, Vassiley VK (2000) Principles in the evolutionary design of digital circuits. J Genet Progr Evolv Mach 1(1):8–35Google Scholar
  28. Miller JF, Thomson P (2000) Cartesian genetic programming. In: Proceedings of the third european conference on genetic programming (EuroGP), vol 1820. Springer, Berlin, pp. 121–132Google Scholar
  29. Miller JF, Thompson A, Thompson P, Fogarty T (eds) (2000) Proceedings of the 3rd international conference on evolvable systems: from biology to hardware. Lecture notes on computer science, no. 1801. Springer, BerlinGoogle Scholar
  30. Miller JF (2011) Cartesian genetic programming. Springer, BerlinzbMATHGoogle Scholar
  31. Pagliuca P, Milano N, Nolfi S (2018) Maximizing adaptive power in neuroevolution. PLoS ONE 13(7):e0198788Google Scholar
  32. Raman K, Wagner A (2011) The evolvability of programmable hardware. J R Soc Interface 8(55):269–281Google Scholar
  33. Rana S, Whitlev LD, Cogswell R (1996) Searching in the presence of noise. In: Voigt HM (ed) Parallel problem solving from nature. Lecture Notes in Computer Sciences, 1141. Springer, Berlin, pp 198–207Google Scholar
  34. Rechenberg I (1973) Evolutionstrategie—Optimierung technischer Systeme nach Prinzipien der biologischen Evolution. Frommann-Holzboog, StuggartGoogle Scholar
  35. Schuster P, Fontana W, Stadler PF, Hofacker IL (1994) From sequences to shapes and back: a case study in RNA secondary structures. Proc R Soc Lond B 255:279–284Google Scholar
  36. Sniegowski PD, Murphy HA (2006) Evolvability Curr Biol 16:831–834Google Scholar
  37. Sekanina L (2004) Evolvable computing by means of evolvable components. Nat Comput 3(3):253–292MathSciNetzbMATHGoogle Scholar
  38. Thompson A, Layzell P, Zebulum R (1999) Explorations in design space: unconventional electronics design through artificial evolution. IEEE Trans Evol Comput 3(3):167–196Google Scholar
  39. Tononi G, Sporns O, Edelman GM (1999) Measures of degeneracy and redundancy in biological networks. Proc Natl Acad Sci USA 96:3257–3262Google Scholar
  40. Van Nimwegen E, Crutchfield JP, Huynen M (1999) Neutral evolution of mutational robustness. PNAS 96:9716–9720Google Scholar
  41. Wagner A (2008) Robustness and evolvability: a paradox resolved. Proc R Soc B 275:91–100Google Scholar
  42. Wagner A (2011) The origins of evolutionary innovations: a theory of transformative change in living systems. Oxford University Press, OxfordGoogle Scholar
  43. Wagner GP, Altenberg L (1996) Perspective: complex adaptations and the evolution of evolvability. Evolution 50:967–976Google Scholar
  44. Whitacre JM (2010) Degeneracy: a link between evolvability, robustness and complexity in biological systems. Theor Biol Med Model 7:6Google Scholar
  45. Whitley D, Rana S, Heckendorn RB (1998) The island model genetic algorithm: on separability, population size and convergence. J Comput Inf Technol 7:33–47Google Scholar
  46. Wilke CO (2001) Adaptive evolution on neutral networks. Bull Math Biol 63:715–730zbMATHGoogle Scholar

Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Institute of Cognitive Sciences and TechnologiesNational Research Council (CNR)RomeItaly

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