Abstract
Over the last years, the effects of neutrality have attracted the attention of many researchers in the Evolutionary Algorithms (EAs) community. A mutation from one gene to another is considered as neutral if this modification does not affect the phenotype. This article provides a general overview on the work carried out on neutrality in EAs. Using as a framework the origin of neutrality and its study in different paradigms of EAs (e.g., Genetic Algorithms, Genetic Programming), we discuss the most significant works and findings on this topic. This work points towards open issues, which we belive the community needs to address.
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Bäck T, Fogel DB, Michalewicz Z (eds) (1999) Evolutionary computation 1: basic algorithms and operators. IOP Publishing Ltd., Bristol
Banzhaf W (1994) Genotype–phenotype-mapping and neutral variation: a case study in genetic programming. In: Davidor Y, Schwefel H-P, Manner R (eds) PPSN III: proceedings of the 3rd international conference on parallel problem solving from nature. Springer, Jerusalem, Israel, pp 322–332
Banzhaf W, Leier A (2006) Evolution on neutral networks in genetic programming. In: Yu T, Riolo R, Worzel B (eds) Genetic programming—theory and applications III. Kluwer Academic, Dordrecht, pp 207–221
Banzhaf W, Francone FD, Keller RE, Nordin P (1998) Genetic programming: an introduction: on the automatic evolution of computer programs and its applications. Morgan Kaufmann Publishers Inc., San Francisco
Barnett L (1998) Ruggedness and neutrality—the NKp family of fitness landscapes. In: Adami C, Belew RK, Kitano H, Taylor CE (eds) Artificial life VI: Proceedings of the sixth international conference on artificial life. MIT Press, Cambridge, pp 18–27
Barnett L (2001) Netcrawling—optimal evolutionary search with neutral networks. In: Proceedings of the 2001 Congress on evolutionary computation. IEEE Press, Los Alamitos, pp 30–37
Beaudoin W, Verel S, Collard P, Escazut C (2006) Deceptiveness and neutrality. The ND family of fitness landscapes. In: Keijzer M, Cattolico M, Arnold D, Babovic V, Blum C, Bosman P, Butz MV, Coello Coello CA, Dasgupta D, Ficici SG, Foster J, Hernandez-Aguirre A, Hornby G, Lipson H, McMinn P, Moore J, Raidl G, Rothlauf F, Ryan C, Thierens D (eds) GECCO 2006: Proceedings of the 2006 conference on genetic and evolutionary computation, vol 1. ACM Press, Seattle, 8–12 July 2006, pp 507–514
Beyer H (2001) The theory of evolution strategies. Springer, Berlin
Chow R (2004a) Effects of phenotypic feedback and the coupling of genotypic and phenotypic spaces in genetic searches. In: Proceedings of the 2004 IEEE Congress on evolutionary computation (CEC-2004), vol 1, IEEE, Portland, pp 242–249
Chow R (2004b) Evolving genotype to phenotype mappings with a multiple-chromosome genetic algorithm. In: Deb K, Poli R, Banzhaf W, Beyer H-G, Burke EK, Darwen PJ, Dasgupta D, Floreano D, Foster JA, Harman M, Holland O, Lanzi PL, Spector L, Tettamanzi A, Thierens D, Tyrrell AM (eds) GECCO 2004: Proceedings of the 2004 conference on genetic and evolutionary computation, volume 1 of Lecture Notes in Computer Science, Springer, Seattle, WA, USA, 26–30 June 2004, pp 1006–1017
Clergue M, Collard P, Tomassini M, Vanneschi L (2002) Fitness distance correlation and problem difficulty for genetic programming. In: Langdon WB, Cantú-Paz E, Mathias KE, Roy R, Davis D, Poli R, Balakrishnan K, Honavar V, Rudolph G, Wegener J, Bull L, Potter MA, Schultz AC, Miller JF, Burke EK, Jonoska N (eds) Proceedings of the genetic and evolutionary computation conference, GECCO 2002, Morgan Kaufmann Publishers, New York, 9–13 July 2002, pp 724–732
Collins M (2005) Finding needles in haystacks is harder with neutrality. In: Beyer H-G, O’Reilly U-M, Arnold DV, Banzhaf W, Blum C, Bonabeau EW, Cantu-Paz E, Dasgupta D, Deb K, Foster JA, de Jong ED, Lipson H, Llora X, Mancoridis S, Pelikan M, Raidl GR, Soule T, Tyrrell AM, Watson J-P, Zitzler E (eds) GECCO 2005: Proceedings of the 2005 conference on genetic and evolutionary computation, vol 2. ACM Press, Washington DC, USA, 25–29 June 2005, pp 1613–1618
Corsi P (1988) The age of lamarck evolutionary theories in France. University of California Press, USA
Darwin C (1859) On the origin of species by means of natural selection. John Murray, London
Dasgupta D, McGregor DR (1992) Nonstationary function optimization using the structured genetic algorithm. In: Manner R, Manderick B (eds) PPSN II: Proceedings of the 2nd international conference on parallel problem solving from nature. Elsevier, Brussels, Belgium, pp 145–154
Doerr B, Gnewuch M, Hebbinghaus N, Neumann F (2007) A rigorous view on neutrality. In: IEEE Congress on evolutionary computation, IEEE, pp 2591–2597
Downing RM (2005) Evolving binary decision diagrams using implicit neutrality. In: Proceedings of congress on evolutionary computation (CEC 2005), vol 3, IEEE Press, Edinburgh, Scotland, pp 2107–2113
Ebner M (1999) On the search space of genetic programming and its relation to nature’s search space. In: Proceedings of the 1999 Congress on evolutionary computation, 1999, CEC 99, 1999
Ebner M, Langguth P, Albert J, Shackleton M, Shipman R (2001a) On neutral networks and evolvability. In: Proceedings of the 2001 IEEE Congress on evolutionary computation, IEEE Press, 27–30 May 2001, pp 1–8
Ebner M, Shackleton M, Shipman R (2001b) How neutral networks influence evolvability. Complexity 7(2):19–33
Eiben AE, Hinterding R, Michalewicz Z (1999) Parameter control in evolutionary algorithms. IEEE Trans Evol Comput 3(2):124–141
Eiben AE, Smith JE (2003) Introduction to evolutionary computing. Springer, Berlin
Finding Needles in Haystacks is not Hard with Neutrality. In: Foster JA, Lutton E, Miller JF, Ryan C, Tettamanzi A (eds) Genetic programming. Proceedings of the 5th European conference, EuroGP 2002, volume 2278 of LNCS, Springer, Kinsale, Ireland, 3–5 April 2002, pp 13–25
Fisher RA (1922) On the dominance ratio. In: Proceedings of the royal society of Edinburgh, vol 42, pp 321–341
Fonseca C, Correia M (2005) Developing redudant binary representations for genetic search. In: Proceedings of the 2005 IEEE Congress on evolutionary computation (CEC 2005), IEEE, Edinburgh, 2–4 September 2005, pp 372–379
Fontana W, Schuster P (1998) Continuity in evolution: On the nature of transitions. Science 280:1431–1452
Galván-López E (2007) Effects of neutrality on evolutionary search. In: EvoPhD—second European Graduate Student Workshop on Evolutionary Computation, Valencia, Spain, 11–13 April 2007
Galván-López E, Dignum S, Poli R (2008) The effects of constant neutrality on performance and problem hardness in GP. In: ONeill M, Vanneschi L, Gustafson S, Esparcia Alcazar AI, De Falco I, Della Cioppa A, Tarantino E (eds) EuroGP 2008—11th European conference on genetic programming, volume 4971 of LNCS, Springer, Napoli, Italy, 26–28 March 2008, pp 312–324
Galván-López E, McDermott J, O’Neill M, Brabazon A (2010a) Defining locality in problem hardness in genetic programming. Genetic Programming and Evolvable Machines
Galván-López E, McDermott J, O’Neill M, Brabazon A (2010b) Defining locality in genetic programming to predict performance. In: 2010 IEEE World Congress on computational intelligence, IEEE Computational Intelligence Society, Barcelona, Spain, 18–23 July 2010, pp 1828–1835
Galván-López E, McDermott J, O’Neill M, Brabazon A (2010c) Towards an understanding of locality in genetic programming. In: GECCO ’10: Proceedings of the 12th annual conference on Genetic and evolutionary computation, ACM, New York, NY, USA, pp 901–908
Galván-López E, Poli R (2006a) An empirical investigation of how and why neutrality affects evolutionary search. In: Keijzer M, Cattolico M, Arnold D, Babovic V, Blum C, Bosman P, Butz MV, Coello Coello CA, Dasgupta D, Ficici SG, Foster J, Hernandez-Aguirre A, Hornby G, Lipson H, McMinn P, Moore J, Raidl G, Rothlauf F, Ryan C, Thierens D (eds) GECCO 2006: Proceedings of the 2006 conference on genetic and evolutionary computation. ACM Press, Seattle, WA, USA, 8–12 July 2006, pp 1149–1156
Galván-López E, Poli R (2006b) Some steps towards understanding how neutrality affects evolutionary search. In: Runarsson TP, Beyer H.-G., Burke E, Merelo-Guervós JJ, Whitley LD, Yao X (eds) Parallel problem solving from nature (PPSN IX). 9th International Conference, volume 4193 of LNCS, Springer, Reykjavik, Iceland, 9–13 September 2006, pp 778–787
Galván-López E, Poli R (2010) The effects of constant and bit-wise neutrality on problem hardness, fitness distance correlation and phenotypic mutation rates. IEEE Trans Evol Comput 4(1):1–15
Geard N, Wiles J, Hallinan J, Tonkes B, Skellett B (2002) A Comparison of neutral landscapes—NK, NKp and NKq. In: Fogel DB, El-Sharkawi MA, Yao X, Greenwood G, Iba H, Marrow P, Shackleton M (eds) Proceedings of Congress on evolutionary computation (CEC 2002), vol 1, IEEE Press, pp 205–210
Goldberg DE (1992) Construction of high-order deceptive functions using low-order Walsh coefficients. Ann Math Artif Intell 5(1):35–47
Goldberg DE, Deb K, Horn J (1992) Massive multimodality, deception, genetic algorithms. In: Männer R, Manderick B (eds) PPSN II: Proceedings of the 2nd international conference on parallel problem solving from nature. Elsevier Science Publishers, B. V., Amsterdam, pp 37–48
Haldane JBS (1957) The cost of natural selection. J Genet 55:511–524
Harvey I, Thompson A (1996) Through the labyrinth evolution finds a way: a silicon ridge. In: Higuchi T, Iwata M, Liu W (eds) Proceedings of the first international conference on evolvable systems: from biology to hardware, vol 1259, Springer, Berlin, pp 406–422
Holland JH (1975) Adaptation in natural and artificial systems. University of Michigan Press, Ann Arbor
Huynen MA (1996) Exploring phenotype space through neutral evolution. Mol Evol 43:165–169
Huynen M, Stadler P, Fontana W (1996) Smoothness Within ruggedness: the role of neutrality in adaptation. Proc Natl Acad Sci USA 93:397–401
Jones T (1995) Evolutionary algorithms, fitness landscapes and search. PhD thesis, University of New Mexico, Albuquerque
Kargupta H, Deb K, Goldberg D (1992) Ordering genetic algorithms and deception. In Männer R, Manderick B (eds) PPSN II: Proceedings of the 2nd international conference on parallel problem solving from nature. Elsevier, Amsterdam, pp 49–58
Katada Y, Ohkura K (2006) Estimating the degree of neutrality in fitness landscapes by the nei’s standard genetic distance—an application to evolutionary robotics. In: Yen GG, Lucas SM, Fogel G, Kendall G, Salomon R, Zhang B-T, Coello Coello CA, Runarsson TP (eds) Proceedings of the 2006 IEEE Congress on evolutionary computation, IEEE Press, Vancouver, BC, Canada, 16–21 July 2006, pp 483–490
Katada Y, Ohkura K (2009) Analysis on topologies of fitness landscapes with both neutrality and ruggedness based on neutral networks. In: Proceedings of the 11th annual conference on genetic and evolutionary computation, ACM, GECCO ’09, New York, NY, USA, pp 1855–1856
Katada Y, Ohkura K, Ueda K (2004) An approach to evolutionary robotics using a genetic algorithm with a variable mutation rate strategy. In: Yao X, Burke EK, Lozano JA, Smith J, Merelo Guervós JJ, Bullinaria JA, Rowe JE, Tiño P, Kabán A, Schwefel H-P (eds) PPSN, volume 3242 of Lecture Notes in Computer Science, Springer, Berlin. pp 952–961
Kauffman SA (1993) The origins of order—organization and selection in evolution. Oxford University Press, New York
Kimura M (1968) Evolutionary rate at the molecular level. In: Nature, vol 217, pp 624–626
Kimura M (1983) The neutral theory of molecular evolution. Cambridge University Press, Cambridge
King JL, Jukes TH (1969) Non-Darwinian evolution. Science 164:788–798
Knowles JD, Watson RA (2002) On the utility of redundant encodings in mutation-based evolutionary search. In: Guervós JM, Adamidis P, Beyer H-G, F-Villacañas Martín JL, Schwefel H-P (eds) Parallel problem solving from nature— PPSN VII: 7th international conference, Springer, Granada, Spain, pp 88–98
Koza JR (1992) Genetic programming: on the programming of computers by means of natural selection. The MIT Press, Cambridge, Massachusetts
Langdon WB, Poli R (2002) Foundations of genetic programming. Springer, Berlin
Lehre PK, Haddow PC (2005) Accessibility between neutral networks in indirect genotype–phenotype mappings. In: The 2005 IEEE Congress on evolutionary computation (CEC 2005), vol 1, IEEE Press, Edinburgh, UK, pp 419–426
Lehre PK, Haddow PC (2006) Phenotypic complexity and local variations in neutral degree. BioSystems 87(2–3):233–42
Lobo J, Miller JH, Fontana W (2004) Neutrality in technological landscapes. In: Santa Fe Working Paper
Miller JF (1999) An empirical study of the efficiency of learning Boolean functions using a Cartesian genetic approach. In: Banzhaf W, Daida JM, Eiben AE, Garzon MH, Honavar V, Jakiela MJ, Smith RE (eds) Proceedings of the genetic and evolutionary computation conference GECCO’99, vol 2, Morgan Kaufmann, Orlando, Florida, 13–17 July 1999, pp 1135–1142
Miller JF, Smith SL (2006) Redundancy and computational efficiency in cartesian genetic programming. IEEE Trans Evol Comput 10(2):167–174
Miller JF, Thomson P (2000) Cartesian genetic programming. In: Poli R, Banzhaf W, Langdon W, Miller J, Nordin P, Fogarty T (eds) Third European conference on genetic programming EuroGP 2000, volume 1802 of LNCS, Springer, Edinburgh, 15–16 April 2000, pp 121–132
Mitchell M, Forrest S, Holland JH (1992) The royal road for genetic algorithms: fitness landscapes and GA performance. In: Varela FJ, Bourgine P (eds) Towards a practice of autonomous systems: Proceedings of the first European conference on artificial life. MIT Press, Cambridge, MA, pp 245–254
Mitchell TM (1996) Machine learning. McGraw Hill, New York
Newman M, Engelhardt R (1998a) Effects of selective neutrality on the evolution of molecular species. Proc R Soc Lond 265(1403):1333–1338
Newman MEJ, Engelhardt R (1998b) Effects of neutral selection on the evolution of molecular species. Working Papers 98-01-001, Santa Fe Institute, January 1998
Poli R, Galván-López E (2007) On the effects of bit-wise neutrality on fitness distance correlation, phenotypic mutation rates and problem hardness. In: Stephens CR, Toussaint M, Whitley D, Stadler PF (eds) Foundations of genetic Algorithms IX, Lecture Notes in Computer Science, Springer, Mexico City, Mexico, 8–11 January 2007, pp 138–164
Poli R, Langdon WB, McPhee NF (2008) A field guide to genetic programming. Published via and freely available at http://www.gp-field-guide.org.uk (with contributions by J. R. Koza)
Poli R, Vanneschi L (2007) Fitness-proportional negative slope coefficient as a hardness measure for genetic algorithms. In: Proceedings of the 9th annual conference on Genetic and evolutionary computation, GECCO ’07, ACM, New York, NY, USA, pp 1335–1342
Reidys C, Stadler PF, Schuster P (1997) Generic properties of combinatory maps—neutral networks of RNA secondary structures. Bull Math Biol 59:339–397
Reidys CM, Stadler PF (2001) Neutrality in fitness landscapes. Appl Math Comput 117(2–3):321–350
Ridley M (2003) Evolution. Blackwell publishing, Hoboken
Rothlauf F, Goldberg D (2003) Redundant representations in evolutionary algorithms. Evol Comput 11(4):381–415
Schuster P, Fontana W, Stadler PF, Hofacker IL (1994) From sequences to shapes and back: a case study in RNA secondary structures. R Soc Lond Proc Ser B 255:279–284
Schuster P (1997) Genotypes with phenotypes: adventures in an RNA toy world. Biophys Chem 66(2):75–110
Shackleton MA, Shipman R, Ebner M (2000) An investigation of redundant genotype–phenotype mappings and their role in evolutionary search. In: Zalzala A, Fonseca C, Kim JH, Smith A (eds) Proceedings of the international congress on evolutionary computation (CEC 2000), IEEE Press, pp 493–500
Shipman R (1999) Genetic redundancy: Desirable or problematic for evolutionary adaptation. In: Dobnikar A, Steele NC, Pearson DW, Albrecht RF (eds) 4th international conference on artificial neural networks and genetic algorithms (ICANNGA’99), Springer, Berlin, pp 337–344
Shipman R, Shackleton M, Ebner M, Watson R (2000) Neutral search spaces for artificial evolution: a lesson from life. In: Bedau M, Rasmussen S, McCaskill J, Packard N (eds) Artificial life: Proceedings of the seventh international conference on artificial life, MIT Press, pp 162–169
Smith T, Husbands P, Layzell P, O’Shea M (2001a) Neutral networks and evolvability with complex genotype–phenotype mapping. In: ECAL ’01: Proceedings of the 6th European conference on advances in artificial life, Springer, London, UK, pp 272–281
Smith T, Husbands P, Layzell P, O’Shea M (2001b) Neutral networks in an evolutionary robotics search space. In: Proceedings on evolutionary computation 2001, IEEE Press, pp 136–145
Smith T, Husbands P, Layzell P, O’Shea M (2002) Fitness landscapes and evolvability. Evol Comput 10:1–34
Toussaint M (2003) On the evolution of phenotypic exploration distributions. In: De Jong KA, Poli R, Rowe J (eds) Foundations of genetic algorithms 7 (FOGA 2003), Morgan Kaufmann, pp 169–182
Toussaint M, Igel C (2002) Neutrality: a necessity for self-adaptation. In: Proceedings of the IEEE Congress on evolutionary computation (CEC 2002), pp 1354–1359
Van Nimwegen E, Crutchfield JP, Huynen M (1999a) Neutral evolution of mutational robustness. Proc Natl Acad Sci USA 96(17):9716–9720
van Nimwegen E, Crutchfield JP, Mitchell M (1999b) Statistical dynamics of the royal road genetic algorithm. Theor Comput Sci 229:41–102
Vanneschi L (2004) Theory and practice for efficient genetic programming. PhD thesis, Faculty of Science, University of Lausanne, Switzerland
Vanneschi L (2007) Investigating problem hardness of real life applications. In: Riolo et al. (ed) Genetic programming theory and practive V, chapter 7, Springer US, pp 107–124
Vanneschi L (2009) Fitness landscapes and problem hardness in genetic programming. In: Proceedings of the 11th annual conference companion on genetic and evolutionary computation conference: late breaking papers, GECCO ’09, ACM, New York, NY, USA, pp 3657–3684
Vanneschi L, Clergue M, Collard P, Tomassini M, Verel S (2004) Fitness clouds and problem hardness in genetic programming. In: EuroGP, LNCS, Springer, pp 690–701
Vanneschi L, Tomassini M, Collard P, Clergue M (2003) Fitness distance correlation in structural mutation genetic programming (2003) In: Ryan C, Soule T, Keijzer M, Tsang EPK, Poli R, Costa E (eds) Proceedings of the sixth European conference on genetic programming, EuroGP 2003, volume 2610 of LNCS, Springer, Essex, 14–16 April 2003, pp 455–464
Vanneschi L, Pirola Y, Collard P, Tomassini M, Verel S, Mauri G (2006) A quantitative study of neutrality in GP Boolean landscapes. In: Keijzer M, Cattolico M, Arnold D, Babovic V, Blum C, Bosman P, Butz M-V, Coello Coello CA, Dasgupta D, Ficici SG, Foster J, Hernandez-Aguirre A, Hornby G, Lipson H, McMinn P, Moore J, Raidl G, Rothlauf F, Ryan C, Thierens D (eds) GECCO 2006: Proceedings of the 2006 conference on genetic and evolutionary computation, vol 1, ACM Press, Seattle, WA, USA, 8-12 July 2006, pp 895–902
Vanneschi L, Tomassini M, Collard P, Vérel S, Pirola Y, Mauri G (2007) A comprehensive view of fitness landscapes with neutrality and fitness clouds. In: EuroGP’07: Proceedings of the 10th European conference on genetic programming, Springer, Berlin, Heidelberg, pp 241–250
Vanneschi L, Valsecchi A, Poli R (2009) Limitations of the fitness-proportional negative slope coefficient as a difficulty measure. In: GECCO ’09: Proceedings of the 11th annual conference on genetic and evolutionary computation, ACM, New York, NY, USA, pp 1877–1878
Vassilev VK, Fogarty TC, Miller JF (2000) Information characteristics and the structure of landscapes. Evol Comput 8:31–60
Vassilev VK, Miller JF (2000) The advantages of landscape neutrality in digital circuit evolution. In: ICES ’00: Proceedings of the third international conference on evolvable systems, Springer, London, UK, pp 252–263
Vérel S, Collard P, Clergue M (2007) Scuba search: when selection meets innovation. CoRR, abs/0707.0643, 2007
Wagner A (2005) Robustness, evolvability and neutrality. FEBS Lett 579(8):1772–1778
Weicker K, Weicker N (2000) Burden and benefits of redundancy. In: Martin W, Spears W (eds) Foundations of genetic algorithms 6, San Francisco, Morgan Kaufmann, pp 313–333
Wilke CO, Wang JL, Ofria C, Lenski RE, Adami C (2001) Evolution of digital organisms at high mutation rates leads to surviva of the flattest. Nature 412:331–333
Wright S (1932) The roles of mutation, inbreeding, crossbreeding and selection in evolution. In: Jones DF (ed) Proceedings of the sixth international Congress on genetics, vol 1, pp 356–366
Yu T, Miller J (2001) Neutrality and the evolvability of Boolean function landscape. In: Miller JF, Tomassini M, Lanzi PL, Ryan C, Tettamanzi AGB, Langdon WB (eds) Genetic programming, Proceedings of EuroGP’2001, vol 2038, Springer, Lake Como, Italy, 18–20, pp 204–217
Yu T, Miller J (2002) The role of neutral and adaptive mutation in an evolutionary search on the OneMax problem. In Langdon WB, Cantú-Paz E, Mathias KE, Roy R, Davis D, Poli R, Balakrishnan K, Honavar V, Rudolph G, Wegener J, Bull L, Potter MA, Schultz AC, Miller JF, Burke EK, Jonoska N (eds) Late breaking papers at the genetic and evolutionary computation conference (GECCO-2002), Morgan Kaufmann Publishers, New York, 9–13 July 2002
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We would like to thank the editor, associate editor and reviewers for their fair and useful comments and ideas. The paper has been considerable strengthened thanks to their feedback. This research is based upon works supported by Science Foundation Ireland under Grant No. 08/IN.1/I1868.
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Galván-López, E., Poli, R., Kattan, A. et al. Neutrality in evolutionary algorithms… What do we know?. Evolving Systems 2, 145–163 (2011). https://doi.org/10.1007/s12530-011-9030-5
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DOI: https://doi.org/10.1007/s12530-011-9030-5