Abstract
Neutral genotype-phenotype mappings can be observed in natural evolution and are often used in evolutionary computation. In this article, important aspects of such encodings are analyzed.
First, it is shown that in the absence of external control neutrality allows a variation of the search distribution independent of phenotypic changes. In particular, neutrality is necessary for self-adaptation, which is used in a variety of algorithms from all main paradigms of evolutionary computation to increase efficiency.
Second, the average number of fitness evaluations needed to find a desirable (e.g., optimally adapted) genotype depending on the number of desirable genotypes and the cardinality of the genotype space is derived. It turns out that this number increases only marginally when neutrality is added to an encoding presuming that the fraction of desirable genotypes stays constant and that the number of these genotypes is not too small.
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References
Angeline PJ (1996) Two self-adaptive crossover operations for genetic programming. In: Angeline P and Kinnear K (eds) Advances in Genetic Programming, Vol. 2. MIT Press, Cambridge
Bäck T (1992) Self-adaptation in genetic algorithms. In: Varela FJ and Bourgine P (eds) Towards a Practice of Autonomous Systems: Proceedings of the First European Conference on Artificial Life, pp. 263–271. MIT Press, Cambridge, MA
Bäck T (1998) An overview of parameter control methods by self-adaptation in evolutionary algorithms. Fundamenta Informaticae 35(1–4): 51–66
Banzhaf W, Nordin P, Keller RE and Francone FD (1998) Genetic Programming – An Introduction; On the Automatic Evolution of Computer Programs and its Applications. Morgan Kaufmann, dpunkt.verlag
Barnett L (1998) Ruggedness and neutrality – The NKp family of fitness landscapes. In: Adami C, Belew RK, Kitano H and Taylor CE (eds) Alive VI: Sixth International Conference on Articial Life, pp. 18–27. MIT Press, Cambridge, MA
Conrad M (1990) The geometry of evolution. Biosystems 24: 61–81
Ebner M, Langguth P, Albert J, Shackleton M and Shipman R (2001) On neutral networks and evolvability. In: Proceedings of the 2001 Congress on Evolutionary Computation (CEC 2001), pp. 1–8. IEEE Press
Eiben AE, Hinterding R and Michalewicz Z (1999) Parameter control in evolutionary algorithms. IEEE Transactions on Evolutionary Computation 3(2): 124–141
Fogel DB (1995) Evolutionary Computation: Toward a New Philosophy of Machine Intelligence. IEEE Press
Fogel LJ, Angeline PJ and Fogel DB (1995) An evolutionary programming approach to selfadaptation on finite state machines. In: McDonnell JR, Reynolds RG and Fogel DB (eds) Proceedings of the Fourth Annual Conference on Evolutionary Programming, pp. 355–365. MIT Press
Graham RL, Knuth DE and Patashnik O (1994) Concrete Mathematics: A Foundation for Computer Science. Addison-Wesley, 2 edition
Huynen MA (1996) Exploring phenotype space through neutral evolution. Journal of Molecular Evolution 43: 165–169
Igel C and Kreutz M (2003) Operator adaptation in evolutionary computation and its application to structure optimization of neural networks. Neurocomputing, in press
Igel C and Stagge P (2002) Effects of phenotypic redundancy in structure optimization. IEEE Transactions on Evolutionary Computation 6(1): 74–85
Igel C and Toussaint M (2003) On classes of functions for which no free lunch results hold. Information Processing Letters, in press
Kimura M (1968) Evolutionary rate at the molecular level. Nature 217: 624–626
Mahner M and Kary M (1997) What exactly are genomes, genotypes and phenotypes? And what about phenomes? Journal of Theoretical Biology 186(1): 55–63
Newman MEJ and Engelhardt R (1998) Effects of neutral selection on the evolution of molecular species. Proceedings of the Royal Society of London, Series B: Biological Sciences 265(1403): 1333–1338
Radcliffe NJ (1991) Equivalence class analysis of genetic algorithms. Complex Systems 5: 183–205
Rechenberg I (1994) Evolutionsstrategie '94, Werkstatt Bionik und Evolutionstechnik. Frommann-Holzboog, Stuttgart
Schaffer JD and Morishima A (1987) An adaptive crossover distribution mechanism for genetic algorithms. In: Grefenstette JJ (ed) Proceedings of the Second International Conference on Genetic Algorithms (ICGA'87), pp. 36–40. Lawrence Erlbaum Associates, Cambridge, MA
Schumacher C, Vose MD and Whitley LD (2001) The no free lunch and description length. In: Spector L, Goodman E, Wu A, Langdon W, Voigt H-M, Gen M, Sen S, Dorigo M, Pezeshk S, Garzon M and Burke E (eds) Genetic and Evolutionary Computation Conference (GECCO 2001), pp. 565–570. Morgan Kaufmann
Schuster P (1996) Landscapes and molecular evolution. Physica D 107: 331–363
Schuster P (2002) Molecular insights into evolution of phenotypes. In: Crutchfield JP and Schuster P (eds) Evolutionary Dynamics – Exploring the Interplay of Accident, Selection, Neutrality and Function, Santa Fe Institute Series in the Science of Complexity. Oxford University Press
Schwefel H-P (1977) Numerische Optimierung von Computer-Modellen mittels der Evolutionsstrategie, Vol. 26 of Interdisciplinary Systems Research. Birkhäuser Verlag, Basel
Schwefel H-P (1995) Evolution and Optimum Seeking, Sixth-Generation Computer Technology Series. John Wiley & Sons, New York
Shackleton MA, Shipman R and Ebner M (2000) An investigation of redundant genotypephenotype mappings and their role in evolutionary search. In: Zalzala A, Fonseca C, Kim J-H and Smith A (eds) Proceedings of the International Congress on Evolutionary Computation (CEC 2000), pp. 493–500. IEEE Press, Piscataway, NJ
Shipman R (1999) Genetic redundancy: Desirable or problematic for evolutionary adaptation. In: Bedau MA, Rasmussen S, McCaskill JS and Packard NH (eds) Proceedings of the 4th International Conference on Artificial Neural Networks and Genetic Algorithms (ICANNGA), pp. 337–344. Springer-Verlag
Smith JE and Fogarty TC (1997) Operator and parameter adaptation in genetic algorithms. Soft Computing 1(2), 81–87
Stephens CR and Waelbroeck H (1999) Codon bias and mutability in HIV sequences. Journal of Molecular Evolution 48: 390–397
Toussaint M (2001) Self-adaptive exploration in evolutionary search. Technical Report IRINI 2001-05, Institut für Neuroinformatik, Lehrstuhl für Theoretische Biologie, Ruhr-Universität Bochum, 44780 Bochum, Germany
Toussaint M (2003) On the evolution of phenotypic exploration distributions. In: Cotta C, De Jong K, Poli R and Rowe J (eds) Foundations of Genetic Algorithms 7 (FOGA VII). Morgan Kaufmann, in press
Toussaint M and Igel C (2002) Neutrality: A necessity for self-adaptation. In: IEEE Congress on Evolutionary Computation 2002 (CEC 2002), pp. 1354–1359. IEEE Press
van Nimwegen E, Crutchfield JP and Huynen M (1999) Neutral evolution of mutational robustness. Proceedings of the National Academy of Sciences 96: 9716–9720
Weicker K and Weicker N (2000) Burden and benefits of redundancy. In: Martin WN and Spears WM (eds) Foundations of Genetic Algorithms 6 (FOGA 6), pp. 313–333. Morgan Kaufmann
Wilke CO (2001) Adaptive evolution on neutral networks. Bulletin of Mathematical Biology 63, 715–730
Wolpert DH and Macready WG (1997) No free lunch theorems for optimization. IEEE Transactions on Evolutionary Computation 1(1), 67–82
Zhigljavsky AA (1991) Theory of global random search. Kluwer Academic Publishers
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Igel, C., Toussaint, M. Neutrality and self-adaptation. Natural Computing 2, 117–132 (2003). https://doi.org/10.1023/A:1024906105255
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DOI: https://doi.org/10.1023/A:1024906105255