Abstract
Genetic Algorithms have been successfully applied to the learning process of neural networks simulating artificial life. In previous research we compared mutation and crossover as genetic operators on neural networks directly encoded as real vectors (Manczer and Parisi 1990). With reference to crossover we were actually testing the building blocks hypothesis, as the effectiveness of recombination relies on the validity of such hypothesis. Even with the real genotype used, it was found that the average fitness of the population of neural networks is optimized much more quickly by crossover than it is by mutation. This indicated that the intrinsic parallelism of crossover is not reduced by the high cardinality, as seems reasonable and has indeed been suggested in GA theory (Antonisse 1989). In this paper we first summarize such findings and then propose an interpretation in terms of the spatial correlation of the fitness function with respect to the metric defined by the average steps of the genetic operators. Some numerical evidence of such interpretation is given, showing that the fitness surface appears smoother to crossover than it does to mutation. This confirms indirectly that crossover moves along privileged directions, and at the same time provides a geometric rationale for hyperplanes.
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References
Antonisse J (1989) A new interpretation of schema notation that overturns the binary encoding constraint. In: Schaffer JD (ed) Proc. 3rd Int. Conf. on Genetic Algorithms, Kaufmann, Palo Alto, Calif, pp. 86–91
Belew RK, McInerney J, Schraudolph NN (1990) Evolving networks using the genetic algorithm with connectionist learning. CSE Technical Report #CS90–174, University of California, San Diego
Fogel DB, Fogel LJ, Porto VW (1990) Evolving neural networks. Biol Cybern 63:487–493
Goldberg DE (1989) Genetic algorithms in search, optimization and machine learning. Addison-Wesley, Reading, Mass
Holland JH (1975) Adaptation in natural and artificial systems. University of Michigan Press, Ann Arbor
Kauffman SA (1989) Adaptation on rugged fitness landscapes. In: Stein D (ed) Lectures in the Sciences of Complexity. Addison-Wesley, Reading, Mass
Langton CG (ed) (1989) Artificial life. Addison-Wesley, Reading, Mass
Menczer F, Parisi D (1990) “Sexual” reproduction in neural networks. PCIA Technical Report, Institute of Psychology CNR, Rome, Italy
Montana DJ, Davis L (1989) Training feedforward neural networks using genetic algorithms. Proc. 11th IJCAI. Kaufmann, Palo Alto, Calif, pp 762–767
Moscato P (1989) On evolution, search, optimization, genetical algorithms and martial arts: towards memetic algorithms. Caltech, Concurrent Computation Technical Report C3P-826
Nolfi S, Elman JL, Parisi D (1990) Learning and evolution in neural networks. CRL Technical Report #9019, University of California, San Diego
Parisi D, Cecconi F, Nolfi S (1990) ECONETS: neural networks that learn in an environment. Network 1:149–168
Patarnello S, Carnevali P (1989) A neural network model to simulate a conditioning experiment. Int J Neural Syst 1 47–53
Rumelhart DE, McClelland JL (1986) Parallel distributed processing: Explorations in the microstucture of cognition, vol 1. MIT Press, Cambridge, Mass
Whitley D, Hanson T (1989) Optimizing neural networks using faster, more accurate genetic search. In: Schaffer JD (ed) Proc. 3rd Int. Conf. on Genetic Algorithms, Kaufmann, Palo Alto, Calif, pp 391–396
Wilson SW (1985) Knowledge growth in an artificial animal. In: Grefenstette JJ (ed) Proc. 1st Int. Conf. on Genetic Algorithms and Their Applications. Erlbaum, Hillsdale, NJ, pp 16–23
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Menczer, F., Parisi, D. Evidence of hyperplanes in the genetic learning of neural networks. Biol. Cybern. 66, 283–289 (1992). https://doi.org/10.1007/BF00198482
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DOI: https://doi.org/10.1007/BF00198482