Hoeffding bound based evolutionary algorithm for symbolic regression

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  author =       "Li Zhao and Lei Wang and Du-wu Cui",
  title =        "Hoeffding bound based evolutionary algorithm for
                 symbolic regression",
  journal =      "Engineering Applications of Artificial Intelligence",
  volume =       "25",
  number =       "5",
  pages =        "945--957",
  year =         "2012",
  ISSN =         "0952-1976",
  DOI =          "doi:10.1016/j.engappai.2012.04.005",
  URL =          "http://www.sciencedirect.com/science/article/pii/S0952197612000930",
  keywords =     "genetic algorithms, genetic programming, Hoeffding
                 bound, Fitness approximation, Symbolic regression",
  abstract =     "In symbolic regression area, it is difficult for
                 evolutionary algorithms to construct a regression model
                 when the number of sample points is very large. Much
                 time will be spent in calculating the fitness of the
                 individuals and in selecting the best individuals
                 within the population. Hoeffding bound is a probability
                 bound for sums of independent random variables. As a
                 statistical result, it can be used to exactly decide
                 how many samples are necessary for choosing i
                 individuals from a population in evolutionary
                 algorithms without calculating the fitness completely.
                 This paper presents a Hoeffding bound based
                 evolutionary algorithm (HEA) for regression or
                 approximation problems when the number of the given
                 learning samples is very large. In HEA, the original
                 fitness function is used in every k generations to
                 update the approximate fitness obtained by Hoeffding
                 bound. The parameter is the probability of correctly
                 selecting i best individuals from population P, which
                 can be tuned to avoid an unstable evolution process
                 caused by a large discrepancy between the approximate
                 model and the original fitness function. The major
                 advantage of the proposed HEA algorithm is that it can
                 guarantee that the solution discovered has performance
                 matching what would be discovered with a traditional
                 genetic programming (GP) selection operator with a
                 determinate probability and the running time can be
                 reduced largely. We examine the performance of the
                 proposed algorithm with several regression problems and
                 the results indicate that with the similar accuracy,
                 the HEA algorithm can find the solution more
                 efficiently than tradition EA. It is very useful for
                 regression problems with large number of training

Genetic Programming entries for Li Zhao Lei Wang Du-Wu Cui