Abstract
This paper describes a hierarchical genetic algorithm (GA) framework for identifying closed form functions for multi-variate data sets. The hierarchy begins with an upper GA that searches for appropriate functional forms given a user defined set of primitives and the candidate independent variables. Each functional form is encoded as a tree structure, where variables, coefficients and functional primitives are linked. The functional forms are sent to the second part of the hierarchy, the lower GA, that optimizes the coefficients of the function according to the data set and the chosen error metric. To avoid undue complication of the functional form identified by the upper GA, a penalty function is used in the calculation of fitness. Because of the computational effort required for this sequential optimization of each candidate function, the system has been implemented on a Cray supercomputer. The GA code was vectorized for parallel processing of 128 array elements, which greatly speeded the calculation of fitness. The system is demonstrated on five data sets from the literature. It is shown that this hierarchical GA framework identifies functions which fit the data extremely well, are reasonable in functional form, and interpolate and extrapolate well.
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Gulsen, M., Smith, A.E. (1999). A Hierarchical Genetic Algorithm for System Identification and Curve Fitting with a Supercomputer Implementation. In: Davis, L.D., De Jong, K., Vose, M.D., Whitley, L.D. (eds) Evolutionary Algorithms. The IMA Volumes in Mathematics and its Applications, vol 111. Springer, New York, NY. https://doi.org/10.1007/978-1-4612-1542-4_6
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DOI: https://doi.org/10.1007/978-1-4612-1542-4_6
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