Abstract
In herein presented work, the relation between a number of ES iterations and convergence of the whole GPA-ES hybrid algorithm will be studied due to increasing needs to analyze and model large data sets. Evolutionary algorithms are applicable in the areas which are not covered by other artificial intelligence or soft computing techniques like neural networks and deep learning like a search of an algebraic model of data. The difference between time and algorithmic complexity will be also mentioned as well as the problems of multitasking implementation of GPA, where external influences complicate increasing of GPA efficiency via Pseudo Random Number Generator (PRNG) choice optimization. Hybrid evolutionary algorithms like GPA-ES uses GPA for solution structure development and Evolutionary Strategy (ES) for parameters identification are controlled by many parameters. The most significant are sizes of GPA population and sizes of ES populations related to each particular individual in GPA population. There is also a limit of ES algorithm evolutionary cycles. This limit plays two contradictory roles. On one side the bigger number of ES iterations means less chance to omit good solution for wrongly identified parameters, on the opposite side large number of ES iterations significantly increases computational time and thus limits application domain of GPA-ES algorithm. This is an Open Access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium provided the original work is properly cited.
Highlights
Increasing amount of data to be processed forces needs for improving eciency of existing algorithms
The most signicant are sizes of GeneticProgramming Algorithms (GPA) population and sizes of Evolutionary Strategy (ES) populations related to each particular individual in GPA population
Lorenz attractor system served as test case for experiments with symbolic regression of dierential equations describing this dynamic system on the base of pre-computed data set
Summary
Increasing amount of data to be processed forces needs for improving eciency of existing algorithms. The bigger number of ES iterations means less chance to omit good solution for wrongly identied parameters [3]- [9] and it was the main idea of GPAES hybrid algorithm development but the large number of ES iterations signicantly increases computational time and limits application domain of GPA-ES algorithm. The number of ES algorithm cycles was xed and equal to 40 (it was not shorten in tness value of the best individual in the population reached residual error limit, in contrary to superior GP algorithm) Such large populations causes small numbers of iterations and small resolution of obtained results. Each task was running ES for parameter optimization as single-thread one without any communication with others
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