Abstract
In this paper, we present the hierarchical chromosome based genetic algorithm, which is used in design systems to solve complex design problems. The main goal of our work is creating of the markov chain model for the algorithm. The model contains a method of coding of the artifacts, represented by different length trees, by means of fixed length binary strings and a method of the hierarchical crossover modeling. Presented formalization is used for finding the transition matrix and the investigation of ergodicity and asymptotic properties of genetic algorithms. It also follows from the model that each population can be found with the probability equal to one within the finite number of steps.
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Paszyńska, A., Jabloński, M., Grabska, E. (2007). Markov Chain Model for Tree-Based Genetic Algorithm Used in Computer Aided Design. In: Kurzynski, M., Puchala, E., Wozniak, M., Zolnierek, A. (eds) Computer Recognition Systems 2. Advances in Soft Computing, vol 45. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-75175-5_37
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DOI: https://doi.org/10.1007/978-3-540-75175-5_37
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-75174-8
Online ISBN: 978-3-540-75175-5
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