Abstract
When evolutionary algorithms (EAs) are unlikely to locate precise global optimal solutions with satisfactory performances, it is important to substitute alternative theoretical routine for the analysis of hitting time/running time. In order to narrow the gap between theories and applications, this paper is dedicated to perform an analysis on approximation error of EAs. First, we proposed a general result on upper bound and lower bound of approximation errors. Then, several case studies are performed to present the routine of error analysis, and theoretical results show the close connections between approximation errors and eigenvalues of transition matrices. The analysis validates applicability of error analysis, demonstrates significance of estimation results, and then, exhibits its potential to be applied for theoretical analysis of elitist EAs.
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Notes
- 1.
In linear algebra, a nilpotent matrix is a square matrix M such that \(N^{k}=0\) for some positive integer k. The smallest such k is called the index of M [26].
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Acknowledgements
This work was supported in part by the National Nature Science Foundation of China under Grants 61303028 and 61763010, in part by the Guangxi “BAGUI Scholar” Program, and in part by the Science and Technology Major Project of Guangxi under Grant AA18118047.
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Wang, C., Chen, Y., He, J., Xie, C. (2020). Estimating Approximation Errors of Elitist Evolutionary Algorithms. In: Pan, L., Liang, J., Qu, B. (eds) Bio-inspired Computing: Theories and Applications. BIC-TA 2019. Communications in Computer and Information Science, vol 1159. Springer, Singapore. https://doi.org/10.1007/978-981-15-3425-6_26
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DOI: https://doi.org/10.1007/978-981-15-3425-6_26
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