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Innovative Genetic Algorithmic Approach to Select Potential Patches Enclosing Real and Complex Zeros of Nonlinear Equation

Innovative Genetic Algorithmic Approach to Select Potential Patches Enclosing Real and Complex Zeros of Nonlinear Equation

Vijaya Lakshmi V. Nadimpalli, Rajeev Wankar, Raghavendra Rao Chillarige
Copyright: © 2017 |Volume: 6 |Issue: 2 |Pages: 20
ISSN: 1947-928X|EISSN: 1947-9298|EISBN13: 9781522513506|DOI: 10.4018/IJNCR.2017070102
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MLA

Nadimpalli, Vijaya Lakshmi V., et al. "Innovative Genetic Algorithmic Approach to Select Potential Patches Enclosing Real and Complex Zeros of Nonlinear Equation." IJNCR vol.6, no.2 2017: pp.18-37. http://doi.org/10.4018/IJNCR.2017070102

APA

Nadimpalli, V. L., Wankar, R., & Chillarige, R. R. (2017). Innovative Genetic Algorithmic Approach to Select Potential Patches Enclosing Real and Complex Zeros of Nonlinear Equation. International Journal of Natural Computing Research (IJNCR), 6(2), 18-37. http://doi.org/10.4018/IJNCR.2017070102

Chicago

Nadimpalli, Vijaya Lakshmi V., Rajeev Wankar, and Raghavendra Rao Chillarige. "Innovative Genetic Algorithmic Approach to Select Potential Patches Enclosing Real and Complex Zeros of Nonlinear Equation," International Journal of Natural Computing Research (IJNCR) 6, no.2: 18-37. http://doi.org/10.4018/IJNCR.2017070102

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Abstract

In this article, an innovative Genetic Algorithm is proposed to find potential patches enclosing roots of real valued function f:R→R. As roots of f can be real as well as complex, the function is reframed on to complex plane by writing it as f(z). Thus, the problem now is transformed to finding potential patches (rectangles in C) enclosing z such that f(z)=0, which is resolved into two components as real and imaginary parts. The proposed GA generates two random populations of real numbers for the real and imaginary parts in the given regions of interest and no other initial guesses are needed. This is the prominent advantage of the method in contrast to various other methods. Additionally, the proposed ‘Refinement technique' aids in the exhaustive coverage of potential patches enclosing roots and reinforces the selected potential rectangles to be narrow, resulting in significant search space reduction. The method works efficiently even when the roots are closely packed. A set of benchmark functions are presented and the results show the effectiveness and robustness of the new method.

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