Genetic Programming and Automatic Differentiation Algorithms Applied to the Solution of Ordinary and Partial Differential Equation
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- @InProceedings{Lobao:2016:CEC,
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author = "Waldir J. A. Lobao and Douglas Mota Dias and
Marco Aurelio C. Pacheco",
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title = "Genetic Programming and Automatic Differentiation
Algorithms Applied to the Solution of Ordinary and
Partial Differential Equation",
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booktitle = "Proceedings of 2016 IEEE Congress on Evolutionary
Computation (CEC 2016)",
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year = "2016",
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editor = "Yew-Soon Ong",
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pages = "5286--5292",
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address = "Vancouver",
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month = "24-29 " # jul,
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publisher = "IEEE Press",
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keywords = "genetic algorithms, genetic programming",
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isbn13 = "978-1-5090-0623-6",
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DOI = "doi:10.1109/CEC.2016.7748362",
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abstract = "This paper investigates the potential of evolutionary
algorithms, developed by the combination of genetic
programming (GP) and automatic differentiation methods
(AD), in determining analytic solutions to ordinary and
partial differential equations (ODE and PDE). In turn,
AD is a set of techniques based on the mechanical
application of the chain rule to numerically evaluate
the derivative of a function specified by a computer
program. The AD method has a fundamental role in this
work since it calculates the exact values of the
derivatives of a function for a given set of input
values while numerical differentiation methods
introduce unacceptable round-off errors in the
discretization process. With this purpose, and using
the Matlab programming environment, we developed
several algorithms (namely GPAD) and addressed problems
of different kinds of differential equations. The
results are promising, with exact solutions obtained
for most of the addressed problems, which include
equations where not even commercial systems could find
a symbolic solution. These results empirically indicate
that GPAD can be an efficient and robust methodology to
find analytic solutions for ODE and PDE.",
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notes = "WCCI2016",
- }
Genetic Programming entries for
Waldir J A Lobao
Douglas Mota Dias
Marco Aurelio Cavalcanti Pacheco
Citations