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<META name=vsisbn content="0849398010">
<META name=vstitle content="Industrial Applications of Genetic Algorithms">
<META name=vsauthor content="Charles Karr; L. Michael Freeman">
<META name=vsimprint content="CRC Press">
<META name=vspublisher content="CRC Press LLC">
<META name=vspubdate content="12/01/98">
<META name=vscategory content="Web and Software Development: Artificial Intelligence: Other">
<TITLE>Industrial Applications of Genetic Algorithms:Gauss-Legendre Integration Using Genetic Algorithms</TITLE>
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<P><FONT SIZE="+1"><B>SUMMARY</B></FONT></P>
<P>A hybrid scheme for solving the systems of nonlinear equations resulting from the application of Gauss-Legendre quadrature has been described and tested. Gauss-Legendre quadrature is an effective numerical integration technique because it simultaneously selects the best values of both the quadrature nodes and the weights, whereas most quadrature methods focus solely on the value of the weights. However, solving the systems of nonlinear equations resulting from the implementation of this quadrature method is difficult. Thus, a hybrid scheme capturing the strengths of both a traditional Newton method and a GA was developed. The hybrid scheme combines the rapid convergence characteristics of the derivative-based Newton-Raphson method (once a quality initial guess is determined) and the global search capabilities of GAs. The result is a method that dramatically reduces the computational time and effort required to implement Gauss-Legendre quadrature.
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<P><FONT SIZE="+1"><B>REFERENCES</B></FONT></P>
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<DD><B>1</B> Press, W. J., Flannery, B. P., Teukolsky, S. A., & Vetterling, W. T. (1988). <I>Numerical recipes in C: The art of scientific computing</I>. Cambridge: Cambridge University Press.
<DD><B>2</B> Mathews, J. H. (1992). <I>Numerical methods for mathematics, science, and engineering</I>. Englewood Cliffs, NJ: Prentice Hall.
<DD><B>3</B> James, M. L., Smith, G. M., & Wolford, J. C. (1977). <I>Applied numerical methods for digital computation with FORTRAN and CSMP, 2nd edition</I>. New York, NY: Harper & Row Publishers.
<DD><B>4</B> Rice, J. R. (1983). <I>Numerical methods, software, and analysis</I>. New York, NY: McGraw-Hill Book Company.
<DD><B>5</B> Polak, E. (1971). <I>Computational methods in optimization</I>. New York, NY: Academic Press.
<DD><B>6</B> Acton, F. S. (1970). <I>Numerical methods that work</I>. New York, NY: Harper and Row Publishers.
<DD><B>7</B> Nelder, J. A. & Mead, R. (1965). A simplex method for function minimization. <I>Computer Journal</I>, 7, 308-321.
<DD><B>8</B> Goldberg, D. E. (1989). <I>Genetic algorithms in search, optimization, and machine learning</I>. Reading, MA: Addison-Wesley.
<DD><B>9</B> Holland, J. H. (1975). <I>Adaptation in natural and artificial systems</I>. Ann Arbor, MI: The University of Michigan Press.
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